Ravichetan Dharenni, Ashok M H, Santoshkumar Malipatil

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1 Modal Analysis of Laminated Composite Material with Actuators on Cantilever Beam Using ANSYS Ravichetan Dharenni, Ashok M H, Santoshkumar Malipatil Department of Mechanical Engineering, VTU University, Karnataka, India Abstract It s important to design a higher load carrying in mechanical design at a lighter capacity which is essential. When it becomes lighter in weight vibration may cause prominent, hence active control methods can be used to reduce the undesired vibration. By using different damping methods vibration of system can be controlled. Researchers found smarter way reducing the vibration that is called as active vibration control using smart materials. In our case smart materials are used on composite materials which produce signals such as temperature, voltage, pressure and magnitude and so on. These materials have ability to transform one type of energy into another. In present work it is aimed on Modal analysis of composite structure with piezoelectric material under free and force vibrations. ANSYS software provides a mean FE modeling of smart structures. Piezoelectric materials are able to exhibit a strong coupling between the mechanical degrees of freedom and the electrical degrees of freedom. Modal analysis is carried out through ANSYS on smart materials. Keywords Active control, Modal analysis, Smart material, Vibration. I. INTRODUCTION Vibration control is an important and rapidly developing field for lightweight flexible structures. These structures may get damaged or become ineffective under the undesired vibration loads they constantly experience. Hence, they require an effective control mechanism to attenuate the vibration levels in order to preserve the structural integrity. The inherent damping of these structures to suppress vibration response is very small. Hence active vibration control methods are very useful to control the vibration [1, 2]. A large number of techniques have been tried to produce better control against vibration of flexible structures which are subjected to severe environmental loadings. These techniques can be classified into two categories: Passive control and Active control. II. VIBRAION CONTROL USING SMART MATERIALS Smart materials produce response to signals such as temperature, voltage, pressure, magnetic fields, etc. These materials have the ability to transform one type of energy into another and therefore use of these materials improves the overall performance of a device/structure. Smart structure is a device that involves integration of actuators, sensors and a processor [3, 4]. Smart materials can be grouped under the following categories. Piezoelectric Materials Electro and Magneto Rheological Fluids Shape Memory Alloys Optical Fibers Electro and Magnetostrictive Materials III. OBJECTIVE OF PRESENT WORK The present work is aimed at static analysis, modal analysis and active vibration control of a composite beam using a piezoelectric layer (PZT) as sensor and actuator. It includes vibration control of composite laminates with different configurations under free and forced vibration. This project describes the development and validation of finite element model for coupled field analysis of piezoelectric fields. The aim of the project is to perform coupled field numerical analysis of a composite structure with piezoelectric layer to control vibration of the structure. The focus is on the active vibration control of a composite beam.[3] Specific objectives of the project are: Development of finite element model of laminated composite beam with piezoelectric layer using ANSYS software. Validation of finite element model developed using benchmark problems available in open literature. Study of Modal analysis by using ANSYS software. Active vibration control of composite beam with different ply orientation configurations under free and forced vibration cases. Page 1

2 IV. PIEZOELECTRIC ANALYSIS Piezoelectric analysis is the coupling of structural and electric fields. Applying a voltage to a piezoelectric material creates a displacement, and vibrating a piezoelectric material generates voltage. Piezoelectric analysis types, available in ANSYS Multiphysics or ANSYS Mechanical products are static, modal, prestressed modal, harmonic, pre-stressed harmonic, and transient. The elements in ANSYS library which support the piezoelectric analysis are listed in table1.1.the key point settings activate the piezoelectric degrees of freedom, displacements and VOLT. For SOLID5, setting KEYOPT(1) = 3 activates the piezoelectric only option. Automatic solution control is not available for a piezoelectric analysis. The SOLCONTROL default settings are only available for a pure structural or pure thermal analysis. For a large deflection piezoelectric analysis, we must use nonlinear solution.[6] V. SOLUTION METHOD Finite Element Modeling is defined here as analyst's choice of material models, finite elements, specific preprocessing and post processing options implemented in ANSYS to perform piezoelectric analysis. The first step in Coupled-Field Finite Element Analysis of a composite beam involves development of a Finite Element model. The model so developed needs to be validated using benchmarks, a set of standard problems for which solutions exist.[7] The sparse direct solver is based on a direct elimination of equations, as opposed to iterative solvers, where the solution is obtained through an iterative process that successively refines an initial guess to a solution that is within an acceptable tolerance of the exact solution. Direct elimination requires the factorisation of an initial very sparse linear system of equations into a lower triangular matrix followed by forward and backward substitution using these triangular systems. The lower triangular matrix factors are typically much larger than the initial assembled sparse matrix, hence the large disk or in-core memory requirements for direct methods. Sparse direct solvers seek to minimize the cost of factorizing the matrix as well as the size of the factor using sophisticated equation reordering strategies. Iterative solvers do not require a matrix factorization and typically iterate towards the solution using series of very sparse matrix-vector multiplications along with a preconditioning step, both of which require less memory and time per iteration. The convergence of iterative methods is not guaranteed and the number of iterations required to reach an acceptable solution may be so large that direct methods are faster in some cases. VI. STATIC ANALYSIS OF SMART COMPOSITE BEAM Finite Element Modeling is defined here as analyst's choice of material models, finite elements, specific preprocessing and post processing options implemented in ANSYS to perform piezoelectric analysis. The first step in Coupled-Field Finite Element Analysis of a composite beam involves development of a Finite Element model. The model so developed needs to be validated using benchmarks, a set of standard problems for which solutions exist. For the present work, a smart cantilever beam consisting of a symmetric laminated epoxyglass composite beam with a piezoelectric actuator mounted on it is considered. Dimensional Parameters a) Composite Beam: Number of Plies n = 4 Ply orientation[45/-45]s Length of Beam L = 1000 mm Width of Beam b = 25 mm Thickness of Beam t 1 = 50 mm Thickness of layer t 2 = 12.5 mm b) PZT Actuator: Length of Actuator B = 25 mm Width of Actuator b = 20 mm Thickness of Actuator t 3 = 0.5 mm Actuator distance from d a = 5mm Fig.1: (a) Cantilever beam with free vibration Fig.1:(b) Top view of Cantilever beam with free vibration Page 2

3 Fig.1:(c) Cantilever beam with forced vibration descretized into 276 elements (mesh size 69 x 4 x 1) and actuator with 20 elements (mesh size 17 x 4 x 1, 34 x 4 x 1, 51 x 4 x 1 ). The material properties given in tables.1 using TBDATA command in ANSYS. The corresponding elements at the interface of beam and actuator are rigidly connected using GLUE option. a) Modal analysis with stacking sequence[45/-45]s The finite element model of the smart cantilever beam is shown in figure.3. All the nodes at the actuator end of the cantilever beam are constrained for displacement along x, y, and z-directions. Stacking sequence is [45/-45]s and gap of actuator is 5mm from fixed end. Fig.2: stacking sequence of composite beam [45/-45]s Figure.2 shows the geometry of the smart cantilever beam. The beam is considered to be made of epoxy-glass composite laminates with symmetric laminates of [45/- 45]s ply orientations. The table.1gives the material properties considered for composite and the actuators respectively. Fig.3.1: Meshed model of composite beam [45/-45]s with actuator Table 1 Material properties for composite beam [8] Material Epoxy-Glass Density 1830 kg/m 3 Young's Modulus in x-direction (Ex) N/m 2 Young's Modulus in y-direction (Ey) N/m 2 Young's Modulus in z-direction (Ez) N/m 2 Shear Modulus in x-y direction (Gxy) N/m 2 Shear Modulus in y-z direction (Gyz) N/m 2 Shear Modulus in z-x direction (Gzx) N/m 2 Poisson's ratio in x-y direction (νxy) 0.22 Poisson's ratio in x-y direction (νyz) 0.11 Poisson's ratio in x-y direction (νzx) 0.22 Fig.3.2 :Modal analysis of composite beam [45/-45]s with actuator VII. DEVELOPMENT OF FINITE ELEMENT MODEL OF SMART COMPOSITE STRUCTURE A smart cantilever beam is modeled using ANSYS software. 8-noded hexahedral layered solid elements (SOLID185) are used to model composite beam and 8- Fig.3.3: with stacking sequence [45/-45]s obtained noded coupled field hexahedral solid elements (SOLID5) deformation is 1.312mm are used to model piezoelectric actuator. The beam is Page 3

4 VIII. Fig.4: composite laminates with symmetric laminates of [0/90]s Above figure shows the geometry of the smart cantilever beam. The beam is considered to be made of epoxy-glass composite laminates with symmetric laminates of [0/90]s ply orientations. Using same material properties as given in Table.1. Different modal analysis is carried out. b) Modal analysis with stacking sequence[0/90]s The finite element model of the smart cantilever beam is shown in figure.5. Stacking sequence is [0/90]s and gap of actuator is 5mm from fixed end. Fig.5.3: Modal analysis of composite beam [0/90]s with actuator VIII. CONCLUSION Following are the conclusions based on the present work. Piezoelectric materials have major role in active vibration control and ANSYS software provides a means for FE modelling of smart structures, coupled field analysis and closed loop control actions can be simulated by integrating control laws into the ANSYS. The composite beam with [0/90]s ply orientation takes shorter settling time than that with [45/-45]s ply-orientation. The control action depends on the ply orientations. Caution needs to be exercised while using higher values of control gains as the actuator voltage may exceed the saturation voltage of the actuator material causing damage to the structure. Fig 5.1: composite laminates with symmetric laminates of [0/90]s Fig.5.2: with stacking sequence [0/90]s obtained deformation is mm REFERENCES [1] D. Hull, An Introduction to Composite Materials. Cambridge: Cambridge University Press, [2] Daniel B. Miracle and Steven L. Donaldson, Air Force Research Laboratory: Introduction to Composites. [3] G. Akhras, 1997 Smart Structures and their Applications in Civil Engineering, Civil Engineering Report, CE97-2, RMC, Kingston, Ontario, Canada, [4] Young Kyukang, Hyun Chul Park, Jaehwn Kim, and Seung-Bok Choi, 2002 Interaction of active and passive vibration control of laminated composite beams with piezoceramic sensors/actuators Materials and Design, Vol. 23, (2002), pp [5] H. Boudaoud, E. M. Daya, S. Belouettar, L. Duigou and M. potier-ferry, (2009) Damping analysis of beams submitted to passive and active control Engineering Structures, Vol. 31, (2009), pp [6] S. Narayanan and V. Balamurugan, 2003 Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors Page 4

5 and actuators Journal of Sound and Vibration, Vol. 262, (2003), pp [7] H. Karagulle, L. Malgaca and H. F. Oktem, 2004 Analysis of active vibration control in smart structures by ANSYS Smart Materials and Structures, Vol. 13, (2004), pp [8] Jose M. SimoesMoita, Isidoro F. P. Correia, Cristovao M. Moto Soares, and Carlos A. MotaSoares, 2004 Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators Computers and Structures, Vol. 82, (2004), pp Authors Biographies 1. Ravicheatan Dharenni- Completed B.E in Mechanical from K.L.E.College Belagavi, Presently pursuing M.Tech in Machine Design from M M Engineering College, Belagavi. 2. Ashok M Hulgabali He completed his Masters degree in Mechanical system from IIT, Kharagpur in 2008 and presently he is pursuing Ph.D at VTU, Belagavi. His areas of interest are Control Engineering, Composite Mechanics, Smart materials. 3. Santoshkumar Malipatil-He Completed Masters degree in Machine Design from M M Engineering College, Belagavi affiliated to VTU Belagavi, his areas of interest are Finite element analysis, Composite Materials, Tribology, and Mechanical Vibration. Page 5