In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To ve...

In this study, the free vibration of partially fluid-filled laminated composite circular cylindrical shell with arbitrary boundary conditions has been investigated by using Rayleigh-Ritz method. The analysis has been carried out with strain-displacement relations based on Love’s thin shell theory and the contained fluid is assumed irrotational, incompressible and inviscid. After determining the...

This paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. Previous studies on the solution of triangular plates with different boundary conditions are mostly based on the Rayleigh-Ritz principle which is performed in the Cartesian coordinates. Consequently, manipulation of the geometry and numerical calculation of the int...

The open profile thin elastic wavy shell natural oscillations problem is considered. proposed method for determining the numerical values of lowest frequencies and corresponding forms vibrations shells with a complicated shape based on Rayleigh-Ritz energy method. results calculation rigidly pinched lower contour are presented.

Global projection methods have been used for solving numerous large matrix equations, but nothing has been known on if and how a global projection method can be proposed for solving large eigenproblems. In this paper, based on the global Arnoldi process that generates an Forthonormal basis of a matrix Krylov subspace, a global Arnold method is proposed for large eigenproblems. It computes certa...

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...

The harmonic Arnoldi method can be used to compute some eigenpairs of a large matrix, and it is more suitable for finding interior eigenpairs. However, the harmonic Ritz vectors obtained by the method may converge erratically and may even fail to converge, so that resulting algorithms may not perform well. To improve convergence, a refined harmonic Arnoldi method is proposed that replaces the h...

We investigate the generalized second-order Arnoldi (GSOAR) method, a generalization of the SOAR method proposed by Bai and Su [SIAM J. Matrix Anal. Appl., 26 (2005): 640–659.], and the Refined GSOAR (RGSOAR) method for the quadratic eigenvalue problem (QEP). The two methods use the GSOAR procedure to generate an orthonormal basis of a given generalized second-order Krylov subspace, and with su...