Narrow Results

This study examined the free vibration of a three-layered annular microplate, whose core and face sheets are composed of functionally graded saturated porous (FGSP) materials and functionally graded-graphene platelet-reinforced composites (FG-GPLRC), respectively. The microplate is supported by an elastic base, with the mechanical characteristics of all layers varying along the thickness direction. Employing the extended dynamic formulation of Hamilton’s principle, the equations of motion and boundary conditions are derived from the modified version of couple stress and first-order shear deformation theories, subsequently solved using the generalized differential quadrature method as an effective numerical approach. The study examines the impact of many parameters, including pore distributions, porosity coefficient, pore compressibility, dispersion patterns of graphene platelets, elastic foundation, small-scale parameter, and microplate aspect ratio. The results of this study may be beneficial for the construction of lightweight and sophisticated buildings.

In this work the exact axisymmetric vibration frequencies of circular and annular variable thickness plates are found. The solution is obtained using the exact element method developed earlier. It allows for the exact solution of problems with general polynomial variation in thickness using infinite power series. The solution is exact up to the accuracy of the computer. The natural frequencies of vibration are found as the solutions of the frequency equation. Normalized values for the natural frequencies are given for linear, parabolic and cubic variations of the plate thickness, for circular and annular plates, with four types of boundary conditions on the inner and outer boundaries.

This paper is concerned with the plastic buckling of moderately thick annular plates under a uniform compressive stress state. The analysis is based on the incremental theory of plasticity which employs the Prandtl–Reuss equations and the plate material is assumed to obey the Ramberg–Osgood stress–strain relation. The effect of transverse shear deformation is taken into consideration by adopting the Mindlin plate theory. The governing differential equations for the plastic buckling problem are solved analytically and the plastic buckling stress factors for annular plates with the allowance of transverse shear deformation are presented for the first time. The influences of the boundary conditions, thickness to outer radius ratios, and inner to outer radius ratios on the buckling stress factors are also examined.

This article deals with the free axisymmetric vibration of two-directional functionally graded annular plates. Ceramic and metal are considered two constituents of the functionally graded material (FGM), which are graded through thickness and radial directions of the plate. The Chebyshev collocation technique and differential quadrature method are employed to derive the frequency equations for an annular plate with both edges clamped and another one with both edges simply supported. The results for nonhomogeneous isotropic annular plates are also presented. The accuracy and efficiency of the present approach are confirmed through comparison of the frequencies obtained for homogeneous isotropic annular plates. Identical results are obtained for the two methods used. The effects of volume fraction index, coefficient of radial variation, exponent of power law, inner to outer radii ratio, and boundary conditions are discussed on the first three natural frequencies. It is found that the frequency of a functionally graded annular plate is greater than that of a homogeneous annular plate.

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.