Dual series representation and its applications to a string subjected to support motions

Abstract

Dual series representation (DSR) for the dynamic response of a finite elastic body subjected to boundary traction and boundary support excitations is proposed in this paper. To confirm the validity of the present model, a string subjected to support motions is solved. Four analytical methods including (1) a diamond rule, (2) a series solution with the quasi-static decomposition method, (3) DSR by the Cesáro sum technique, and (4) DSR by the Stokes' transformation method are presented. It is found that the numerical results obtained by using these four methods are in good agreement, and that both the Cesáro sum and Stokes' transformation regularization techniques can extract the finite part of the divergent series. The advantages and disadvantages of these four methods are discussed. In comparison with the quasi-static decomposition method and the Cesáro sum technique, the Stokes' transformation is the best way not only because it is free from calculation of the quasi-static solution, but also because its convergence rate is as fast as that of the mode acceleration method.