Flexural Vibration Characteristics of Initially Stressed Composite Plates

The influence of localised in-plane load on the flexural vibration characteristics of isotropic and composite plates have been studied using a four-noded shear flexible high precision plate bending finite element. First, the critical buckling loads of such plates subjected to partial or concentrated compressive loads were calculated, then the linear and nonlinear flexural vibration frequencies were obtained. Limited parametric study was carried out to study the influences of location and distribution of tensile or compressive in-plane load on the vibration frequencies of such plates.Defence Science Journal, 2010, 60(1), pp.106-111, DOI:http://dx.doi.org/10.14429/dsj.60.11

Nonlinear free vibration analysis of the functionally graded beams

Nonlinear natural oscillations of beams made from functionally graded material (FGM) are studied in this paper. The equation of motion is derived according to the EulerBernoulli beam theory and von Karman geometric nonlinearity. Subsequently, Galerkin’s solution technique is applied to obtain the corresponding ordinary differential equation (ODE) for the FGM beam. This equation represents a kind of a nonlinear ODE containing quadratic and cubic nonlinear terms. This nonlinear equation is then solved by means of three efficient approaches. Homotopy perturbation method is applied at the first stage and the corresponding frequency-amplitude relationship is obtained. Frequency-amplitude formulation and Harmonic balance method are then employed and the consequent frequency responses are determined. In addition, Parameter Expansion Method is utilized for evaluating the nonlinear vibration of the system. A parametric study is then conducted to evaluate the influence of the geometrical and mechanical properties of the FGM beam on its frequency responses. Different types of material properties and boundary conditions are taken into account and frequency responses of the system are evaluated for different gradient indexes. The frequency ratio (nonlinear to linear natural frequency) is obtained in terms of the initial amplitude and compared for different materials and end conditions

Exact 3D solution for static and damped harmonic response of simply supported general laminates

The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes. Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes. The damped harmonic response of a non symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [-15/15], [0/30/0] and [-10/0/40] laminates are studied for various length-to-thickness ratios

Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks

In this paper a novel device aimed at controlling the mechanical vibrations of plates by means of a set of electrically-interconnected piezoelectric actuators is described. The actuators are embedded uniformly in the plate wherein they connect every node of an electric network to ground, thus playing the two-fold role of capacitive element in the electric network and of couple suppliers. A mathematical model is introduced to describe the propagation of electro-mechanical waves in the device; its validity is restricted to the case of wave-forms with wave-length greater than the dimension of the piezoelectric actuators used. A self-resonance criterion is established which assures the possibility of electro-mechanical energy exchange. Finally the problem of vibration control in simply supported and clamped plates is addressed; the optimal net-impedance is determined. The results indicate that the proposed device can improve the performances of piezoelectric actuationComment: 22 page

Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness

AbstractThe present work deals with geometrically non-linear post-buckling load–deflection behavior of functionally graded material (FGM) Timoshenko beam under in-plane thermal loading. Thermal loading is applied by providing non-uniform temperature rise across the beam thickness at steady-state condition. FGM is modeled by considering continuous distribution of metal and ceramic constituents across the thickness using power law variation of volume fraction. The effect of geometric non-linearity at large post-buckled configuration is incorporated using von Kármán type non-linear strain–displacement relationship. The governing equations are obtained using the minimum potential energy principle. The system of non-linear algebraic equations is solved using Broyden’s algorithm. Four different FGMs are considered. A comparative study for post-buckling load–deflection behavior in non-dimensional form is presented for different volume fraction exponents and also for different FGMs, each for different length–thickness ratios

Finite Element Model of Imperfect Plate in Thermal Environment

In this paper a finite element model for thermal buckling of imperfect plates using Layer Wise (LW) plate mode [1] is presented. The model assumes layerwise variation of in-plane displacements and constant transverse displacement through the thickness of the plate, non-linear strain-displacement relations (in von Karman sense) and linear thermo mechanical material properties. The Koiter model for imperfection is adopted. The Principle of virtual displacements (PVD) is used to derive the weak form of linearized buckling problem. The weak form is discretized using Lagrangian nine-node isoparametric finite element. The original MATLAB program is coded for finite element solution. The effects of imperfection amplitude, imperfection form and plate aspect ratio a/h on critical temperature are analyzed. The accuracy of the numerical model is verified by comparison with the available results from the literature

Finite Element Model of Imperfect Plate in Thermal Environment

In this paper a finite element model for thermal buckling of imperfect plates using Layer Wise (LW) plate mode [1] is presented. The model assumes layerwise variation of in-plane displacements and constant transverse displacement through the thickness of the plate, non-linear strain-displacement relations (in von Karman sense) and linear thermo mechanical material properties. The Koiter model for imperfection is adopted. The Principle of virtual displacements (PVD) is used to derive the weak form of linearized buckling problem. The weak form is discretized using Lagrangian nine-node isoparametric finite element. The original MATLAB program is coded for finite element solution. The effects of imperfection amplitude, imperfection form and plate aspect ratio a/h on critical temperature are analyzed. The accuracy of the numerical model is verified by comparison with the available results from the literature