Author(s)

H.K. Hong & J.T. Chen

Abstract

On the dual integral representation and its application to vibration problems H.-K. Hong, J.-T. Chen Department of Civil Engineering, Taiwan University, Taipei, Taiwan ABSTRACT In this paper, the dual integral representation in series forms or briefly the dual series representation for transient vibration problems is derived using the concept of modal dynamics. The four kernel functions in this represen- tation are in degenerate series forms which display symmetric and transpose symmetric properties. Assembling the four kernel functions, the total sym- metry can be obtained. The potentials induced by the kernels are expressed in terms of uniformly convergent, pointwise convergent, and divergent series for modal dynamic problems investigated in this paper, instead of continu- ous, discontinuous, and pseudo-continuous functions in the form of integrals with different degrees of singularity for static and direct transient problems. The technique used for the extra

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