• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.493-500
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• 2023

The multiparameter eigenvalue method can be used to solve the damped finite element model updating problems. This method transforms the original problems into multiparameter eigenvalue problems. Comparing with the numerical methods based on various optimization methods, a big advantage of this method is that it can provide all possible choices of physical parameters. However, when solving the transformed singular multiparameter eigenvalue problem, the proposed method based on the generalised inverse of a singular matrix has some computational challenges and may fail. In this paper, more details on the transformation from the dynamic model updating problem to the multiparameter eigenvalue problem are presented and the structure of the transformed problem is also exposed. Based on this structure, the rigorous mathematical deduction gives the upper bound of the number of possible choices of the physical parameters, which confirms the singularity of the transformed multiparameter eigenvalue problem. More importantly, we present a row and column compression method to overcome the defect of the proposed numerical method based on the generalised inverse of a singular matrix. Also, two numerical experiments are presented to validate the feasibility and effectiveness of our method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.117-119
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• 2005

For large structural eigen-analysis, the whole structure is divided into some partitioned structures and through synthesis of partitioned structural model the eigen-data of structure can be obtained. In that case, eigenvalue problem consists of semidefinite mass matrix form because of displacement constraint condition. In this work the eigenvalue problem is considered by means of several method, determinant search and null space reduction method.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.467-481
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• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.87-98
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• 2006

In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.213-221
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• 2011

In this paper, we establish a multiple critical points theorem for a one-parameter family of non-smooth functionals. The obtained result is then exploited to prove a multiplicity result for a class of periodic eigenvalue problems driven by the p-Laplacian and with a non-smooth potential. Under suitable assumptions, we locate an open subinterval of the eigenvalue.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.579-587
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• 1998

In this paper we will estimate the lower bound of k-th Dirichlet eigenvalue $ \lambda_{k}$ / of Laplace equation on bounded domain in sphere.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.609-622
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• 1997

We investigate the existence of solutions of the nonlinear beam equation under the Dirichlet boundary condition on the interval $-\frac{2}{\pi}, \frac{2}{\pi}$ and periodic condition on the varible t, $Lu + bu^+ -au^- = f(x, t)$, when the jumping nonlinearity crosses the first positive eigenvalue.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.317-323
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• 2018

We study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact manifolds with zero boundary condition. In particular, we obtain some geometric estimates for the first eigenvalue.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.629-633
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• 2010

In this paper we provide a sharp lower bound of the first Neumann eigenvalue of a compact hypersurface $\Sigma$ inside a convex set C in a Riemannian manifold under the assumption that ${\partial}{\Sigma}$ meets ${\partial}C$ orthogonally.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.925-935
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• 2023

In this paper, we consider a boundary value problem for a sixth order difference equation. We prove the monotone behavior of the eigenvalue of the problem as the coefficients in the difference equation change values and the existence of a positive solution for a class of problems.