In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To ve...

We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation sche...

|For crystal resonators, it is always desirable to calculate the electric properties accurately for application purposes. As an extension of the Mindlin plate theory based nite element analysis of crystal resonators, a new theory for the electroded plates is derived and the piezoelectrically forced vibrations are formulated and implemented in this paper in a manner similar to our previous work....

Classical plate buckling theory is obtained systematically as the small-thickness limit of the three-dimensional linear theory of incremental elasticity with null incremental data. Various a priori assumptions associated with classical treatments of plate buckling, including the Kirchhoff–Love hypothesis, are here derived rather than imposed, and the conditions under which they emerge are state...

The Magneto-Electro-Elastic (MEE) material exhibits pyroelectric and pyromagnetic effects under thermal environment. The effects of such pyroelectric and pyromagnetic behavior on vibration, buckling and deflection analysis of partially cracked thin MEE plate is presented and discussed in this paper. The aim of the study is to develop an analytical model for the vibration and geometrically linea...

A brief review is presented of the theory of flexural edge waves, first predicted in 1960 by Yu K. Konenkov using Kirchhoff plate theory. It is demonstrated that the flexural edge wave is also predicted by Mindlin’s plate theory, and that the prediction agrees with measured data. It is noted that the edge wave was erroneously presented as a new type of bending wave solution in a recently publis...

This paper proposes the refined first order shear deformation theory to investigate the free vibration behavior of bidirectional functionally graded porous plates. This theory satisfies the transverse shear stress free conditions at the top and bottom of the plate, thus avoids the need of a shear correction factor. The rule of mixtures is employed to compute the effective material properties an...