A Lie-Group Shooting Method for Simultaneously Estimating the Time-Dependent Damping and Stiffness Coefficients
Chein-Shan Liu

doi:10.3970/cmes.2008.027.137
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 27, No. 3, pp. 137-150, 2008
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Keywords Inverse vibration problem, Time-dependent damping and stiffness coefficients, Lie-group shooting method
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 resulting to closed-form estimating equations without needing of any iteration and initial guess of coefficient functions, and more importantly, it does not require to assume a priori the functional forms of unknown coefficients. The estimated results are rather accurate convicing that the new method can be employed in the vibrational engineering to identify viscoelastic property of time-aging materials.
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