In this paper, the Ritz method has been employed to analyze the free in-plane vibration of heterogeneous (non-uniform) rectangular nanoplates corresponding to Eringen’s nonlocal elasticity theory. The non-uniformity is taken into account using combinations of linear and quadratic forms in the thickness, material density and Young’s modulus. Two-dimensional boundary characteristic orthogonal pol...

The uniform formulation of dynamic vibration analysis multispan beams is presented by using an efficient domain decomposition method in this paper. Firstly, the structure divided into several equal sections based on method. Next, artificial spring used to simulate complex boundaries and continuity condition beam. Finally, admissible displacement functions are expanded through Jacobi orthogonal ...

in the realistic manner, piles are similar to the slender columns that soil around them acts as a lateral support. the piles situated in the liquefiable soil layers, loss their lateral supports due to the liquefaction resulted from the seismic ground motion. in this case, pile has the potency of axial instability similar to the unsupported columns. this instability can lead to the lateral buckl...

This paper presents an error analysis of the Lanczos algorithm in finite-precision arithmetic for solving the standard nonsymmetric eigenvalue problem, if no breakdown occurs. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. The theory developed illustra...

This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show ...

Abstract: In this article a numerical method is proposed to approximate the solution of the system of integrodifferential equations describing biological species living together. The method is based upon Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with Ritz-Galerkin method are then utilized to reduce the equations ...