An accurate solution for the in-plane transient response of a circular arch

A systematic and straightforward approach to obtain accurate transient responses of circular arches subjected to point loading and support motions is presented. The Laplace transform is applied to the time variable. Then, an analytical solution is formulated in the s-domain. Finally, an efficient and accurate numerical technique is applied to obtain the inverse of the Laplace transforms. The proposed approach gives highly accurate results not only for displacement components, but also for stress resultants, which are functions of higher derivatives of the displacement. Besides, it is not necessary to find vibration modes or an auxiliary solution (such as a quasi-static solution) that are required in most of the approaches given in previous technical publications considering the case of base excitations. Two examples are given to demonstrate the validity of the proposed method: one is a fixed-end arch subjected to excitation at one end, the other one is the same arch subjected to a dynamic normal point loading at its middle. (C) 1996 Academic Press Limited