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  • Open Access

    ARTICLE

    Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

    R Sivaprasad1,2, S Venkatesha1, C S Manohar1,3

    CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 179-208, 2009, DOI:10.3970/cmc.2009.009.179

    Abstract The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on More >

  • Open Access

    ARTICLE

    Simultaneously Estimating the Time-Dependent Damping and Stiffness Coefficients with the Aid of Vibrational Data

    Chein-Shan Liu1, Jiang-Ren Chang2, Kai-Huey Chang2, Yung-Wei Chen2

    CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 97-108, 2008, DOI:10.3970/cmc.2008.007.097

    Abstract For the inverse vibration problem a mathematical method is required to determine unknown parameters from the measurement of vibration data. When both damping and stiffness functions are identified, it is a rather difficult problem. In this paper we will propose a feasible method to simultaneously estimate both the time-dependent damping and stiffness coefficients through three mathematical transformations. First, the second-order equation of motion is transformed into a self-adjoint first-order system by using the concept of integrating factor. Then, we transform these two ODEs into two hyperbolic type PDEs. Finally, we apply a one-step group preserving More >

  • Open Access

    ARTICLE

    Mechanics of Elastomer--Shim Laminates

    A. H. Muhr1

    CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 11-30, 2007, DOI:10.3970/cmc.2007.005.011

    Abstract The mechanics of laminates of elastomer and shims of high modulus material are reviewed. Such structures are often built to provide engineering components with specified, and quite different, stiffnesses in different modes of deformation. The shims may either be rigid or flexible, flat or curved, but are usually close to inextensible, being made of a high modulus material such as steel. On the other hand, rubber has an exceptionally low shear modulus, about one thousandth of its bulk modulus, so that shear of the rubber layers and flexure of the high modulus layers (if thin)… More >

  • Open Access

    ARTICLE

    The Spring-Damping Regularization Method and the Lie-Group Shooting Method for Inverse Cauchy Problems

    Chein-Shan Liu1,2, Chung-Lun Kuo3, Dongjie Liu4

    CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 105-124, 2011, DOI:10.3970/cmc.2011.024.105

    Abstract The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is More >

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