Finite difference method is used to calculate the via-plate capacitances for vias with pad. Due to the symmetric structure, the solving domain is reduced to a rectangular ρ − z region. Boundary conditions along the region are discussed. Both barrel-plate and pad-plate capacitances are studied with various geometric parameters. The results could be used as validations for possible analytical exp...

Piezoelectric materials can be used as actuators for the active vibration control of smart structural systems. In this work, piezoelectric patches are surface bonded to a composite laminate plate and used as vibration actuators. A static analysis based on the piezoelectricity and elasticity is conducted to evaluate the loads induced by the piezoelectric actuators to the host structure. The load...

In this study, the analysis of transverse vibrations of rectangular plate with circular central hole with different boundary conditions is studied and the natural frequencies and natural modes of a rectangular plate with circular hole have been obtained. To solve the problem, it is necessary to use both Cartesian and polar coordinate system. The complexity of the method is to apply an appropria...

In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension (m,n ≥ 1) is proposed in a canonical fashion, which includes the (2m−1)-th Hermite interpolation element (n = 1), the n-linear finite element (m = 1) and the Adini element (m = 2). A nonconforming triangular finite element for the plate bending problem, with convergent order O(h)...

The a posteriori error analysis of conforming finite element discretisations of the biharmonic problem for plates is well established, but nonconforming discretisations are more easy to implement in practice. The a posteriori error analysis for the Morley plate element appears very particular because two edge contributions from an integration by parts vanish simultaneously. This miracle does no...

The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy-Na'dai approach and the mixed boundary equation at the...

Spring constant calibration of the atomic force microscope (AFM) cantilever is of fundamental importance for quantifying the force between the AFM cantilever tip and the sample. The calibration within the framework of thin plate theory undoubtedly has a higher accuracy and broader scope than that within the well-established beam theory. However, thin plate theory-based accurate analytic determi...

This study concerns the dynamic characteristics of a prestressed isotropic, rectangular plate continuously supported by an elastic foundation and carrying accelerating mass M. Closed form solutions of the governing fourth order partial differential equations with variable and singular coefficients are presented. For the twodimensional plate problem, the solution techniques is based on the doubl...