In the present study, buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study made functionally graded materials longitudinal direction and varies continuously throughout axial direction. Bernoulli–Euler beam theory conjunction modified strain gradient are employed to model structure by considering size effect. Rayleigh–R...

We consider a parallel method for solving generalized eigenvalue problems that arise from molecular orbital calculation of the biochemistry application. Our focus is to develop scalable parallel implementations of the method that achieves high performance on multi-core clusters. In a Rayleigh-Ritz type method using a contour integral (CIRR method), the computation at each contour involves linea...

The finite temperature effective potential of the Abelian Higgs Model is studied using the self-consistent composite operator method, which can be used to sum up the contributions of daisy and superdaisy diagrams. The effect of the momentum dependence of the effective masses is estimated by using a Rayleigh-Ritz variational approximation.

Microvibrations at frequencies between 1 and 1000 Hz generated by on-board equipment can propagate through a satellite's structure and hence signiicantly reduce the performance of sensitive payloads. This paper describes a Lagrange-Rayleigh-Ritz method for developing models suitable for the design of active control schemes. Here Loop Transfer Recovery based controller design methods are employe...

We present some new error estimates for the eigenvalues and eigenfunctions obtained by the Rayleigh-Ritz method, the common variational method to solve eigenproblems. The errors are bounded in terms of the error of the best approximation of the eigenfunction under consideration by functions in the ansatz space. In contrast to the classical theory, the approximation error of eigenfunctions other...

In the present paper, the free vibration of moderately thick trapezoidal plates has been studied. The analysis is based on the Mindlin shear deformation theory. The solutions are determined using the pb-2 Rayleigh-Ritz method. The transverse displacement and the rotations of the plate are approximated by Ritz functions defined as two dimensional polynomials of the trapezoidal domain variables a...