Parametric Instability of Woven Fiber Composite Plates

Abstract

Composites have increasing applications in aerospace, civil, automobile and marine engineering. Structural components are often subjected to in-plane periodic loads which may lead to parametric instability, due to certain combinations of the applied in-plane forcing parameters and natural frequency of transverse vibrations. This phenomenon is called parametric
instability or parametric resonance and is often studied in the spectrum of natural frequency and buckling load of structures. The present study deals with free vibration, buckling and parametric instability behavior of industry driven laminated woven fiber composite plates under harmonic in-plane periodic loads. In this analysis, the effects of various parameters such as increase in number of layers, aspect ratios, side-to thickness ratios, ply-orientations, and increase in static load factors, lamination angle and the degree of orthotropic are studied. The study is experimental but also includes numerical analysis using finite element method (FEM). A simple laminated plate model based on first order shear deformation theory (FSDT) is
developed for the free vibration, buckling and parametric instability effects of composite plates subjected to in-plane loading. The principal instability regions are obtained using Bolotin’s approach employing finite element method (FEM). An eight-node isoparametric quadratic element is employed in the present analysis with five degree of freedom per node considering the effects of transverse shear deformation and rotary inertia. The elastic stiffness matrix, geometric stiffness matrix and mass matrix of the element are derived using the principle of minimum potential energy. They are evaluated using the Gauss quadrature numerical integration technique. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. The composite plates of different layers with different dimension are manufactured using woven glass fiber and epoxy matrices. The experiments are performed for vibration and buckling (both static and dynamic approach) on the industry driven woven fiber Glass/Epoxy plates after tensile testing, used for characterization. Free vibration characteristics are studied using FFT analyzer, accelerometer using impact hammer excitation. The FRFs are studied to obtain a clear understanding of the vibration characteristics of the
specimens. The buckling loads of specimen are found by both static and dynamic approach. Finally, parametric instability experiment is conducted and the effects of increase in static load factor on excitation frequency are studied. Dynamic instability regions (DIR) are plotted for different plate specimens, applying both static and dynamic loading numerically. The numerical and experimental result shows that the natural frequency is the least for cantilever
and highest for fully clamped boundary conditions. Comparisons between experimental and FEM results are much better for the free-free and cantilever boundary conditions than other boundary conditions. The different fiber orientation angle affects the buckling load. When ply
orientation is increased from 0 0 to 45 0 fiber orientation angles, then the buckling load values are observed to decrease in both experimental method and FEM. So the composite plate with [0]8 layup shows highest buckling load and with [45/-45]2s layup had lowest buckling load. The
critical/buckling loads reduce significantly depending upon the side-to-thickness ratios and aspect ratios. It is observed that with the increase of static load factor from 0 to 0.8, the excitation frequencies decrease both numerically and experimentally. The excitation frequencies decrease with increase in lamination angle due to reduction of stiffness and strength of laminated plates. The onset of instability, the width of instability region and its strength are highly dependent on lamination angle. The greater the lamination angle the smaller is the width of instability region for this geometry and material properties. From the above studies, it can be concluded that the parametric instability behavior of woven fiber composite plates is greatly influenced by different parameters such as number of layers, aspect ratios, side-to thickness ratios, ply-orientations, increase in static load factors and dynamic load factors. So, designer has to be cautious while dealing with structures subjected to dynamic loading. This can be used to the advantage of tailoring during design of composite structures. The thesis is presented in six chapters. Chapter 1 deals with the general introduction and
importance of the present structural stability studies. In chapter 2, a detailed review of the literature pertinent to the previous works done in this field is listed. A critical discussion of the earlier studies is done. The aim and scope of the present study is also outlined in this chapter. In chapter 3, a description of the theory and formulation of the problem and the finite element procedure used to analyze the vibration, buckling and parametric instability characteristics of laminated composite panels and it is explained in detail. The computer program based on MATLAB environment used to implement the formulation is also briefly described. In chapter 4, all the experimental work related to fabrication of laminated industry driven woven fiber composite plates, their material constants determination and free vibration test, buckling test and
parametric instability test set up and test procedure are well documented. In chapter 5, the results of experimental investigation obtained in the study are presented in detail. The effects of various parameters like lamination sequence, ply orientation, degree of orthotropy, aspect ratio,
width to thickness ratio and in-plane load parameters on the vibration, buckling and dynamic instability regions is investigated. The studies have been done separately. Finally, in chapter 6, the conclusions drawn from the above studies are described. There is also a brief note on the
scope for further study in this field. At the end, some important publications and books referred during the present investigation have been listed in Bibliography section.