CMES-Vol. 27, No. 3, 2008

Open Access

ARTICLE

A Lie-Group Shooting Method for Simultaneously Estimating the Time-Dependent Damping and Stiffness Coefficients
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 137-150, 2008, DOI:10.3970/cmes.2008.027.137
Abstract For the inverse vibration problem, a Lie-group shooting method is proposed to simultaneously estimate the time-dependent damping and stiffness functions by using two sets of displacement as inputs. First, we transform these two ODEs into two parabolic type PDEs. Second, we formulate the inverse vibration problem as a multi-dimensional two-point boundary value problem with unknown coefficients, allowing us to develop the Lie-group shooting method. For the semi-discretizations of PDEs we thus obtain two coupled sets of linear algebraic equations, from which the estimation of damping and stiffness coefficients can be written out explicitly. The present approach is very interesting, which… More >

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Particular Solutions of Chebyshev Polynomials for Polyharmonic and Poly-Helmholtz Equations
Chia-Cheng Tsai¹
CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 151-162, 2008, DOI:10.3970/cmes.2008.027.151
Abstract In this paper we develop analytical particular solutions for the polyharmonic and the products of Helmholtz-type partial differential operators with Chebyshev polynomials at right-hand side. Our solutions can be written explicitly in terms of either monomial or Chebyshev bases. By using these formulas, we can obtain the approximate particular solution when the right-hand side has been represented by a truncated series of Chebyshev polynomials. These formulas are further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). Numerical experiments, which include eighth order PDEs and three-dimensional… More >

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A Differential Reproducing Kernel Particle Method for the Analysis of Multilayered Elastic and Piezoelectric Plates
Chih-Ping Wu¹, Kuan-Hao Chiu, Yun-Ming Wang
CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163
Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, the Euler-Lagrange equations of three-dimensional… More >

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ARTICLE

Dynamics Analysis of Mechanical Components: a Discrete Model For Damping
F. Cosmi¹
CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 187-196, 2008, DOI:10.3970/cmes.2008.027.187
Abstract The Cell Method is a recent numerical method that can be applied in several fields of physics and engineering. In this paper, the elastodynamics formulation is extended to include system internal damping, highlighting some interesting characteristics of the method. The developed formulation leads to an explicit solving system. The mass matrix is diagonal (without lumping) and in the most general case a time-dependent damping coefficient can be defined for each node. \newline Accuracy and convergence rate have been tested with reference to the classical problem of a particle free vibration with viscous damping.
An application to mechanical components analysis… More >

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