Large amplitude free vibration Analysis of composite plates by finite element method

Abstract

Most of the structural components are generally subjected to dynamic loadings in their working life. Very often these components may have to perform in severe dynamic environment where in the maximum damage results from the resonant vibrations. Susceptibility to fracture of materials due to vibration is determined from stress and frequency. Maximum amplitude of the vibration must be in the limited for the safety of the structure. Hence vibration analysis has become very important in designing a structure to know in advance its response and to take necessary steps to control the structural vibrations and its amplitudes.
The non-linear or large amplitude vibration of plates has received considerable attention in recent years because of the great importance and interest attached to the structures of low flexural rigidity. These easily deformable structures vibrate at large amplitudes. The solution obtained based on the lineage models provide no more than a first approximation to the actual solutions. The increasing demand for more realistic models to predict the responses of elastic bodies combined with the availability of super computational facilities have enabled researchers to abandon the linear theories in favor of non-linear methods of solutions.
In the present investigation, large amplitude free vibration analyses of composite Mindlin’s plates have been carried out using a C0 eight noded Langragian element by finite element method. The formulation is based on “First order shear deformation theory”. The large deformation effect on plate structures has been taken care by the dynamic version of von Karman’s field equation. The effects of variations in the Poisson’s ratio, amplitude ratio, thickness parameter & plate aspect ratio on the non-linear frequency ratio has also been included in the research.
Chapter 1 includes the general introduction and the scope of present investigation. The review of literature confining to the scope of the study has been presented in the Chapter 2. The general methods of analysis of the laminated composite plates have been briefly addressed in this chapter. The chapter 3 presents some information about the theoretical background of finite element method and composite materials. The Chapter 4 comprises the mathematical formulation of the finite elements. The elastic stiffness and the mass matrices for the plate element have been formulated. The boundary conditions have been implemented by eliminating the constrained degrees of freedom from the global stiffness matrix. The Chapter 5 briefly describes the computer program implementation of the theoretical formulation presented in Chapter 4. The different functions and the associated variables which have been used in writing the codes in MATLAB have been presented in brief. A few numbers of flow-chart of the computer program has been illustrated. Several numerical examples which include “large amplitude free vibration analysis” have been presented in the Chapter 6 to validate the formulation of the proposed method. The Chapter 7 sums up and concludes the present investigation. An account of possible scope of extension to the present study has been appended to the concluding remarks. Some important publications and books referred during the present investigation have been listed in the References section.