Response Of Rectangular Plates Research Articles

Analytical solution for thermal buckling analysis of rectangular plates with functionally graded coatings

In this paper, an analytical solution is developed to investigate the thermal buckling behavior of the imperfect rectangular plates with functionally graded (FG) coatings under uniform temperature rise. Material properties of the FG coatings are assumed to be temperature-dependent and to continuously vary in the thickness direction using the power law distribution of volume fraction of metal and ceramic. Theoretical formulations are based on the classical plate theory with von-Karman nonlinear kinematic relations. The initial geometrical imperfections of plates are also accounted. By using the Galerkin method and the Airy stress function, the resulting equations are solved to obtain the closed form expressions for nonlinear equilibrium paths. Effects of power law index, imperfection, geometric parameters, and temperature distributions on the response of rectangular plates with FG coatings are discussed in details.

Application of Spline Element and State-Space Approach to Dynamic Analysis

Application of spline element and state-space approach in analyzing dynamic response of rectangular plates is presented in this paper. The proposed method is on the basis of state-space theory of control systems and spline element interpolation procedure to take advantage of both the time domain and the space domain analysis methods. A state-space recursive scheme is developed for analyzing the dynamic response, such as displacement and internal forces in the structure. The application of the proposed method is demonstrated by two numerical examples.

Fundamental thermo-elasticity equations for thermally induced flexural vibration problems for inhomogeneous plates and thermo-elastic dynamical responses to a sinusoidally varying surface temperature

Equations of motion governing thermally induced vibration of plates with inhomogeneous material properties through the thickness direction are presented. Equations of motion for thermally induced flexural vibration for inhomogeneous rectangular plates in which the material properties are given in the form of a power of the thickness coordinate are derived from the above-mentioned fundamental equations. An exact solution of the one-dimensional temperature change is presented for an inhomogeneous plate in which one surface is exposed to a sinusoidally varying temperature, and the other is kept at zero temperature change. The associated quasi-static and dynamic solutions pertinent to deflection and thermal stresses in the inhomogeneous rectangular plate are derived under the condition of simply supported edges. Numerical calculations are performed, and the effects of material inhomogeneity such as Young’s modulus, coefficient of linear thermal expansion, and mass density, angular frequency in cyclic heating, and aspect ratio on the thermo-elastic response of the rectangular plate are shown in graphical form. Comparing the dynamic solutions with quasi-static ones, the effect of inertia on the thermo-elastic response of the inhomogeneous rectangular plate is evaluated.

Vibro-acoustic response of convected fluid loaded plates

This work demonstrates the effects that fluid convection has on the vibro-acoustic response of rectangular plates. The effects of fluid flow on the vibration and stability of plates is reasonably well understood. These effects include dramatic structural modal coupling along with static and dynamic instabilities. However, the resulting effect on sound radiation is not so well understood. The presentation will include a description of the fundamental physics associated with a simply supported, vibrating, rectangular plate in an infinite baffle and radiating into a semi-infinite, convected fluid. Then, simulation results will demonstrate the effects of flow-induced modal coupling and acoustic radiation. It will be demonstrated that convection can significantly increase the radiated sound power and dramatically affect the vibro-acoustic response.

A Theoretical Analysis on the Deformation of Rectangular Plate Under Out-of-Plane Tearing

A theoretical analysis is proposed to predict the out-of-plane tearing response of rectangular plates with two or three legs. The nonlinear differentiate equation for deformation and the double linear strain-hardening constitutive relation for bending moment against curvature are used in the analysis. The external work is assumed dissipated through the bending deformation of the legs and the crack propagation at the tip of the crack between the legs. A good agreement has been achieved between the theoretical predictions and the experimental results for the variation of external force with displacement. It has been found that the variation of bending force with displacement significantly depends on the strain-hardening modulus and the tearing force.

Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method

In this paper the Fourier series method is introduced to obtain the solution for the displacement response of rectangular plates subjected to a blast loading. Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of deflection history and stress resultants which uses one perturbation term sufficiently correlated with results coming from both related literature as well as the finite element method.

Dynamic response of rectangular plates under drop mass impact

A theoretical analysis is presented which examines the dynamic response of thin rectangular plates struck transversely by a wedge. The analysis employs a pure membrane model with two traveling hinge phases. Material strain rate sensitive effects are considered with the aid of the Cowper-Symonds equation and the Perrone and Bhadra's approximation. A new phenomenon called effective area ratio has been found for relatively narrow plates. The displacement produced by traveling hinge phases is significant and dominant for high speed impact. Good agreement between the theoretical predictions and the experimental results has been obtained on the maximum permanent deflections for various impact energies.

Influence of the Aspect Ratio on the Dynamic Stability and Nonlinear Response of Rectangular Plates

The dynamic stability and nonlinear response of simply-supported rectangular plates subjected to parametric excitation are investigated. The large-deflection plate theory used in the analysis is derived in terms of the stress function F and lateral displacement w and is applied to rectangular plates with stress-free supported edges and uniformly stressed loaded edges. General rectangular plates are considered, the aspect ratio of the plate being regarded as an additional parameter of the system. Calculations are carried out for rectangular plates of various aspect ratios, and the relative importance of the principal regions of parametric instability associated with the lower mode shapes is clarified. The stationary response of the system within a principal region of instability is also evaluated. The results obtained indicate that the aspect ratio plays a crucial role in determining the stability of rectangular plates; elongated plates are more susceptible to various parametric resonances than square plates.

Inelastic Dynamic Response of Rectangular Plates by Finite Elements

Inelastic Dynamic Response of Rectangular Plates by Finite Elements

Response of rectangular thick plates to moving single loads

The response of a rectangular plate to a moving load is investigated. An improved plate theory which includes the effects of shear deformation and rotatory inertia as well as normal stress to the plate surface is introduced and the equation of motion in terms of single displacement is derived. Solutions are obtained by applying Fourier transforms. The effects of the approximation methods of the plate theory on the response of the displacement and the stress couples are examined with regard to the load velocity, plate dimensions, etc., in addition to the comparison with the results due to the classical plate theory.

Response of rectangular plates with edges possessing different degrees of elastic rotational restraints, in harmonic excitation

The response of thin elastic plates having edges elastically restrained in rotation to different degrees and subjected to sinusoidal excitation has been investigated. The displacement and bending moment amplitudes have been determined for plates having different aspect ratios, rotational restraints at supports and frequency values. Comparison with available results indicated good accuracy. The formulation is based on a simple numerical procedure.

Dynamic Shear Response of Rectangular Plates with Initial Imperfections

The paper presents an analysis of the elastic response of a simply supported, imperfect, rectangular plate subjected to an in-plane supercritical shear force, suddenly applied at one of the edges in the form of a square pulse. The influence of the initial plate irregularities on the overall response during both loading and postloading period is investigated. The averaged in-plane inertia forces are taken into account. The analysis is an extension of the studies of the response to in-plane normal forces of plates of infinite width and finite length given in [1], and of a finite plate given in [2]. The results indicate that the frequency spectra of free vibrations during the post-loading regime are controlled by the initial irregularities distribution, plate geometry and the load levels.