IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 01, 2015 | ISSN (online): 2321-0613 All rights reserved by www.ijsrd.com 546 Free Vibration Analysis of Composite Laminate for Different Simply Supported Boundary Condition Deepesh Bhavsar 1 1 Assistant Professor 1 Department of Mechanical Engineering 1 AISECT University Bhopal, Village Mendua - 464993, India Abstract— This paper analyzed free vibration characteristics of Rectangular Composite laminate Plate for different boundary conditions. The analysis is performed using ANSYS APDL software package, in which SHELL element is used. The effects of Aspect ratios, Side-to-Thickness ratios and Modulus ratios on the plate vibration for different boundary condition are studied in this investigation and the first five frequencies mode shapes are studied. It is found from analysis that the natural frequencies of composite plate increases with increasing the constraint on the edges of plate. This work investigated the effects of four types of edge conditions such as a combination of simply supported, clamped and free boundaries condition like as SSSS, SSSF, SFSF and CFSF. 2D graphs used effectively for comparing various conditions. The results compared with available literatures and found that ANSYS is a good tool in the hand of a design engineer. Key words: Free Vibration analysis; CFRP; Modal Analysis; Finite element method; ANSYS I. INTRODUCTION Composite materials are defined as a material composed of two or more constitutes combined on a macroscopic scale by mechanical and chemical bonding. But that constitute of composite material retain their identities in composite. Due to their high specific modulus, high strength to weight ratio, excellent fatigue and corrosion resistance have made it more useful in aerospace, marine and civil infrastructure. The composite materials are more important as compare to the other materials due to their some superior properties. But some failures occur by de-lamination and vibration. Therefore natural vibration and stability problems are attracted the attention of many researchers for analysis the behaviour of composite laminated plates. In order to optimally design a composite plate, the no. of layers and plies necessary as identified by their angles of fibre orientation must be decided upon, as well as their require thickness for a specified loads carrying capacity. Laminated composite materials are usually fabricated from unidirectional plies of given thickness and with fibre orientations limited to a small set of angles e.g., 0°, 45°, - 45° and 90° [1-5]. To avoid the resonant behaviours of a composite laminated structures. The results of the free vibration analysis for laminated composite structure in structural design are very important. The free vibration analysis of composite laminated right triangular plates is analyzed based on Mindlin plate theory by using the finite element method [6]. He studied the effects of the fibre orientation, boundary conditions, material properties, and side to thickness ratio b/h on the vibration frequencies. To make the structure more flexible and economically viable, the use of composite materials has been introduce in order to decrease the weight. But still the effect due to vibration could not be minimised to satisfactory level and if it was done by any way i.e. compromising the flexibility of structure. In this context different numerical methods are used depending on the suitability of the problems. Unfortunately practical plates problems are quit complex due to it arbitrary geometry, loading and boundary condition. In this work the initiation has been taken to carry on analysis of free vibration rectangular plates by FEM tool ANSYS and result has been validated with the literature available. In this paper, therefore, a plate FEM formulation and problem modelled in ANSYS platform are provided with emphasis on the terms related to the stiffness and mass matrices. Then a set of results are presented to show the applicability of the present vibration analysis for different 4- Boundary conditions like as SSSS, SSSF, SFSF and CFSF, lamination parameters and the effect of side-to-thickness ratios, aspect ratios and modulus ratios on the natural frequency of vibration are studied. II. MATHEMATICAL FORMULAS AND MATERIALS DETAILS A. Finite Element Formulation: The equation of motion for free vibration of a laminated composite plate subjected to generalized in-plane may be expressed in matrix form as [[] []]{} 1) Element Stiffness Matrix [] ∫ ∫ [] [][]|| Where [B] is called the strain displacement matrix 2) Element Mass Matrix [] ∫ ∫ [] [][]|| B. Materials and Modelling: The plate material used in the present investigation is carbon fibre reinforced plastic (CFRP). The length and width of the plate are 250mm and thickness of the plate is 2.5mm. The 8- ply symmetric laminated composite plate, whose ply orientation is designed as [90°/-45°/45°/0°] s . The material properties of CFRP [AS1/3501-6] are presented in tables 1: Material [AS1/3501-6] properties (carbon/epoxy) E 1 (GPa) E 2 (GPa) G 12 (GPa) G 23 (GPa) μ 12 ρ(kg/m³) 128 11 4.48 1.53 0.25 1500 Table 2: Plate Material The model is developing using a shell-99 element in ANSYS. The natural frequency and Mode Shapes are obtained by Modal Analysis. The element type used is Shell-99 which 8-noded with 6-degrees of degrees of freedoms at each node. This element is designed to model thin to moderately thick plate & Shell structure with a side