For application of porous and granular materials to vibro-acoustic controls, a finite dynamic strength of the solid component (frame) is an important design factor. The primary goal of this study was to investigate structural vibration damping through this frame wave propagation for various poroelastic materials. A measurement method to investigate the vibration characteristics of the frame was...

The Rayleigh–Ritz method is widely used for eigenvalue approximation. Given a matrix X with columns that form an orthonormal basis for a subspace X , and a Hermitian matrix A, the eigenvalues of XHAX are called Ritz values of A with respect to X . If the subspace X is A-invariant, then the Ritz values are some of the eigenvalues of A. If the A-invariant subspace X is perturbed to give rise to a...

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...

Abstract Based on the Rayleigh-Ritz method, transverse vibration characteristics of a rectangular plate with an arbitrarily shaped inner opening are investigated. A modified two-dimensional Fourier series was chosen as trial function and springs different stiffnesses were used to equate arbitrary boundary conditions plate. The Lagrange generalization open is obtained by equating area special fi...

We study the band structure of semiconductor nanowires with quantum dots embedded in them. The is calculated using Rayleigh–Ritz variational method. consider two different types, one type defined by electrostatic potentials applied to nanowire, while other adding materials offsets respect parameters nanowire. are particularly interested appearance discrete energy levels gap between conduction a...

Microfabrication limitations are of concern especially for suspended Micro-Electro-Mechanical-Systems (MEMS) microstructures such as cantilevers. The static anddynamic qualities of such microscale devices are directly related to the invariant and variantproperties of the microsystem. Among the invariant properties, microfabrication limitationscan be quantified only after the fabrication of the ...

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...