Study on flexural vibration of triangular composite plates influenced by fibre orientation

Two-dimensional orthogonal polynomials for vibration of rectangular composite plates

Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method

Most of the work done for the vibration of composite plates published in the literature is either analytical or numerical studies with few experimental results available on composites with unidirectional fibers. The present study involves extensive experimental works to investigate the free vibration of industry driven woven fiber glass/epoxy composite plates with different boundary conditions including free–free cases. The modern modal testing and subsequent analysis with powerful computer and digital analysis system is an important tool for prediction of behavior of structures. The specimens of woven glass fiber and epoxy matrix composite plates are manufactured by the hand-layup technique. Elastic parameters of the plate are also determined experimentally by tensile testing of specimens using INSTRON 1195. An experimental investigation is carried out using modal analysis technique with Fast Fourier Transform Analyzer, PULSE lab shop, impact hammer and contact accelerometer to obtain the frequency response functions. The computational results are compared with results of previous studies in literature wherever available. The experimental results are also compared with the FEM numerical analysis based on first-order shear deformation theory. The effects of different geometrical parameters including number of layers, aspect ratio, fiber orientation and different boundary conditions of woven fiber composite plates are studied in detail. It is observed that comparisons performed between numerical predictions and experimental tests have a good correlation. The natural frequency is very less for cantilever than simply supported and fully clamped boundary conditions. The prediction of dynamic behavior of laminated composite plates plays a significant role in the future applications of structural composites.

Vibration of arbitrarily-shaped triangular plates with elastically restrained edges

In this paper, a different method, incremental load technique in conjunction with dynamic relaxation (DR) method, is employed to analyze the buckling behavior of composite plates reinforced with functionally graded (FG) distributions of single-walled carbon nanotubes (SWCNTs) along the thickness direction. The properties of carbon-nanotubes reinforced composite (CNTRC) plate were determined through modified rule of mixture. The nonlinear governing relations are obtained incrementally in the form of partial differential equations (PDEs) based on first-order shear deformation theory (FSDT) and Von Karman nonlinear strain. In the proposed method, for finding the critical buckling load, the mechanical loads are applied to the CNTRC plate incrementally so that in each load step the incremental form of PDEs are solved by the DR method combined with the finite difference (FD) discretization technique. Finally, the critical buckling load is determined from the load-displacement curve. In order to verify the accuracy of the present method, the results are compared with those available in the literatures. Finally, a detailed parametric study is carried out and results demonstrate that the change of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, boundary condition and loading condition have pronounced effects on the buckling strength of CNTRC plates. It is seen that for all types of loading, boundary conditions and both cases of with and without presence of elastic foundation the FG-X and FG-O have the highest and lowest values of buckling loads.

Chapter 7 - Vibration Problems of Functionally Graded Triangular Plates

The paper deals with the fully coupled response characteristics of a multilayered composite plate with piezoelectric layers. The response quantities of the plate are coupled by the mechanical field and the electric field. Based on the three-dimensional linear piezoelectricity and the first-order shear deformation theory, the fundamental unknowns, such as the displacements and the electric potential, are assumed to be expandable through the plate thickness coordinate. The governing equations of motion of the plate are presented in terms of the unknown displacement and electrical potential coefficients. When the boundary conditions and electromechanical inputs are specified, the double Fourier series is used to obtain the response of the simply supported multilayered plates. Numerical results for the static and dynamic response of the laminated composite plates with different lamination schemes and having a PIC-151 piezoelectric material layer are obtained. The effects of the plate thinness ratio, plate aspect ratio, lamination scheme, fiber orientations, and piezoelectric coupling on the static and dynamic response are presented.

Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method

A novel experiment-based approach on nonlinear bending analysis of thermoplastic composite laminates

The buckling behavior of laminated composite plates reinforced by carbon nanotubes (CNTs) resting on Winkler–Pasternak elastic foundations under in-plane loads is investigated using reproducing kernel particle method (RKPM) based on first-order shear deformation theory. The minimum potential energy approach is utilized to obtain the governing equations and the stiffness matrices. The single-walled CNTs and poly-co-vinylene are used for the fibers and the matrix, respectively. The carbon nanotube fibers are uniformly distributed in the polymer matrix. The material properties of a carbon nanotube-reinforced composite (CNTRC) plate are estimated through a micromechanical model based on the extended rule of mixture. Full transformation approach is employed to enforce essential boundary conditions. The accuracy and convergency of the RKPM method is established by comparing the obtained results with the available literature. Then, the effects of volume fraction and orientation of CNTs, plate aspect ratio, plate width-to-thickness ratio and the elastic foundation parameters on the critical buckling load are investigated. The obtained results demonstrate that the geometric and mechanical properties and boundary conditions have noticeable effects on the buckling behavior of laminated CNTRC plates.

FREE-VIBRATION ANALYSIS OF RIGHT TRIANGULAR PLATES WITH VARIABLE THICKNESS

Nowadays, shape-memory alloys (SMAs) are used in many applications to improve the mechanical behaviors of the structures. In this paper, the natural vibration and buckling behaviors of the composite sandwich plates reinforced by SMA wires are studied. Three-dimensional (3D) finite element method is employed to model and analyze the sandwich plates. The face sheets of the sandwich plates are considered to be layered orthotropic composite plate, while a soft isotropic material is used for the core. The face sheets are armed by the Ni–Ti-based SMA wires. The Active Property Tuning method is used for modeling the SMA-embedded sandwich plates. The modal and eigenvalue buckling analyses are performed to calculate the natural frequencies and buckling loads of the plates. The effects of plate’s thickness, face sheet’s thickness and plate aspect ratio and also boundary conditions on the natural frequencies and buckling loads of the plates are inspected. Comparison between obtained numerical results and those published in the literature confirms that the present modeling and vibration and buckling analyses of the SMA-reinforced composite sandwich plates are reliable and applicable.

Some recent developments on integrated damping mechanics for unidirectional composites, laminates, and composite structures are reviewed. Simplified damping micromechanics relate the damping of on-axis and off-axis composites to constituent properties, fiber volume ratio, fiber orientation, temperature, and moisture. Laminate and structural damping mechanics for thin composites are summarized. Discrete layer damping mechanics for thick laminates, including the effects of interlaminar shear damping, are developed and semianalytical predictions of modal damping in thick simply supported specialty composite plates are presented. Applications show the advantages of the unified mechanics, and illustrate the effect of fiber volume ratio, fiber orientation, structural geometry, and temperature on the damping. Additional damping properties for composite plates of various laminations, aspect ratios, fiber content, and temperature illustrate the merits and ranges of applicability of each theory (thin or thick laminates).

This study presents a novel approach for optimizing the critical buckling load of the stiffened piezolaminated composite plates using a self-adaptive special relativity search (SASRS) algorithm. The fiber orientations in the layers are considered as design variables. The stability equations are first derived based on the classical laminated plate theory (CLPT) with von Karman nonlinearity. The optimization problem is implemented in MATLAB. The optimization results are obtained to indicate the effecs of various boundary conditions, applied voltages, grid shapes, angles of diagonal ribs, and plate aspect ratios on the optimal design. Numerical investigations are carried out for 10-ply symmetrical stiffened piezolaminated plates. The robustness and efficiency of the proposed SASRS algorithm in maximizing the critical buckling load of the stiffened piezolaminated plates are demonstrated by comparing the optimized results from the standard special relativity search (SRS) algorithm. It is found that the proposed optimization method has better performance than the SRS algorithm.

In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Galerkin method, the nonlinear differential equation of free vibrations of initially stressed composite plate is obtained. This nonlinear equation is solved using two different analytical perturbation methods, namely method of multiple scales (MTS) and homotopy perturbation method (HPM), to analyze the nonlinear vibrations of initially stressed cross-ply composite plates. Effects of tensile and compressive biaxial initial stresses, initial vibration amplitude, thickness, and aspect ratios of the composite plates on the frequency behavior are investigated. The validity of the results is confirmed by making a comparison with those reported in the literature. According to the results, both analytical solutions show increasing trends for natural frequency parameters by increasing normal initial stresses. Regardless of the value of initial biaxial stresses, for both symmetric and non-symmetric plates, the results of MTS and HPM are in close agreement for the smallest initial amplitude. However, for compressive initial stresses, by increasing initial amplitude ratios, the discrepancies between the results of HPM and MTS increase for symmetric and non-symmetric plates. Although HPM includes less computational effort (smaller length of formulation) than MTS, the linear-to-nonlinear frequency ratios obtained using MTS method become closer to those obtained by HPM as initial vibration amplitude is decreased and initial stress is increased.