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Structural Engineering and Mechanics Volume 13, Number 4, April 2002 , pages 437-453 DOI: https://doi.org/10.12989/sem.2002.13.4.437 |
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Computation of dynamic stiffness and flexibility for arbitrarily shaped two-dimensional membranes |
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Chen JT, Chung IL
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| Abstract | ||
| In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to deterinine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases. | ||
| Key Words | ||
| dynamic stiffness and flexibility, an efficient mixed-part dual BEM, overdetermined system | ||
| Address | ||
| Chen JT, Natl Taiwan Ocean Univ, Dept Harbor & River Engn, Chilung, Taiwan Natl Taiwan Ocean Univ, Dept Harbor & River Engn, Chilung, Taiwan | ||