Structural Dynamics Lecture 7. Outline of Lecture 7. Multi-Degree-of-Freedom Systems (cont.) System Reduction. Vibration due to Movable Supports.
|
|
- Berniece Shanna Carson
- 6 years ago
- Views:
Transcription
1 Outline of Multi-Degree-of-Freedom Systems (cont.) System Reduction. Truncated Modal Expansion with Quasi-Static Correction. Guyan Reduction. Vibration due to Movable Supports. Earthquake Excitations. 1
2 Multi-Degree-of-Freedom Systems (cont.) System Reduction Equations of motion for MDOF systems: Dimension of :. A system reduction scheme is a procedure, which reduces the number of dynamic degrees of freedom from to. A system reduction scheme has the general format: 2
3 : Dynamic influenced component of. : Quasi-static influenced component of. : Reduced coordinate vector for dynamic response. Dimension:. : Vector base for dynamic subspace. Dimension:. : Flexibility matrix for quasi-static response. Dimension:. 3
4 4
5 The linear independent column vectors form a vector base, which spans an -dimensional subspace containing the dynamic part of the response. The degrees of freedom indicate the components of in the said vector base. This has been illustrated in Fig. 1 for the 2-dimensionsal case, where the base vectors and span a plane. is not placed in, and is normally not orthogonal to. is the error vector, i.e. the deficit vector on the right hand side of (2) to make this relation exact. Such errors are inherent to most reduction schemes. Minimization of the error can only be achieved by proper choice of the base vectors and the quasi-static flexibility matrix, which in turn requires physical understanding of the dynamic behavior of the structure. The quasi-static nature of implies that the related damping and inertial forces are ignorable. This implies that: In contrast, is influenced by both damping and inertial forces. 5
6 Then, insertion of (2), (3), (4) into (1) provides: Next, (6) is premultiplied by leading to: : Projected mass matrix. Dimension:. : Projected damping matrix. Dimension:. : Projected stiffness matrix. Dimension:. : Projected load vector. Dimension:. 6
7 (7) is of the same type as (1). (7) is solved for, from which is obtained from (2), (3), (4). Truncated Modal Expansion with Quasi-Static Correction Modal analysis with decoupled modal coordinate differential equations is given as, cf. Lecture 5, Eqs. (69), (70): 7
8 The global structural response is typically carried by the lowest modes, whereas the remaining degrees of freedom merely induce a quasi-static response. Then, (8) may be reformulated on the form (2), where (11) may be written on the matrix form: : Dynamic modal coordinates. 8
9 Notice that may include both rigid body and elastic degrees of freedom. Inertial and damping loads may be ignored for the quasi-static modal coordinates, i.e.. Hence, for these degrees of freedom (9) reduces to: Then, (12) may be written as: 9
10 where: Further, Mercer s theorem for the flexibility matrix has been used, cf. Lecture 6, Eq. (14): Insertion of (13) and (17) into (2) provides the reduction scheme: 10
11 Hence, and: The reduction scheme requires that the flexibility matrix is known, along with the eigenmodes and the modal stiffnesses for. The differential equations (9) for the dynamic modal coordinates may be written on the matrix form: where is given by (18) and: 11
12 The projected load vector should be a vector of the modal loads. This is shown as follows: Hence, (22) is merely a matrix formulation of the first decoupled modal differential equations (9). 12
13 Example 1: Dynamic response of a jacket offshore structure In shallow water ( ) the structure is relatively stiff, and the response to travelling waves is merely quasi-static. At deeper water a dynamic response, primarily in the fundamental mode, may be present. 13
14 Guyan Reduction 14
15 Guyan has indicated a system reduction scheme, which is based on a partition of the degrees of freedom into two subvectors of the dimension and of the dimension : The degrees of freedom stored in is presumed to be influenced by inertial, damping, elastic and external dynamic loads. Especially, the kinetic energy of the structure is primarily carried by these degrees of freedom. In contrast, the degrees of freedom stored in are primarily influenced by elastic and external dynamic loads, whereas inertial and damping forces is assumed to be ignorable. Typically, and store displacement and rotational degrees of freedom, respectively, as illustrated for the plane frame structure in Fig. 3a and the plate structure in Fig. 3b. 15
16 Corresponding to the partition (26) the equations of motion (1) are partitioned as: where,. The quasi-static assumption implies that the lower part of the matrix equation is ignorable affected by inertial and damping forces. Hence: Insertion of (28) into (26) provides the reduction scheme: 16
17 Hence, and: The projected mass-, damping- and stiffness matrices become: 17
18 The projected load vector becomes: 18
19 Vibration due to Movable Supports 19
20 The supports of the structure may undergo motions due to earthquakes or heavy traffic. The structural response from such prescribed support motions will be determined. The degrees of freedom of the structure is partitioned into interior degrees of freedom stored in the vector of dimension, and boundary degrees of freedom stored in the vector of dimension. If mechanical boundary conditions (specified forces or moments) are prescribed at the boundary, the conjugated displacements and rotations are included in as illustrated for the rotation of the plane frame in Fig. 4. Eq. (1) may be written on the following partioned form: 20
21 (33) represents the structure of the equations of motion obtained by a FEanalysis in which the global system matrices ( ) have not been corrected for kinematical boundary conditions at the boundary degrees of freedom stored in. and denote the mass matrix, damping matrix and stiffness matrix of the interior degrees of freedom for. stores the reaction forces acting at the boundary degrees of freedom. Hence, this vector is determined from the last equations in (33) for known and. Then, is determined of the first equations of (33) for known : Since,, and are assumed to be explicitly known as a function of time, the right-hand side of (34) represents the equivalent dynamic load vector for the determination of the motion of the interior degrees of freedom. 21
22 Often, the inertial and damping loads the right hand side of (34) are ignorable comparable to the elastic load, or disappear completely in cases, where. This provides the so-called quasi-static solution, which may be written on the form: Let denote the quasi-static displacement vector of the interior degrees of freedom, where the boundary degrees of freedom are deformed sufficiently slow that no inertial- or damping forces are induced on the left-hand side of (35). It follows from (35) that is given as: where 22
23 is an influence matrix for the quasi-static support point motion of the dimension. The th column of indicates the quasi-static deformation of for,,, see Fig. 4b. Examples of the calculation of for a three-storey shear building are shown below in Example 2. Then, the solution to (35) may be decomposed on the form: specifies the dynamic response at the top of the quasi-static contribution, caused by the external load vector and the inertial and damping forces. 23
24 For quasi-static support point motions inducing a rigid body notion on the structure as shown below in Figs. 5a and 5b, may be interpreted as the elastic part of the displacement vector. These are determined by insertion of (38) in (35): where it has been used that cf. (37). Further, a rigid body motion cannot induce dissipation in the structure, so. 24
25 Example 2: Determination of the influence matrix for a three-storey building In Fig. 5a the two support points are subjected to the same horizontal. In Fig. 5b the foundation of the structure is rotated the angle as a rigid body. In Fig. 5c the two support points are subjected to different horizontal motions. 25
26 Earthquake Excitations In earthquake engineering the formulation (39) is preferred. Normally, there is no significant external loading (wind, traffic) present simultaneous with the earthquake loading, so it may assumed. Further, only a common scalar horizontal support point motion is is presumed, so (39) reduces to: 26
27 The influence vector induces a horizontal rigid body motion in all modes. For the three-storey frame in Fig. 6, is given as: The elastic displacement vector may be represented by the following modal expansion: : Eigenmodes of interior degrees of freedom for. 27
28 Usually, in earthquake engineering the eigenmodes are normalized to for the horizontal displacement of the top storey. Then, the th modal coordinate may be interpreted as the contribution from the th mode to the horizontal displacement of the top storey relative to the ground surface. 28
29 The modal coordinates are assumed to be decoupled. Hence, cf. Lecture 5, Eq. (70): : Mode partition factor. Save the factor, Eq. (43) has the same form as the differential equation for the relative displacement of a single storey frame exposed to horizontal earthquake excitations, cf. Lecture 3, Eq. (47). 29
30 Hence, the numerical maximum modal displacement and acceleration of the modal coordinate for a known time series of the ground surface acceleration is given as: and are the spectral displacement and acceleration of the single storey frame calculated with the damping ratio and the angular eigenfrequency, cf. Lecture 3, Eqs. (48) and (50). As mentioned before Eq. (51) in Lecture 3 the relation for is only approximative. 30
31 The th components of the elastic acceleration vector becomes: : Contribution to from the th mode. : th component of the th eigenmode. Numerical maximum of : It is the numerical maximum of, rather than the maxima of the separate modal components, which are of interest. The modal components will not attain their maximum at the same time. Hence, a simple addition of will overestimate unacceptable. Instead, is calculated from 31
32 A theoretical support of (48) is given in stochastic dynamics, where the modal components under certain conditions can be shown to be uncorrelated random variable. The variance of the sum,, becomes equal to the sum of the variance of the components,. Hence: 32
33 As explained in Lecture 3 in earthquake resistant design the inertial forces are next applied as loads on the storey masses as shown in Fig. 8, and the structure is designed by standard static analysis. 33
34 Summary of System Reduction General format: : Reduced degrees-of-freedom vector. Dimension:. : Vector base for dynamic subspace. Dimension:. : Flexibility matrix for quasi-static response. Dimension:. Truncated Modal Expansion with Quasi-Static Correction. 34
35 : Modal stiffness matrix Guyan Reduction 35
36 Vibrations due to Movable Supports Unsupported structure. The degrees of freedoms are partitioned into interior degrees of freedom and support degrees of freedom : : Quasi-static approximation. Earthquake Excitations. : Dynamic (elastic) degrees of freedom induced by and. : Quasi-static displacement induced by. 36
Structural Dynamics Lecture 4. Outline of Lecture 4. Multi-Degree-of-Freedom Systems. Formulation of Equations of Motions. Undamped Eigenvibrations.
Outline of Multi-Degree-of-Freedom Systems Formulation of Equations of Motions. Newton s 2 nd Law Applied to Free Masses. D Alembert s Principle. Basic Equations of Motion for Forced Vibrations of Linear
More informationStochastic Dynamics of SDOF Systems (cont.).
Outline of Stochastic Dynamics of SDOF Systems (cont.). Weakly Stationary Response Processes. Equivalent White Noise Approximations. Gaussian Response Processes as Conditional Normal Distributions. Stochastic
More informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. Bernoulli-Euler Beams.
More informationDesign of Structures for Earthquake Resistance
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Design of Structures for Earthquake Resistance Basic principles Ioannis N. Psycharis Lecture 3 MDOF systems Equation of motion M u + C u + K u = M r x g(t) where:
More informationStructural Dynamics Lecture 2. Outline of Lecture 2. Single-Degree-of-Freedom Systems (cont.)
Outline of Single-Degree-of-Freedom Systems (cont.) Linear Viscous Damped Eigenvibrations. Logarithmic decrement. Response to Harmonic and Periodic Loads. 1 Single-Degreee-of-Freedom Systems (cont.). Linear
More informationReduction in number of dofs
Reduction in number of dofs Reduction in the number of dof to represent a structure reduces the size of matrices and, hence, computational cost. Because a subset of the original dof represent the whole
More informationResponse Analysis for Multi Support Earthquake Excitation
Chapter 5 Response Analysis for Multi Support Earthquake Excitation 5.1 Introduction It is very important to perform the dynamic analysis for the structure subjected to random/dynamic loadings. The dynamic
More informationStructural 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:
More informationAdvanced Vibrations. Elements of Analytical Dynamics. By: H. Ahmadian Lecture One
Advanced Vibrations Lecture One Elements of Analytical Dynamics By: H. Ahmadian ahmadian@iust.ac.ir Elements of Analytical Dynamics Newton's laws were formulated for a single particle Can be extended to
More informationAA242B: MECHANICAL VIBRATIONS
AA242B: MECHANICAL VIBRATIONS 1 / 50 AA242B: MECHANICAL VIBRATIONS Undamped Vibrations of n-dof Systems These slides are based on the recommended textbook: M. Géradin and D. Rixen, Mechanical Vibrations:
More informationReliability Theory of Dynamically Loaded Structures (cont.)
Outline of Reliability Theory of Dynamically Loaded Structures (cont.) Probability Density Function of Local Maxima in a Stationary Gaussian Process. Distribution of Extreme Values. Monte Carlo Simulation
More informationRESPONSE SPECTRUM METHOD FOR ESTIMATION OF PEAK FLOOR ACCELERATION DEMAND
RESPONSE SPECTRUM METHOD FOR ESTIMATION OF PEAK FLOOR ACCELERATION DEMAND Shahram Taghavi 1 and Eduardo Miranda 2 1 Senior catastrophe risk modeler, Risk Management Solutions, CA, USA 2 Associate Professor,
More informationDesign of Earthquake-Resistant Structures
NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY OF EARTHQUAKE ENGINEERING Design of Earthquake-Resistant Structures Basic principles Ioannis N. Psycharis Basic considerations Design earthquake: small
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 Outline of the chapter *One degree of freedom systems in real life Hypothesis Examples *Response
More informationTable of Contents. Preface... 13
Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...
More informationSPECIAL DYNAMIC SOIL- STRUCTURE ANALYSIS PROCEDURES DEMONSTATED FOR TWO TOWER-LIKE STRUCTURES
2010/2 PAGES 1 8 RECEIVED 21. 9. 2009 ACCEPTED 20. 1. 2010 Y. KOLEKOVÁ, M. PETRONIJEVIĆ, G. SCHMID SPECIAL DYNAMIC SOIL- STRUCTURE ANALYSIS PROCEDURES DEMONSTATED FOR TWO TOWER-LIKE STRUCTURES ABSTRACT
More informationSeismic Analysis of Structures Prof. T.K. Datta Department of Civil Engineering Indian Institute of Technology, Delhi
Seismic Analysis of Structures Prof. T.K. Datta Department of Civil Engineering Indian Institute of Technology, Delhi Lecture - 20 Response Spectrum Method of Analysis In the last few lecture, we discussed
More informationUNIT IV FLEXIBILTY AND STIFFNESS METHOD
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SA-II (13A01505) Year & Sem: III-B.Tech & I-Sem Course & Branch: B.Tech
More information1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction
1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction Lesson Objectives: 1) List examples of MDOF structural systems and state assumptions of the idealizations. 2) Formulate the equation of motion
More informationFREE VIBRATION RESPONSE OF UNDAMPED SYSTEMS
Lecture Notes: STRUCTURAL DYNAMICS / FALL 2011 / Page: 1 FREE VIBRATION RESPONSE OF UNDAMPED SYSTEMS : : 0, 0 As demonstrated previously, the above Equation of Motion (free-vibration equation) has a solution
More informationSTRUCTURAL DYNAMICS BASICS:
BASICS: STRUCTURAL DYNAMICS Real-life structures are subjected to loads which vary with time Except self weight of the structure, all other loads vary with time In many cases, this variation of the load
More informationCodal Provisions IS 1893 (Part 1) 2002
Abstract Codal Provisions IS 1893 (Part 1) 00 Paresh V. Patel Assistant Professor, Civil Engineering Department, Nirma Institute of Technology, Ahmedabad 38481 In this article codal provisions of IS 1893
More informationChapter 2: Rigid Bar Supported by Two Buckled Struts under Axial, Harmonic, Displacement Excitation..14
Table of Contents Chapter 1: Research Objectives and Literature Review..1 1.1 Introduction...1 1.2 Literature Review......3 1.2.1 Describing Vibration......3 1.2.2 Vibration Isolation.....6 1.2.2.1 Overview.
More informationReliability Theory of Dynamic Loaded Structures (cont.) Calculation of Out-Crossing Frequencies Approximations to the Failure Probability.
Outline of Reliability Theory of Dynamic Loaded Structures (cont.) Calculation of Out-Crossing Frequencies Approximations to the Failure Probability. Poisson Approximation. Upper Bound Solution. Approximation
More informationComputational non-linear structural dynamics and energy-momentum integration schemes
icccbe 2010 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor) Computational non-linear structural dynamics and energy-momentum
More informationFigure 5.16 Compound pendulum: (a) At rest in equilibrium, (b) General position with coordinate θ, Freebody
Lecture 27. THE COMPOUND PENDULUM Figure 5.16 Compound pendulum: (a) At rest in equilibrium, (b) General position with coordinate θ, Freebody diagram The term compound is used to distinguish the present
More informationDynamic Loads CE 543. Examples. Harmonic Loads
CE 543 Structural Dynamics Introduction Dynamic Loads Dynamic loads are time-varying loads. (But time-varying loads may not require dynamic analysis.) Dynamics loads can be grouped in one of the following
More informationStructural Dynamics A Graduate Course in Aerospace Engineering
Structural Dynamics A Graduate Course in Aerospace Engineering By: H. Ahmadian ahmadian@iust.ac.ir The Science and Art of Structural Dynamics What do all the followings have in common? > A sport-utility
More informationChapter 4 Analysis of a cantilever
Chapter 4 Analysis of a cantilever Before a complex structure is studied performing a seismic analysis, the behaviour of simpler ones should be fully understood. To achieve this knowledge we will start
More informationon the figure. Someone has suggested that, in terms of the degrees of freedom x1 and M. Note that if you think the given 1.2
1) A two-story building frame is shown below. The mass of the frame is assumed to be lumped at the floor levels and the floor slabs are considered rigid. The floor masses and the story stiffnesses are
More informationIntroduction to structural dynamics
Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static
More informationBI-DIRECTIONAL SEISMIC ANALYSIS AND DESIGN OF BRIDGE STEEL TRUSS PIERS ALLOWING A CONTROLLED ROCKING RESPONSE
Proceedings of the 8 th U.S. National Conference on Earthquake Engineering April 18-22, 2006, San Francisco, California, USA Paper No. 1954 BI-DIRECTIONAL SEISMIC ANALYSIS AND DESIGN OF BRIDGE STEEL TRUSS
More informationMulti Degrees of Freedom Systems
Multi Degrees of Freedom Systems MDOF s http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March 9, 07 Outline, a System
More informationMissing Mass in Dynamic Analysis
Missing Mass in Dynamic Analysis Introduction: The common practice of performing a dynamic analysis of a structure is to evaluate the response of a structure mode by mode and then combining the results
More informationAdvanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian
Advanced Vibrations Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian ahmadian@iust.ac.ir Distributed-Parameter Systems: Exact Solutions Relation between Discrete and Distributed
More informationBoundary Nonlinear Dynamic Analysis
Boundary Nonlinear Dynamic Analysis Damper type Nonlinear Link Base Isolator type Nonlinear Link Modal Nonlinear Analysis : Equivalent Dynamic Load Damper type Nonlinear Link Visco-Elastic Damper (VED)
More informationPreliminary Examination in Dynamics
Fall Semester 2017 Problem 1 The simple structure shown below weighs 1,000 kips and has a period of 1.25 sec. It has no viscous damping. It is subjected to the impulsive load shown in the figure. If the
More informationInternational Journal of Advance Engineering and Research Development
Scientific Journal of Impact Factor (SJIF): 4.72 International Journal of Advance Engineering and Research Development Volume 4, Issue 11, November -2017 e-issn (O): 2348-4470 p-issn (P): 2348-6406 Study
More informationStructural Matrices in MDOF Systems
in MDOF Systems http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano April 9, 2016 Outline Additional Static Condensation
More informationStatic & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering
Static & Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward LWilson Professor Emeritus of Civil Engineering University of California, Berkeley Fourth Edition
More informationControl of Earthquake Induced Vibrations in Asymmetric Buildings Using Passive Damping
Control of Earthquake Induced Vibrations in Asymmetric Buildings Using Passive Damping Rakesh K. Goel, California Polytechnic State University, San Luis Obispo Abstract This paper summarizes the results
More information3. MDOF Systems: Modal Spectral Analysis
3. MDOF Systems: Modal Spectral Analysis Lesson Objectives: 1) Construct response spectra for an arbitrarily varying excitation. 2) Compute the equivalent lateral force, base shear, and overturning moment
More informationTHE EFFFCT OF TORSIONAL OSCILLATIONS ON EARTHQUAKE STRESSES
Bulletin of the Seismological Society of America. Vol. 48, pp. 221-229. July 1958 THE EFFFCT OF TORSIONAL OSCILLATIONS ON EARTHQUAKE STRESSES By GEORGE W. HOUSNER and HANNU OUTINEN ABSTRACT A comparison
More informationDYNAMIC RESPONSE OF EARTHQUAKE EXCITED INELASTIC PRIMARY- SECONDARY SYSTEMS
DYNAMIC RESPONSE OF EARTHQUAKE EXCITED INELASTIC PRIMARY- SECONDARY SYSTEMS Christoph ADAM 1 And Peter A FOTIU 2 SUMMARY The objective of the paper is to investigate numerically the effect of ductile material
More informationProgram System for Machine Dynamics. Abstract. Version 5.0 November 2017
Program System for Machine Dynamics Abstract Version 5.0 November 2017 Ingenieur-Büro Klement Lerchenweg 2 D 65428 Rüsselsheim Phone +49/6142/55951 hd.klement@t-online.de What is MADYN? The program system
More informationIntroduction to Mechanical Vibration
2103433 Introduction to Mechanical Vibration Nopdanai Ajavakom (NAV) 1 Course Topics Introduction to Vibration What is vibration? Basic concepts of vibration Modeling Linearization Single-Degree-of-Freedom
More informationOutline. Structural Matrices. Giacomo Boffi. Introductory Remarks. Structural Matrices. Evaluation of Structural Matrices
Outline in MDOF Systems Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano May 8, 014 Additional Today we will study the properties of structural matrices, that is the operators that
More informationAA 242B / ME 242B: Mechanical Vibrations (Spring 2016)
AA 242B / ME 242B: Mechanical Vibrations (Spring 206) Solution of Homework #3 Control Tab Figure : Schematic for the control tab. Inadequacy of a static-test A static-test for measuring θ would ideally
More information3.4 Analysis for lateral loads
3.4 Analysis for lateral loads 3.4.1 Braced frames In this section, simple hand methods for the analysis of statically determinate or certain low-redundant braced structures is reviewed. Member Force Analysis
More informationUniversity of California at Berkeley Structural Engineering Mechanics & Materials Department of Civil & Environmental Engineering Spring 2012 Student name : Doctoral Preliminary Examination in Dynamics
More informationStochastic Structural Dynamics Prof. Dr. C. S. Manohar Department of Civil Engineering Indian Institute of Science, Bangalore
Stochastic Structural Dynamics Prof. Dr. C. S. Manohar Department of Civil Engineering Indian Institute of Science, Bangalore Lecture No. # 32 Probabilistic Methods in Earthquake Engineering-1 (Refer Slide
More informationDr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum
STRUCTURAL DYNAMICS Dr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum Overview of Structural Dynamics Structure Members, joints, strength, stiffness, ductility Structure
More informationSEISMIC RELIABILITY ANALYSIS OF BASE-ISOLATED BUILDINGS
International Symposium on Engineering under Uncertainty: Safety Assessment and Management January 4 to 6, 2012 Paper No.: CNP 070 SEISMIC RELIABILITY ANALYSIS OF BASE-ISOLATED BUILDINGS M.C. Jacob 1,
More informationPreliminary Examination - Dynamics
Name: University of California, Berkeley Fall Semester, 2018 Problem 1 (30% weight) Preliminary Examination - Dynamics An undamped SDOF system with mass m and stiffness k is initially at rest and is then
More informationStructural System, Machines and Load Cases
Machine-Induced Vibrations Machine-Induced Vibrations In the following example the dynamic excitation of two rotating machines is analyzed. A time history analysis in the add-on module RF-DYNAM Pro - Forced
More informationAlireza Mehdipanah BEHAVIOUR OF BUILDINGS FEATURING TRANSFER BEAMS IN THE REGIONS OF LOW TO MODERATE SEISMICITY
BEHAVIOUR OF BUILDINGS FEATURING TRANSFER BEAMS IN THE REGIONS OF LOW TO MODERATE SEISMICITY Alireza Mehdipanah PhD Candidate at The University of Melbourne SUPERVISORS: A/PROF. NELSON LAM DR. ELISA LUMANTARNA
More informationA Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic Demands of Tall Buildings
Fawad A. Najam Pennung Warnitchai Asian Institute of Technology (AIT), Thailand Email: fawad.ahmed.najam@ait.ac.th A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic
More informationSoftware Verification
EXAMPLE 6-6 LINK SUNY BUFFALO DAMPER WITH LINEAR VELOCITY EXPONENT PROBLEM DESCRIPTION This example comes from Section 5 of Scheller and Constantinou 1999 ( the SUNY Buffalo report ). It is a two-dimensional,
More informationEmbedded Foundation with Different Parameters under Dynamic Excitations
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 2287 Embedded Foundation with Different Parameters under Dynamic Excitations Jaya K P 1 and Meher Prasad
More informationModule 4 : Deflection of Structures Lecture 4 : Strain Energy Method
Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under
More informationExperimental Aerodynamics. Experimental Aerodynamics
Lecture 3: Vortex shedding and buffeting G. Dimitriadis Buffeting! All structures exposed to a wind have the tendency to vibrate.! These vibrations are normally of small amplitude and have stochastic character!
More informationThe sensitivity analysis of the translation and the rotation angle of the first-order mode shape of the joints in frame structures
The sensitivity analysis of the translation and the rotation angle of the first-order mode shape of the joints in frame structures Yi Chen Yuan 1, Lin Li 2, Hongping Zhu 3 School of Civil Engineering and
More informationTruncation Errors Numerical Integration Multiple Support Excitation
Errors Numerical Integration Multiple Support Excitation http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano April 10,
More informationModal analysis of shear buildings
Modal analysis of shear buildings A comprehensive modal analysis of an arbitrary multistory shear building having rigid beams and lumped masses at floor levels is obtained. Angular frequencies (rad/sec),
More informationMethods of Analysis. Force or Flexibility Method
INTRODUCTION: The structural analysis is a mathematical process by which the response of a structure to specified loads is determined. This response is measured by determining the internal forces or stresses
More informationDynamics of Structures
Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum
More informationCOPYRIGHTED MATERIAL. Index
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,
More informationNUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS
NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS ABSTRACT : P Mata1, AH Barbat1, S Oller1, R Boroschek2 1 Technical University of Catalonia, Civil Engineering
More informationSound Propagation through Media. Nachiketa Tiwari Indian Institute of Technology Kanpur
Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur LECTURE-13 WAVE PROPAGATION IN SOLIDS Longitudinal Vibrations In Thin Plates Unlike 3-D solids, thin plates have surfaces
More informationINELASTIC SEISMIC DISPLACEMENT RESPONSE PREDICTION OF MDOF SYSTEMS BY EQUIVALENT LINEARIZATION
INEASTIC SEISMIC DISPACEMENT RESPONSE PREDICTION OF MDOF SYSTEMS BY EQUIVAENT INEARIZATION M. S. Günay 1 and H. Sucuoğlu 1 Research Assistant, Dept. of Civil Engineering, Middle East Technical University,
More informationEfficient Reduced Order Modeling of Low- to Mid-Frequency Vibration and Power Flow in Complex Structures
Efficient Reduced Order Modeling of Low- to Mid-Frequency Vibration and Power Flow in Complex Structures Yung-Chang Tan Graduate Student Research Assistant Matthew P. Castanier Assistant Research Scientist
More informationD && 9.0 DYNAMIC ANALYSIS
9.0 DYNAMIC ANALYSIS Introduction When a structure has a loading which varies with time, it is reasonable to assume its response will also vary with time. In such cases, a dynamic analysis may have to
More informationFORMULA FOR FORCED VIBRATION ANALYSIS OF STRUCTURES USING STATIC FACTORED RESPONSE AS EQUIVALENT DYNAMIC RESPONSE
FORMULA FOR FORCED VIBRATION ANALYSIS OF STRUCTURES USING STATIC FACTORED RESPONSE AS EQUIVALENT DYNAMIC RESPONSE ABSTRACT By G. C. Ezeokpube, M. Eng. Department of Civil Engineering Anambra State University,
More informationLecture 4 Dynamic Analysis of Buildings
1 Lecture 4 Dynamic Analysis of Buildings Course Instructor: Dr. Carlos E. Ventura, P.Eng. Department of Civil Engineering The University of British Columbia ventura@civil.ubc.ca Short Course for CSCE
More informationDynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras
Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras Module - 1 Lecture - 10 Methods of Writing Equation of Motion (Refer
More informationEvaluation of the ductility demand in partial strength steel structures in seismic areas using non-linear static analysis
Evaluation of the ductility demand in partial strength steel structures in seismic areas using non-linear static analysis Pedro Nogueiro Department of Applied Mechanics, ESTiG, Polytechnic Institute of
More information41514 Dynamics of Machinery
41514 Dynamics of Machinery Theory, Experiment, Phenomenology and Industrial Applications Ilmar Ferreira Santos 1. Recapitulation Mathematical Modeling & Steps 2. Example System of Particle 3. Example
More informationCE6701 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING QUESTION BANK UNIT I THEORY OF VIBRATIONS PART A
CE6701 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING QUESTION BANK UNIT I THEORY OF VIBRATIONS PART A 1. What is mean by Frequency? 2. Write a short note on Amplitude. 3. What are the effects of vibration?
More informationDEPENDENCE OF ACCIDENTAL TORSION ON STRUCTURAL SYSTEM PROPERTIES
th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 4 Paper No. 6 DEPENDENCE OF ACCIDENTAL TORSION ON STRUCTURAL SYSTEM PROPERTIES Julio J. HERNÁNDEZ and Oscar A. LÓPEZ SUMMARY
More informationMODAL ANALYSIS OF PLANE FRAMES
MODAL ANALYSIS OF PLANE FRAMES Mr. Mohammed Siraj Professor, Department of Civil Engineering, Deogiri Institute of Engineering and Management Studies Aurangabad, M.S, India. ABSTRACT In the modal analysis
More informationIndeterminate Analysis Force Method 1
Indeterminate Analysis Force Method 1 The force (flexibility) method expresses the relationships between displacements and forces that exist in a structure. Primary objective of the force method is to
More informationStructural Dynamics Prof. P. Banerji Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 1 Introduction
Structural Dynamics Prof. P. Banerji Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 1 Introduction Hello, I am Pradipta Banerji from the department of civil engineering,
More informationMECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT - I
MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT - I Engineering Mechanics Branch of science which deals with the behavior of a body with the state of rest or motion, subjected to the action of forces.
More informationAPPLIED MATHEMATICS AM 02
AM SYLLABUS (2013) APPLIED MATHEMATICS AM 02 SYLLABUS Applied Mathematics AM 02 Syllabus (Available in September) Paper I (3 hrs)+paper II (3 hrs) Applied Mathematics (Mechanics) Aims A course based on
More informationNonlinear static analysis PUSHOVER
Nonlinear static analysis PUSHOVER Adrian DOGARIU European Erasmus Mundus Master Course Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC Structural
More informationEXAMPLE OF PILED FOUNDATIONS
EXAMPLE OF PILED FOUNDATIONS The example developed below is intended to illustrate the various steps involved in the determination of the seismic forces developed in piles during earthquake shaking. The
More informationGiacomo Boffi. Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano
http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano April 21, 2017 Outline of Structural Members Elastic-plastic Idealization
More informationSHAKE TABLE STUDY OF SOIL STRUCTURE INTERACTION EFFECTS ON SEISMIC RESPONSE OF SINGLE AND ADJACENT BUILDINGS
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1918 SHAKE TABLE STUDY OF SOIL STRUCTURE INTERACTION EFFECTS ON SEISMIC RESPONSE OF SINGLE AND ADJACENT
More informationDynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras
Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras Module - 01 Lecture - 09 Characteristics of Single Degree - of -
More informationAN INTRODUCTION TO LAGRANGE EQUATIONS. Professor J. Kim Vandiver October 28, 2016
AN INTRODUCTION TO LAGRANGE EQUATIONS Professor J. Kim Vandiver October 28, 2016 kimv@mit.edu 1.0 INTRODUCTION This paper is intended as a minimal introduction to the application of Lagrange equations
More informationAnalysis of Tensioner Induced Coupling in Serpentine Belt Drive Systems
2008-01-1371 of Tensioner Induced Coupling in Serpentine Belt Drive Systems Copyright 2007 SAE International R. P. Neward and S. Boedo Department of Mechanical Engineering, Rochester Institute of Technology
More information2C9 Design for seismic and climate changes. Jiří Máca
2C9 Design for seismic and climate changes Jiří Máca List of lectures 1. Elements of seismology and seismicity I 2. Elements of seismology and seismicity II 3. Dynamic analysis of single-degree-of-freedom
More informationAeroelastic effects of large blade deflections for wind turbines
Aeroelastic effects of large blade deflections for wind turbines Torben J. Larsen Anders M. Hansen Risoe, National Laboratory Risoe, National Laboratory P.O. Box 49, 4 Roskilde, Denmark P.O. Box 49, 4
More informationCE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao
CE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao Associate Professor Dept. of Civil Engineering SVCE, Sriperumbudur Difference between static loading and dynamic loading Degree
More informationInclusion of a Sacrificial Fuse to Limit Peak Base-Shear Forces During Extreme Seismic Events in Structures with Viscous Damping
Inclusion of a Sacrificial Fuse to Limit Peak Base-Shear Forces During Extreme Seismic Events in Structures with Viscous Damping V. Simon, C. Labise, G.W. Rodgers, J.G. Chase & G.A. MacRae Dept. of Civil
More informationSome Aspects of Structural Dynamics
Appendix B Some Aspects of Structural Dynamics This Appendix deals with some aspects of the dynamic behavior of SDOF and MDOF. It starts with the formulation of the equation of motion of SDOF systems.
More informationReview of modal testing
Review of modal testing A. Sestieri Dipartimento di Meccanica e Aeronautica University La Sapienza, Rome Presentation layout - Modelling vibration problems - Aim of modal testing - Types of modal testing:
More informationPart 6: Dynamic design analysis
Part 6: Dynamic design analysis BuildSoft nv All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, electronic or manual, for any purpose, without written
More informationSoftware Verification
EXAMPLE 1-026 FRAME MOMENT AND SHEAR HINGES EXAMPLE DESCRIPTION This example uses a horizontal cantilever beam to test the moment and shear hinges in a static nonlinear analysis. The cantilever beam has
More informationContents. Dynamics and control of mechanical systems. Focus on
Dynamics and control of mechanical systems Date Day 1 (01/08) Day 2 (03/08) Day 3 (05/08) Day 4 (07/08) Day 5 (09/08) Day 6 (11/08) Content Review of the basics of mechanics. Kinematics of rigid bodies
More information