• Geomechanics and Engineering
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• v.32 no.2
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• pp.137-144
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• 2023

The current article studied wave propagation in a nonlocal porous thermoelastic half-space with temperature-dependent properties. The problem is solved in the context of the Green-Lindsay theory (G-L) and the Lord- Shulman theory (L-S) based on thermoelasticity with memory-dependent derivatives. The governing equations of the porous thermoelastic solid are solved using normal mode analysis with an eigenvalue approach. In order to illustrate the analytical developments, the numerical solution is carried out, and the effect of local parameter and temperature-dependent properties on the physical fields are presented graphically.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.551-560
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• 2007

We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condition $$\{^{-{\Delta}^2u-c{\Delta}u+{\gamma}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega},\;}_{-{\Delta}^2u-c{\Delta}u+{\delta}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega}}$$, where $u^+$ = max{u, 0}, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.105-112
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• 1994

In a local vibration analysis of a large steel frame, a large eigenvalue problem results. Due to computer storage and the expense of a complete solution, it is desirable to minimize the size of the resulting matrices. A new and efficient method of local vibration analysis for large steel frames is presented. It reduces the order of dynamic matrices by dynamic condensation method. Examples are given for local vibration of a plane frame. Results are compared to the complete solution of the full eigenvalue problem.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.943-956
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• 2000

We investigate a relation between multiplicity of solutions and source terms of jumping problem in wave equation when the nonlinearity crosses an eigenvalue and the source term is generated by finite eigenfunctions. We also show that the jumping problem has infinitely many solutions when the source term is positive multiple of the positve eigenfunction.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.669-684
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• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1123-1135
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• 2010

In this paper, we consider the eigenvalue problem of biharmonic equation with Hardy potential. We improve the results of references by introducing a new Hilbert space.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.467-474
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• 2006

We present and study the stability and convergence of a deflation-preconditioned conjugate gradient(PCG) scheme for the interior generalized eigenvalue problem $Ax = {\lambda}Bx$, where A and B are large sparse symmetric positive definite matrices. Numerical experiments are also presented to support our theoretical results.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.211-230
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• 2008

Owing to the growing size of the eigenvalue problem and the growing number of eigenvalues desired, solution methods of iterative nature are becoming more popular than ever, which however suffer from low efficiency and lack of proper convergence criteria. In this paper, three efficient iterative eigenvalue algorithms are considered, i.e., subspace iteration method, iterative Ritz vector method and iterative Lanczos method based on the cell sparse fast solver and loop-unrolling. They are examined under the mode error criterion, i.e., the ratio of the out-of-balance nodal forces and the maximum elastic nodal point forces. Averagely speaking, the iterative Ritz vector method is the most efficient one among the three. Based on the mode error convergence criteria, the eigenvalue solvers are shown to be more stable than those based on eigenvalues only. Compared with ANSYS's subspace iteration and block Lanczos approaches, the subspace iteration presented here appears to be more efficient, while the Lanczos approach has roughly equal efficiency. The methods proposed are robust and efficient. Large size tests show that the improvement in terms of CPU time and storage is tremendous. Also reported is an aggressive shifting technique for the subspace iteration method, based on the mode error convergence criteria. A backward technique is introduced when the shift is not located in the right region. The efficiency of such a technique was demonstrated in the numerical tests.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.3
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• pp.44-49
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• 2002

A study of free vibration of axisymmetric circular plates based on Mindlin theory using a pseudospectral method is presented. The analysis is based on Chebyshev polynomials that are widely used in the fluid mechanics research community. Clamped, simply supported and flee boundary conditions are considered, and numerical results are presented for various thickness-to-radius ratios.