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 scheme for the semi-discretizations of… More >

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) are the dominant mechanisms of… More >

Chein-Shan Liu^1,2, 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 very cheap. More >