# A Suggested Analytical Solution for Vibration of Honeycombs Sandwich Combined Plate Structure

Save this PDF as:

Size: px
Start display at page:

Download "A Suggested Analytical Solution for Vibration of Honeycombs Sandwich Combined Plate Structure"

## Transcription

2 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 10 and mode shapes were investigated. A numerical technique was employed using ANSYS package In this research the natural frequencies of honeycombs sandwich plate with different Regular Hexagonal Honeycomb dimensions effect were evaluated and compared with those obtained numerically adopting finite element method using ANSYS Ver THE SUGGESTED ANALYTICAL SOLUTION The suggested analytical solution of vibration analysis of honeycomb plate included the determination of the mechanical properties of honeycomb structure and then evaluation the equivalent stresses and the natural frequency of with effect of honeycomb structural parameters. 2.1 Mechanical Properties of Honeycomb Materials The cells in a honeycomb-structure are usually hexagonal but they can also be triangular or square or rhombic. The honeycombs can be made of different types of materials such as metals wood polymer and ceramics or a combination of two or more of these materials. Investigating the in-plane properties ( transverse directions) demonstrate the failure mechanism and deformations of the cellular solid structures i.e defining the plane properties such as those shown in Fig. 1.The stiffness and strength in x-y plane. If the hexagonal honeycomb is regular (all angles are 30 o and wall thicknesses are equal as (Fig. 1.) then the in-plane properties are isotropic. This means that the in-plane properties of the honeycomb can be described by only two independent elastic modules for instance by Young's modulus Fig. 2 shows a hexagonal honeycomb regular structure in which the angles are equal ( 30 0 ) with constant wall thickness. This results in using in-plane properties of the honeycomb structures such as modulus of elasticity E and modulus of rigidiy G 1] as two independent properties. 1 1 Fig. 1. Honeycomb Structure Loaded in x or y-direction 1]. If the honeycomb cellular structure is not regular the in-plane properties are used with four modules (e.g. E h1 E h2 G h12 and h12 ). If the hexagonal honeycomb has a low relative density ( is small) get 1] h ( ) ( ) Fig. 2. A Regular Hexagonal Honeycomb 1]. The deflected shape of the honeycomb when loaded in x- or y- direction ( Fig. 1) is in bending direction for all cell walls (see Figure 3.a) and is described by five module: Young's module E h1 and E h2 a shear modulus G h12 and two Poisson's ratio h12 and h21. Using the reciprocal theorem gives (2) Reduce the five independent modules to four independent modules. When loading in x or y directions the four independent module described as 1] l t 2 2 y x (1) ( ) ( ) (3) Fig. 3b shows the honeycomb structure under shear loading. It is possible to show that the shear module G h12 to be 1]

3 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 11 ( ) ( ) Where E is modulus of elasticity of honeycomb material. 2 (4) And are mechanical properties of plate materials parts in x and y directions. and w is the deflection of plate in z-direction. Then with subjecting eq. 5 to plate structure as shown in fig. 4 to get the assuming bending moments acting on the honeycomb sandwich plate as (6) 1 a. Normal Stress Loaded in x and y b. Shear Stress Fig. 3. Honeycomb Deformed a. Deformed by Normal Stress Loaded in x and y b. Deformed by Shear Stress 1]. 2.2 Vibration Analysis of Honeycombs Sandwich Plate The analysis of honeycomb sandwich plate covered the determination of the general equation of motion of honeycomb sandwich plate structure where the plate is orthotropic properties in x and y direction. Also solving the general equation of motion of plate is included and then evaluating the natural frequency of honeycomb sandwich plate with various parameters for upper and lower plate parts and honeycomb dimensions and properties part. To Derive the general equation of motion of honeycomb sandwich plate using the properties and density of honeycomb sandwich materials equations (1 to 4) into the general equation of motion of plate 9] (10) Where are the bending moments and twisting moment per unit length of the orthotropic plate. The bending and twisting moments per unit length acting on the plate element are as follows 9] h M x x z dz h h M y y z dz h h M xy xy z dz h h h dz (5) h Where And (7) where are density of lower and upper plate parts respectively. For honeycomb sandwich plate shown in Fig. 4 assuming the structure combine of isotropic materials properties of upper and lower plate parts and orthotropic honeycomb sandwich part then stresses formulation giving in equation (6) become 1. Upper plate part since the plate part is isotropic propeties then (8) And Where are mechanical properties of uper plate part. Then by subsutution eq. 8 into eq. 6 givs 2. Orthotropic honeycomb sandwich part since the plate part is orthotropic propeties then (10) Then by subsutution eq. 10 into eq. 6 gives (9) (11)

4 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No: Lower plate part since the plate part has isotropic propeties then (12) Where are mechanical properties of uper plate part. Then by subsutution eq. 8 in to eq. (6) gives a y z x (13) ( ] ] ( ] ) ] ) Then with integration eq. 14 gives ] ] (14) Upper Plate b ( ) Honeycomb structural h Up ( ) ] hh ( ) Lower Plate h l t h Lp ( ) ] ( ) Dimensions of Regular Hexagonal Honeycomb Fig. 4. Dimensions of Honeycomb Sandwich Combined Plate Structure. Therefore by substation eqs and 13 into eq. 7 gives the bending moments acting on the honeycomb sandwich plate as ( ) ] (15) And then by substitution eq. 15 into the general equation of motion of orthotropic plate eq. (10) gives the suggested general equation of motion of honeycomb sandwich plate as ] ] ( ] )

5 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 13 ( ) the suggested general equation of natural frequency for honeycomb sandwich plate structure with various mechanical properties and dimensions of honeycomb sandwich plate combined as ( ) ] ( ) ( ) ( ) ] ( ) ] ( ) ( ) ( ) ] ( ) ( ( ) ] ) (16) To solve equation (16) separation method can be used with assuming the function of deflection as 11] (17) To evaluate the behavior of deflection plate as a function of x and y directions the boundary conditions of the plate are required. Then for the equation of plate as a function of x and y direction as 10] (18) Then by substation eq. 18 into eq. 16 the suggested general equation of motion for honeycomb sandwich plate structure is obtained as ( ) ( ) ] ( ) ( ) ] ( ( ) ] (21) By building a computer program with using Fortran Power Station 4.0 can be evaluated the natural frequency of honeycomb sandwich plate with various parameters effect as 1. Thickness of upper and lower plates and honeycomb parte. 2. Hexagonal honeycomb. 3. t h and l of honeycomb parte. 4. Mechanical properties and density of honeycomb sandwich parte. 3. NUMERICAL INVESTIGATION The numerical investigation is carried out to calculate the natural frequency of honeycomb sandwich plate structure by using the finite elements method ANSYS program (Ver.14). Where the shell element (SHELL93) is used to build the model of honeycomb sandwich plate structure figure 5.It is assumed that the shell element is employed with zero thickness or element tapering down to a zero thickness at any corner is not allowed Also the shear deflections are included in this element. The out-of plane stress for this element varies linearly through the thickness..the transverse shear stresses (SYZ and SXZ) are assumed to be constant through the thickness and the transverse shear strains are assumed to be small in a large strain analysis. ) ( ) ( ( ) ] ) (19) With comparison eq. (19) with general equation of motion of single degree of freedom for free vibration structure as follows 12] (20)

6 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 14 maximum percentage discrepancy between the analytical and numerical results is about (2%). Fig. 5. Shell93-8 Node Element Geometry. 4. RESULTS AND DISCUSSIONS The results evaluated are included the natural frequency of honeycomb sandwich simply supported plate with various angle and thickness of honeycomb part and different upper and lower plates parts thicknesses. The materials are assumed to be distributed to upper and lower plate parts and honeycomb part are aluminium materials with mechanical properties as And the dimensions of plates are (22) the results of natural frequency evaluated are shown in figures 6 to 9 using various parameters. Figs. 6 and 7 show the natural frequency of honeycomb plate structure with different Hexagonal Honeycomb thickness angle various honeycomb parts thickness with upper and lower plates parts are respectively. From figures it is seen that the natural frequency increases with increase the Hexagonal Honeycomb thickness and angle. Figs. 8 and 9 show the natural frequency of honeycomb plate structure with different upper and lower plates parts and various of Hexagonal Honeycomb angle and various honeycomb part thickness for Hexagonal Honeycomb thickness. From figures it is clear that the natural frequency is increasing with increase the Hexagonal Honeycomb angle and honeycomb part thickness. The natural frequency decreases with increasing the upper and lower plates parts thickness. The results indicate that the increasing of Hexagonal Honeycomb thickness and angle and increasing the honeycomb plate part thickness causes an increase in the strength to weight ratio therefore an increase in the natural frequency of plate. The increase of upper and lower plate parts causes a decrease in the strength to weight ratio therefore decreasing the natural frequency of honeycomb sandwich plate. Table I shows the comparison between theoretical and numerical results of fundamental natural frequency of honeycomb plate structure with different honeycomb parts and upper and lower plate parts thickness. It is clear that the suggested analytical solution of honeycomb plate gives a good agreement compared with numerical results evaluated by using finite element technique ANSYS program ver. 14. The Table I Comparison between analytical and numerical natural frequency results for various honeycomb and upper and lower plate thickness. Natural Frequency Case h h =1 cm h Lp =h Up = 1 mm t=0.05 mm h h =2 cm h Lp =h Up = 1 mm t=0.05 mm h h =0.5 cm h Lp =h Up = 1 mm t=0.05 mm h h =0.5 cm h Lp =h Up = 2 mm t=0.05 mm (rad/sec) (Deg Analytica Numerica ) l l a. h h=0.5 cm Discrepancy %

7 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 15 b. h h=1 cm b. h h=1 cm c. h h=1.5 cm Fig. 6. Natural frequency of honeycomb plate with different dimensions of Regular Hexagonal Honeycomb and various honeycomb thickness for thickness of upper and lower plate hlp=hup=1 mm. c. h h=1.5 cm Fig. 7. Natural frequency of honeycomb plate with different dimensions of Regular Hexagonal Honeycomb and various honeycomb thickness for thickness of upper and lower plate hlp=hup=2 mm. a. h h=0.5 cm a. h Lp=h up=1 mm

8 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 16 b. h Lp =h up =1.5 mm b. h h=1 cm c. h Lp=h up=2 mm Fig. 8. Natural frequency of honeycomb plate with different angle of Regular Hexagonal Honeycomb and various honeycomb thickness and thickness of upper and lower plate for t=0.025 mm and. a. h h=0.5 cm c. h h=2 cm Fig. 9. Natural frequency of honeycomb plate with different angle of Regular Hexagonal Honeycomb and various thicknesses of upper and lower plate and honeycomb thickness for t=0.025 mm and. 5. CONCLUSIONS Some concluding observations from the investigation are given below: 1. The increase of Hexagonal Honeycomb thickness causes an increase in the strength of honeycomb structure then increasing the natural frequency of honeycomb plate. 2. With increasing the Hexagonal Honeycomb angle increases the strength and stiffness of Honeycomb structure therefore with increase the Hexagonal Honeycomb angle increases the natural frequency of honeycomb sandwich plate structure. 3. The increase of honeycomb thickness causes an increase in the strength of honeycomb structure then increasing the natural frequency of honeycomb plate. 4. The increasing of upper and lower plate parts thickness of honeycomb sandwich plate causes a decrease in the strength to weight ratio of honeycomb plate structure. Therefore with increasing the upper and lower plate parts thickness decreases the natural frequency of honeycomb sandwich plate structure.

9 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:04 17 REFERENCES 1. Dag Lukkassen and Annette Meidell "Advanced Materials and Structures and their Fabrication Processes" Narrik University College Hin Harish R and Ramesh S Sharma Vibration response analysis of honeycomb sandwich panel with varying Core Height International Journal of Emerging Technologies in Computational and Applied Sciences Vol. 5 No. 6 pp Jeom Kee Paik Anil K. Thayamballi Gyu Sung Kim The strength characteristics of aluminium honeycomb sandwich panels Thin- Walled Structures Vol. 35 pp C. W. Schwingshackl G. S. Aglietti P. R. Cunningham Determination of Honeycomb Material Properties: Existing Theories and an Alternative Dynamic Approach Journal of Aerospace Engineering Vitaly Skvortsov Sergey Krakhmalev Vitaly Koissin Andrey Shipsha Non-Stationary Oscillations of Sandwich Plates Under Local Dynamic Loading Tenth International Congress on Sound and Vibration A.Boudjemai M.H. Bouanane Mankour R. Amri H. Salem B. Chouchaoui MDA of Hexagonal Honeycomb Plates used for Space Applications World academy of science Engineering and technology Vol Jayasree Ramanujan Ancy Joseph and Nibu Mani Dynamic Response of sandwich Plates International Journal of Innovative Research in Science Engineering and Technology Vol. 2 No G. Sakar F. C. Bolat The Free Vibration Analysis of Honeycomb Sandwich Beam Using 3D and Continuum Model World Academy of Science Engineering and Technology International Journal of Mechanical Aerospace Industrial Mechatronic and Manufacturing Engineering Vol. 9 No Eduard Ventsel and Theodor Krauthammer Thin Plates and Shells Theory Analysis and Applications Book Marcel Dekker Inc Werner Soedel Vibrations of Shells and Plates Third Edition Revised and Expanded book Marcel Dekker Inc Muhannad Al-Waily "Analytical and numerical thermal buckling analysis investigation of unidirectional and woven reinforcement composite plate structural "International Journal of Energy and Environment Vol. 6 No Muhsin J. Jweeg Muhannad Al-Waily and Alaa Abdulzahra Deli Theoretical and Numerical Investigation of Buckling of Orthotropic Hyper Composite Plates International Journal of Mechanical and Mechatronics Engineering IJMME-IJENS Vol. 15 No

### Theoretical and Numerical Vibration Investigation Study of Orthotropic Hyper Composite Plate Structure

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 1 Theoretical and Numerical Vibration Investigation Study of Orthotropic Hyper Composite Plate Structure Dr. Mohsin

### Iraq Ref. & Air. Cond. Dept/ Technical College / Kirkuk

International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-015 1678 Study the Increasing of the Cantilever Plate Stiffness by Using s Jawdat Ali Yakoob Iesam Jondi Hasan Ass.

### Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test

Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test M. Praveen Kumar 1 and V. Balakrishna Murthy 2* 1 Mechanical Engineering Department, P.V.P. Siddhartha Institute of Technology,

### BUCKLING COEFFICIENTS FOR SIMPLY SUPPORTED, FLAT, RECTANGULAR SANDWICH PANELS UNDER BIAXIAL COMPRESSION

U. S. FOREST SERVICE RESEARCH PAPER FPL 135 APRIL 1970 BUCKLING COEFFICIENTS FOR SIMPLY SUPPORTED, FLAT, RECTANGULAR SANDWICH PANELS UNDER BIAXIAL COMPRESSION FOREST PRODUCTS LABORATORY, FOREST SERVICE

### A Study on the Tube of Integral Propeller Shaft for the Rear-wheel Drive Automobile Using Carbon Composite Fiber

A Study on the Tube of Integral Propeller Shaft for the Rear-wheel Drive Automobile Using Carbon Composite Fiber Kibong Han Mechatronics Department, Jungwon University, 85 Munmu-ro, Goesan-gun, South Korea.

### Dynamic Response Of Laminated Composite Shells Subjected To Impulsive Loads

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 3 Ver. I (May. - June. 2017), PP 108-123 www.iosrjournals.org Dynamic Response Of Laminated

### Computational Analysis for Composites

Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics

### Lecture 4 Honeycombs Notes, 3.054

Honeycombs-In-plane behavior Lecture 4 Honeycombs Notes, 3.054 Prismatic cells Polymer, metal, ceramic honeycombs widely available Used for sandwich structure cores, energy absorption, carriers for catalysts

### Optimum Height of Plate Stiffener under Pressure Effect

The st Regional Conference of Eng. Sci. NUCEJ Spatial ISSUE vol., No.3, 8 pp 459-468 Optimum Height of Plate Stiffener under Pressure Effect Mazin Victor Yousif M.Sc Production Engineering University of

### Size Effects In the Crushing of Honeycomb Structures

45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 19-22 April 2004, Palm Springs, California AIAA 2004-1640 Size Effects In the Crushing of Honeycomb Structures Erik C.

### COURSE STE6289 Modern Materials and Computations (Moderne materialer og beregninger 7.5 stp.)

Narvik University College (Høgskolen i Narvik) EXAMINATION TASK COURSE STE6289 Modern Materials and Computations (Moderne materialer og beregninger 7.5 stp.) CLASS: Master students in Engineering Design

### Bending of Simply Supported Isotropic and Composite Laminate Plates

Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto Gutierrez-Miravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,

### Stability of Simply Supported Square Plate with Concentric Cutout

International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Stability of Simply Supported Square Plate with Concentric Cutout Jayashankarbabu B. S. 1, Dr. Karisiddappa 1 (Civil Engineering

### DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS).

DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS). Lab Director: Coordinating Staff: Mr. Muhammad Farooq (Lecturer) Mr. Liaquat Qureshi (Lab Supervisor)

### A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,

### Mechanics of Irregular Honeycomb Structures

Mechanics of Irregular Honeycomb Structures S. Adhikari 1, T. Mukhopadhyay 1 Chair of Aerospace Engineering, College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK Sixth International

### Modeling the elastic properties of paper honeycomb panels using the finite element method

Proceedings of the XXVI th International Conference Research for Furniture Industry Modeling the elastic properties of paper honeycomb panels using the finite element method Viktor UTASSY, Levente DÉNES

### EFFECT OF RETROFITTING ON FLEXURAL RIGIDITY OF RECTANGULAR FRP PLATES

EFFECT OF RETROFITTING ON FLEXURAL RIGIDITY OF RECTANGULAR FRP PLATES STEVEN J. MAKONIS, JR. Department of Civil & Environmental Engineering Old Dominion University Norfolk, VA 23528-0241, USA smako001@odu.edu

### UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

### MINIMUM WEIGHT STRUCTURAL SANDWICH

U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADISON, WIS. In Cooperation with the University of Wisconsin U.S.D.A. FOREST SERVICE RESEARCH NOTE Revised NOVEMBER 1970 MINIMUM

### Presented By: EAS 6939 Aerospace Structural Composites

A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have

### DYNAMIC FAILURE ANALYSIS OF LAMINATED COMPOSITE PLATES

Association of Metallurgical Engineers of Serbia AMES Scientific paper UDC:669.1-419:628.183=20 DYNAMIC FAILURE ANALYSIS OF LAMINATED COMPOSITE PLATES J. ESKANDARI JAM 1 and N. GARSHASBI NIA 2 1- Aerospace

### Composite Sandwich Structures with Honeycomb Core subjected to Impact

Clemson University TigerPrints All Theses Theses 12-212 Composite Sandwich Structures with Honeycomb Core subjected to Impact Lei He Clemson University, he6@clemson.edu Follow this and additional works

### FREE VIBRATION ANALYSIS OF THIN CYLINDRICAL SHELLS SUBJECTED TO INTERNAL PRESSURE AND FINITE ELEMENT ANALYSIS

FREE VIBRATION ANALYSIS OF THIN CYLINDRICAL SHELLS SUBJECTED TO INTERNAL PRESSURE AND FINITE ELEMENT ANALYSIS J. Kandasamy 1, M. Madhavi 2, N. Haritha 3 1 Corresponding author Department of Mechanical

### Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.

Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie

### Analytical Strip Method for Thin Isotropic Cylindrical Shells

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 4 Ver. III (Jul. Aug. 2017), PP 24-38 www.iosrjournals.org Analytical Strip Method for

### BEAMS AND PLATES ANALYSIS

BEAMS AND PLATES ANALYSIS Automotive body structure can be divided into two types: i. Frameworks constructed of beams ii. Panels Classical beam versus typical modern vehicle beam sections Assumptions:

### FLEXIBILITY METHOD FOR INDETERMINATE FRAMES

UNIT - I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These

### TABLE OF CONTENTS. Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA

Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA TABLE OF CONTENTS 1. INTRODUCTION TO COMPOSITE MATERIALS 1.1 Introduction... 1.2 Classification... 1.2.1

### APPLICATION OF THE GALERKIN-VLASOV METHOD TO THE FLEXURAL ANALYSIS OF SIMPLY SUPPORTED RECTANGULAR KIRCHHOFF PLATES UNDER UNIFORM LOADS

Nigerian Journal of Technology (NIJOTECH) Vol. 35, No. 4, October 2016, pp. 732 738 Copyright Faculty of Engineering, University of Nigeria, Nsukka, Print ISSN: 0331-8443, Electronic ISSN: 2467-8821 www.nijotech.com

### FREE VIBRATION ANALYSIS OF LAMINATED COMPOSITE SHALLOW SHELLS

IMPACT: International Journal of Research in Engineering & Technology (IMPACT: IJRET) ISSN(E): 2321-8843; ISSN(P): 2347-4599 Vol. 2, Issue 9, Sep 2014, 47-54 Impact Journals FREE VIBRATION ANALYSIS OF

### Parametric study on the transverse and longitudinal moments of trough type folded plate roofs using ANSYS

American Journal of Engineering Research (AJER) e-issn : 2320-0847 p-issn : 2320-0936 Volume-4 pp-22-28 www.ajer.org Research Paper Open Access Parametric study on the transverse and longitudinal moments

### DYNAMIC RESPONSE OF THIN-WALLED GIRDERS SUBJECTED TO COMBINED LOAD

DYNAMIC RESPONSE OF THIN-WALLED GIRDERS SUBJECTED TO COMBINED LOAD P. WŁUKA, M. URBANIAK, T. KUBIAK Department of Strength of Materials, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Łódź,

### Unit 18 Other Issues In Buckling/Structural Instability

Unit 18 Other Issues In Buckling/Structural Instability Readings: Rivello Timoshenko Jones 14.3, 14.5, 14.6, 14.7 (read these at least, others at your leisure ) Ch. 15, Ch. 16 Theory of Elastic Stability

### Open Access Prediction on Deflection of V-core Sandwich Panels in Weak Direction

Send Orders for Reprints to reprints@benthamscience.net The Open Ocean Engineering Journal, 2013, 6, Suppl-1, M5) 73-81 73 Open Access Prediction on Deflection of V-core Sandwich Panels in Weak Direction

### 202 Index. failure, 26 field equation, 122 force, 1

Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic

### AMM06. An Approximate Analytical Modeling of Honeycomb Sandwich Structure Including the Effects of Imperfection, Core Thickness and Impact Damage

9- October, 0, Krabi An Approximate Analytical Modeling of Honeycomb Sandwich Structure Including the Effects of Imperfection, Core Thickness and Impact Damage Tanzeel-ur-Rehman, Hamdan Ajmal Khan, Asif

### ANALYTICAL SOLUTIONS USING HIGH ORDER COMPOSITE LAMINATE THEORY FOR HONEYCOMB SANDWICH PLATES WITH VISCOELASTIC FREQUENCY DEPENDENT DAMPING

Clemson University TigerPrints All Theses Theses 8-11 ANALYTICAL SOLUTIONS USING HIGH ORDER COMPOSITE LAMINATE THEORY FOR HONEYCOMB SANDWICH PLATES WITH VISCOELASTIC FREQUENCY DEPENDENT DAMPING Nan Shan

### CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES

CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric

### MATERIAL PROPERTIES. Material Properties Must Be Evaluated By Laboratory or Field Tests 1.1 INTRODUCTION 1.2 ANISOTROPIC MATERIALS

. MARIAL PROPRIS Material Properties Must Be valuated By Laboratory or Field ests. INRODUCION he fundamental equations of structural mechanics can be placed in three categories[]. First, the stress-strain

### SIZE EFFECTS IN THE COMPRESSIVE CRUSHING OF HONEYCOMBS

43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con 22-25 April 2002, Denver, Colorado SIZE EFFECTS IN THE COMPRESSIVE CRUSHING OF HONEYCOMBS Erik C. Mellquistand Anthony M.

### ISSN: ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 2, Issue 4, July 2013

Delamination Studies in Fibre-Reinforced Polymer Composites K.Kantha Rao, Dr P. Shailesh, K. Vijay Kumar 1 Associate Professor, Narasimha Reddy Engineering College Hyderabad. 2 Professor, St. Peter s Engineering

### five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

### five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

### THE TRANSVERSE OFF-AXIS STIFFNESS AND STRENGTH OF SOFTWOODS. Abstract

THE TRANSVERSE OFF-AXIS STIFFNESS AND STRENGTH OF SOFTWOODS Carl S. Moden 1, Jessica Polycarpe 1 and Lars A. Berglund 2 1 Dept. of Aeronautical and Vehicle Engineering The Royal Institute of Technology

### FLEXURAL RESPONSE OF FIBER RENFORCED PLASTIC DECKS USING HIGHER-ORDER SHEAR DEFORMABLE PLATE THEORY

Asia-Pacific Conference on FRP in Structures (APFIS 2007) S.T. Smith (ed) 2007 International Institute for FRP in Construction FLEXURAL RESPONSE OF FIBER RENFORCED PLASTIC DECKS USING HIGHER-ORDER SHEAR

### International Journal for Ignited Minds (IJIMIINDS) Design and Analysis of Effect of Core Thickness in UAV Wing

International Journal for Ignited Minds (IJIMIINDS) Design and Analysis of Effect of Core Thickness in UAV Wing Puttappa H R 1, Ravi Prakash M 2 & Madhusudhan Reddy 3 1 P G Scholar, Dept of Mechanical

### FINITE ELEMENT ANALYSIS OF EFFECTIVE MECHANICAL PROPERTIES, VIBRATION AND ACOUSTIC PERFORMANCE OF AUXETIC CHIRAL CORE SANDWICH STRUCTURES

Clemson University TigerPrints All Theses Theses 8-2013 FINITE ELEMENT ANALYSIS OF EFFECTIVE MECHANICAL PROPERTIES, VIBRATION AND ACOUSTIC PERFORMANCE OF AUXETIC CHIRAL CORE SANDWICH STRUCTURES Hrishikesh

### Thin-walled Box Beam Bending Distortion Analytical Analysis

Journal of Mechanical Engineering Vol 14(1), 1-16, 217 Thin-walled Box Beam Bending Distortion Analytical Analysis A Halim Kadarman School of Aerospace Engineering Universiti Sains Malaysia, 143 Nibong

### Finite Element Analysis of Piezoelectric Cantilever

Finite Element Analysis of Piezoelectric Cantilever Nitin N More Department of Mechanical Engineering K.L.E S College of Engineering and Technology, Belgaum, Karnataka, India. Abstract- Energy (or power)

### The numerical simulation research of an Ultra-Light Photovoltaic Cell multilayer composite structure

5th International Conference on Civil, Architectural and Hydraulic Engineering (ICCAHE 2016) The numerical simulation research of an Ultra-Light Photovoltaic Cell multilayer composite structure Kangwen

### SANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS

SANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS de Aguiar, José M., josemaguiar@gmail.com Faculdade de Tecnologia de São Paulo, FATEC-SP Centro Estadual de Educação Tecnológica Paula Souza. CEETEPS

### INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 3, No 4, 2013

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 3, No 4, 2013 Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0 Research article ISSN 0976 4399 Pure bending analysis

### Micro-meso draping modelling of non-crimp fabrics

Micro-meso draping modelling of non-crimp fabrics Oleksandr Vorobiov 1, Dr. Th. Bischoff 1, Dr. A. Tulke 1 1 FTA Forschungsgesellschaft für Textiltechnik mbh 1 Introduction Non-crimp fabrics (NCFs) are

### NUMERICAL ANALYSIS OF SANDWICH PANELS SUBJECTED TO POINT LOADS

ECCOMAS Congress 216 VII European Congress on Computational Methods in Applied Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.) Crete Island, Greece, 5 1 June 216

### QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS

QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,

### MEG 741 Energy and Variational Methods in Mechanics I

MEG 741 Energy and Variational Methods in Mechanics I Brendan J. O Toole, Ph.D. Associate Professor of Mechanical Engineering Howard R. Hughes College of Engineering University of Nevada Las Vegas TBE

### TESTING AND ANALYSIS OF COMPOSITE SANDWICH BEAMS

TESTING AND ANALYSIS OF COMPOSITE SANDWICH BEAMS I. M. Daniel, J. L. Abot, and K. A. Wang Walter P. Murphy Professor, Departments of Civil and Mechanical Engineering, Robert R. McCormick School of Engineering

### Strain Measurements. Isaac Choutapalli

Note that for axial elongation (Eaxiai > 0), Erransverse (from Equation C.6), and therefore Strain Measurements Isaac Choutapalli Department of Mechanical Engineering The University of Texas - Pan American

### August 3,1999. Stiffness and Strength Properties for Basic Sandwich Material Core Types UCRL-JC B. Kim, R.M. Christensen.

Preprint UCRL-JC-135347 Stiffness and Strength Properties for Basic Sandwich Material Core Types B. Kim, R.M. Christensen This article was submitted to ASME IMECE 99, Nashville, TN, November 14-19, 1999

### Chapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements

CIVL 7/8117 Chapter 12 - Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness

### Simulation of Mechanical and Thermal Properties for Sandwich Panels with Cellular Wood Cores

Paper 4 Simulation of Mechanical and Thermal Properties for Sandwich Panels with Cellular Wood Cores E. Labans, K. Kalnins and A. Bikovs Institute of Materials and Structures Riga Technical University,

### Frequency Response of Composite Laminates at Various Boundary Conditions

International Journal of Engineering Science Invention (IJESI) ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 www.ijesi.org ǁ PP.11-15 Frequency Response of Composite Laminates at Various Boundary Conditions

### Mechanical Properties of Materials

Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

### Thermal buckling and post-buckling of laminated composite plates with. temperature dependent properties by an asymptotic numerical method

hermal buckling and post-buckling of laminated composite plates with temperature dependent properties by an asymptotic numerical method F. Abdoun a,*, L. Azrar a,b, E.M. Daya c a LAMA, Higher School of

### Piezoelectric Control of Multi-functional Composite Shells Subjected to an Electromagnetic Field

Piezoelectric Control of Multi-functional Composite Shells Subjected to an Electromagnetic Field *Sang-Yun Park 1) and Ohseop Song 2) 1), 2) Department of Mechanical Engineering, Chungnam National University,

### Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

### A *69>H>N6 #DJGC6A DG C<>C::G>C<,8>:C8:H /DA 'D 2:6G - ( - ) +"' ( + -"( (' (& -+" % '('%"' +"-2 ( -!"',- % )% -.C>K:GH>IN D; AF69>HH>6,-+

The primary objective is to determine whether the structural efficiency of plates can be improved with variable thickness The large displacement analysis of steel plate with variable thickness at direction

### VIBRATION AND ACOUSTIC PROPERTIES OF HONEYCOMB SANDWICH STRUCTURES SUBJECT TO VARIABLE INCIDENT PLANE-WAVE ANGLE PRESSURE LOADS

Clemson University TigerPrints All Theses Theses 5-2013 VIBRATION AND ACOUSTIC PROPERTIES OF HONEYCOMB SANDWICH STRUCTURES SUBJECT TO VARIABLE INCIDENT PLANE-WAVE ANGLE PRESSURE LOADS Jiaxue Yan Clemson

### INFLUENCE OF BOUNDARY CONDITIONS IN MODAL TESTING ON EVALUATED ELASTIC PROPERTIES OF MASS TIMBER PANELS

INFLUENCE OF BOUNDARY CONDITIONS IN MODAL TESTING ON EVALUATED ELASTIC PROPERTIES OF MASS TIMBER PANELS Jan Niederwestberg 1, Jianhui Zhou, Ying Hei Chui 3 ABSTRACT: Cross laminated timber (CLT) has the

### Fig. 1. Circular fiber and interphase between the fiber and the matrix.

Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In

### Modelling of delamination damage in composite beams. 1 Introduction. Manudha T. Herath 1*, Kaustav Bandyopadhyay 1 and Joshua D.

6 th Australasian Congress on Applied Mechanics, ACAM 6 12-15 December 2010, Perth, Australia Modelling of delamination damage in composite beams Manudha T. Herath 1*, Kaustav Bandyopadhyay 1 and Joshua

### Unit 15 Shearing and Torsion (and Bending) of Shell Beams

Unit 15 Shearing and Torsion (and Bending) of Shell Beams Readings: Rivello Ch. 9, section 8.7 (again), section 7.6 T & G 126, 127 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering

### INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011

Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.

Index A Admissible function, 163 Amplification factor, 36 Amplitude, 1, 22 Amplitude-modulated carrier, 630 Amplitude ratio, 36 Antinodes, 612 Approximate analytical methods, 647 Assumed modes method,

### NUMERICAL FEM ANALYSIS FOR THE PART OF COMPOSITE HELICOPTER ROTOR BLADE

Journal of KONES Powertrain and Transport, Vol. 19, No. 1 2012 NUMERICAL FEM ANALYSIS FOR THE PART OF COMPOSITE HELICOPTER ROTOR BLADE Hubert D bski Lublin University of Technology, Department of Machine

### Retrospectives on My Studies of Solid Mechanics (II)

Retrospectives on My Studies of Solid Mechanics (II) - a new energy method based on the stationary principle of total energy By Tadahiko Kawai + and Etsu Kazama ++ ABSTRACT A new energy method is proposed

### INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS

INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS SHEN R. WU and LEI GU WILEY A JOHN WILEY & SONS, INC., PUBLICATION ! PREFACE xv PARTI FUNDAMENTALS 1 1 INTRODUCTION 3

### MATERIAL ELASTIC ANISOTROPIC command

MATERIAL ELASTIC ANISOTROPIC command.. Synopsis The MATERIAL ELASTIC ANISOTROPIC command is used to specify the parameters associated with an anisotropic linear elastic material idealization. Syntax The

### Finite element modelling of infinitely wide Angle-ply FRP. laminates

www.ijaser.com 2012 by the authors Licensee IJASER- Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 Finite element modelling of infinitely wide Angle-ply FRP laminates

### Some Aspects Of Dynamic Buckling of Plates Under In Plane Pulse Loading

Mechanics and Mechanical Engineering Vol. 12, No. 2 (2008) 135 146 c Technical University of Lodz Some Aspects Of Dynamic Buckling of Plates Under In Plane Pulse Loading Katarzyna Kowal Michalska, Rados

### The Relationship between the Applied Torque and Stresses in Post-Tension Structures

ECNDT 6 - Poster 218 The Relationship between the Applied Torque and Stresses in Post-Tension Structures Fui Kiew LIEW, Sinin HAMDAN * and Mohd. Shahril OSMAN, Faculty of Engineering, Universiti Malaysia

### CALCULATING STATIC DEFLECTION AND NATURAL FREQUENCY OF STEPPED CANTILEVER BEAM USING MODIFIED RAYLEIGH METHOD

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN 2249-6890 Vol. 3, Issue 4, Oct 2013, 107-118 TJPRC Pvt. Ltd. CALCULATING STATIC DEFLECTION AND NATURAL

### International Journal of Innovative Research in Science, Engineering and Technology Vol. 2, Issue 7, July 2013

ANALYSIS AND MITIGATION OF STRESS CONCENTRATION FACTOR OF A RECTANGULAR ISOTROPIC AND ORTHOTROPIC PLATE WITH CENTRAL CIRCULAR HOLE SUBJECTED TO INPLANE STATIC LOADING BY DESIGN OPTIMIZATION Shubhrata Nagpal

### UNIT- I Thin plate theory, Structural Instability:

UNIT- I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and in-plane loading Thin plates having

### Indentation Energy in Bending of Sandwich Beams with Composite Laminated Faces and Foam Core

Indentation Energy in Bending of Sandwich Beams with Composite Laminated Faces and Foam Core M. SADIGHI, H. POURIAYEVALI, and M. SAADATI Dept. of Mechanical Engineering, Amirkabir University of Tech, Tehran,

### The stiffness of plates

The stiffness of plates 1. Introduction The word plate is a collective term for elements in which forces can be transferred in two directions. Floors, walls, bridge slabs and laminates are all plates.

### COMPRESSIVE EUCICLING CURVES MR SANDWICH PANELS WITH ISOTROPIC FACINGS AND ISOTROPIC OR ORTI1OTROIPIC CORES. No Revised January 1958

SRICULTU RE ROOM I COMPRESSIVE EUCICLING CURVES MR SANDWICH PANELS WITH ISOTROPIC FACINGS AND ISOTROPIC OR ORTI1OTROIPIC CORES No 1854 Revised January 1958 This Report is One of a Series Issued in Cooperation

### AEROELASTIC ANALYSIS OF SPHERICAL SHELLS

11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver

### Parameter Design of High Speed Coupling for 6 MW Wind Turbine Considering Torsional Vibration

Parameter Design of High Speed Coupling for 6 MW Wind Turbine Considering Torsional Vibration JongHun Kang 1, Junwoo Bae 2, Seungkeun Jeong 3, SooKeun Park 4 and Hyoung Woo Lee 1 # 1 Department of Mechatronics

### Application of Finite Element Method to Create Animated Simulation of Beam Analysis for the Course of Mechanics of Materials

International Conference on Engineering Education and Research "Progress Through Partnership" 4 VSB-TUO, Ostrava, ISSN 156-35 Application of Finite Element Method to Create Animated Simulation of Beam

### INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

NSTTUTE OF AERONAUTCAL ENGNEERNG (Autonomous) Dundigal, Hyderabad - 00 043 AERONAUTCAL ENGNEERNG TUTORAL QUESTON BANK Course Name : ARCRAFT VEHCLES STRUCTURES Course Code : A2109 Class : B. Tech Semester

### Bending Load & Calibration Module

Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of

### REPORT TO D-FLEX LTD APRIL 2009 REPORT. (to D-Flex Ltd, NWDA Innovation Vouchers Award, 28 April 2009)

REPORT (to D-Flex Ltd, NWDA Innovation Vouchers Award, 28 April 2009) Finite Element Modelling of Rigidity of Fishing Rods with Various Cross-sections Report to D-Flex Ltd by Z Guan Department of Engineering,

### Analysis Of Naca 2412 For Automobile Rear Spoiler Using Composite Material *

Analysis Of Naca 2412 For Automobile Rear Spoiler Using Composite Material * Kamprasad Chodagudi 1, T.b.s Rao 2 -----------------------------------------------------------------------------------------------------------------------------

### FINITE ELEMENT AND EXPERIMENTAL STUDY OF NOVEL CONCEPT OF 3D FIBRE CELL STRUCTURE

FINITE ELEMENT AND EXPERIMENTAL STUDY OF NOVEL CONCEPT OF 3D FIBRE CELL STRUCTURE M. Růžička, V. Kulíšek 2, J. Had, O. Prejzek Department of Mechanics, Biomechanics and Mechatronics, Faculty of Mechanical

### THE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE

Journal of Applied Mathematics and Computational Mechanics 013, 1(4), 13-1 THE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE Jolanta Błaszczuk