In this paper, we apply He’s semi-inverse method to establish a variational theory for the Boussinesq system. Based on this formulation, a solitary solution can be easily obtained using Ritz method. Moreover, the results are also compared with He’s homotopy perturbation method, Liao’s homotopy analysis method and homotopy padémethod. The results reveal that the proposed method is very effective...

The block preconditioned steepest descent iteration is an iterative eigensolver for subspace eigenvalue and eigenvector computations. An important area of application of the method is the approximate solution of mesh eigenproblems for self-adjoint and elliptic partial differential operators. The subspace iteration allows to compute some of the smallest eigenvalues together with the associated i...

We analyze the Ritz–Galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a simple eigenvalue, we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates th...

The goal of this paper is to increase our understanding of harmonic Rayleigh– Ritz for real symmetric matrices. We do this by discussing different, though related topics: a priori error analysis, a posteriori error analysis, a comparison with refined Rayleigh–Ritz and the selection of a suitable harmonic Ritz vector.

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.

This paper addresses a challenging problem in computational mechanics—the analysis of thick shallow shells vibrating at high modes. Existing methods encounter significant difficulties for such a problem due to numerical instability. A new numerical approach, DSC-Ritz method, is developed by taking the advantages of both the discrete singular convolution (DSC) wavelet kernels of the Dirichlet ty...

Experimentally determined natural frequencies and modes shapes are presented for an elastically point-supported isotropic plate with attached masses under impulsive loading. These results are compared to frequencies and to modes shapes determined from the Rayleigh–Ritz method and a finite element analysis using COMSOL. Accelerometers mounted at three locations on the plate, provide input for ME...

The main objective of this research work was to investigate three-dimensional free vibration of thick annular plates which are composed of carbon nanotube (CNT) reinforced composites materials using the Chebyshev–Ritz method. In order to obtain precise results, a new form of the rule of mixtures including an exponential shape function, length efficiency parameter, orientation efficiency factor,...

In this paper, a modified Fourier series method is presented for the free vibration of moderately thick orthotropic functionally graded plates with general boundary restraints based on the first-order shear deformation theory. Regardless of boundary restraints, displacements and rotations of each plate are described as an improved form of double Fourier cosine series and several closed-form aux...