This paper presents a study on nonlinear asymmetric vibrations in shallow spherical caps under pressure loading. The Novozhilov’s shell theory is used for modeling the structural strains. A reduced-order model developed through Rayleigh–Ritz method and Lagrange equations. equations of motion are numerically integrated using an implicit solver. bifurcation scenario addressed by varying external ...

The radiation impedance is an essential parameter in analyzing the vibroacoustic response of planar source. In order to calculate acoustic rectangular plate with arbitrary boundary conditions, a unified approximate approach proposed this study. displacement function expressed form supplemented two-dimensional Fourier cosine series, which can be solved by Rayleigh–Ritz method. radiated field fro...

In this article, authors dealt with general solution of differential equation orthotropic rectangular plate clamped boundary conditions under bi-parabolic temperature variations. Rayleigh Ritz technique is adopted to solve the resultant and evaluate frequencies for first four modes vibration. The effect circular thickness density on are analyzed which not done yet. objective study optimize freq...

Aggressive early deflation has proven to significantly enhance the convergence of the QR algorithm for computing the eigenvalues of a nonsymmetric matrix. One purpose of this paper is to point out that this deflation strategy is equivalent to extracting converged Ritz vectors from certain Krylov subspaces. As a special case, the single-shift QR algorithm enhanced with aggressive early deflation...

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh-Ritz method, is introduced. Asymptotic properties of ...

Mechanics of tympanic membrane (TM) is crucial for investigating the acoustic transmission through the ear. In this study, we studied the wrinkling behavior of tympanic membrane when it is exposed to mismatched air pressure between the ambient and the middle ear. The Rayleigh-Ritz method is adopted to analyze the critical wrinkling pressure and the fundamental eigenmode. An approximate analytic...

We consider a parallel method for solving generalized eigenvalue problems that arise from large-scale molecular orbital computations. We use a moment-based method that finds several eigenvalues and their corresponding eigenvectors in a given domain, which is suitable for master-worker type parallel programming models. We also show the efficiency of the Rayleigh-Ritz procedure for improving the ...