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...

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...

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.

The Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR method) finds the eigenvalues in a certain domain of the complex plane of large quadratic eigenvalue problems (QEPs). The SS-RR method can suffer from numerical instability when the coefficient matrices of the projected QEP vary widely in norm. To improve the numerical stability of the SS-RR method, we combine it with a numerically...