In this work we have proposed an improvement in the shape of the V-shaped microcantilever by varying the width profile. In this paper we have studied the variation of resonant frequency as a function of changes in profile determined by the length of the microcantilever, keeping constant the active area for binding. It is observed that for the optimized nonlinear profile the angle at the tip is ...

Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...

The article touches upon the problem of natural oscillations a thin elastic wavy shell an open profile. proposed method for determining numerical values lowest frequencies and corresponding forms shells complicated shape is based on Rayleigh-Ritz energy method.
 results calculation this with hinge-fixed attachment along lower contour generatrix are presented.

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane...

This paper considers in general the problem of finding the minimum of a given functional f(u) over a set B by approximately minimizing a sequence of functionals /„(«„) over a "discretized" set B„; theorems are given proving the convergence of the approximating points un in Bn to the desired point u in B. Applications are given to the Rayleigh-Ritz method, regularization, Chebyshev solution of d...

In the present study, a vibration analysis of functionally graded rectangular nano-/microplates was considered based on modified nonlinear coupled stress exponential and trigonometric shear deformation plate theories. Modified coupled stress theory is a non-classical continuum mechanics theory. In this theory, a material-length scale parameter is applied to account for the effect of nanostructu...

This paper is concerned with the reduction of the spectral problem for symmetric linear operator pencils to a spectral problem for the single operator. Also, a Rayleigh–Ritz–like bounds on eigenvalues of linear operator pencils are obtained.