CMES-Vol. 84, No. 5, 2012

Open Access

ARTICLE

On Determination of a Finite Jacobi Matrix from Two Spectra
Gusein Sh. Guseinov¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 405-422, 2012, DOI:10.3970/cmes.2012.084.405
Abstract In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. More >

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Numerical Solutions of the Symmetric Regularized Long Wave Equation Using Radial Basis Functions
Ayşe Gül Kaplan¹, Yılmaz Dereli
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 423-438, 2012, DOI:10.3970/cmes.2012.084.423
Abstract In this study, the nonlinear symmetric regularized long wave equation was solved numerically by using radial basis functions collocation method. The single solitary wave solution, the interaction of two positive solitary waves and the clash of two solitary waves were studied. Numerical results and simulations of the wave motions were presented. Validity and accuracy of the method was tested by compared with results in the literature. More >

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Mode-III Stress Intensity Factors of a Three-Phase Composite with an Eccentric Circular Inclusion
C.K. Chao¹, A. Wikarta¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 439-458, 2012, DOI:10.3970/cmes.2012.084.439
Abstract An analytical solution to a three-phase composite with an eccentric circular inclusion under a remote uniform shear load is given in this work. Mode-III stress intensity factors for an arbitrarily oriented crack embedded in an infinite matrix or a core inclusion are provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation located either in the core inclusion or in the infinite matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack are More >

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ARTICLE

A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation, and its Equivalence to the High Dimensional Harmonic Balance Method: Subharmonic Oscillations
Hong-Hua Dai^1,2, Matt Schnoor², Satya N. Atluri²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.084.459
Abstract In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a kind of "harmonic balance method" but essentially a cumbersome version of the collocation method. In using the collocation method,… More >

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