The purpose of this study is to investigate the applicability of multi-stage homotopy perturbation method to shallow arches in order to obtain a semi-analytical solution. For this research purpose, a nonlinear governing equation of the arches was formulated and a homotopy equation was derived using the formulated differential equation. The result of a dynamic analysis on a symmetric mode and an asymmetric one was compared with the classical homotopy perturbation method and the 4th order Runge-Kutta method.

Large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. However, the study of the behavior of such structures shows the existence of critical parameters. A small change in such parameters causes a significant change in the motion behavior. In this paper we study the parameter identification problem for shallow sinusoidal arches considering damping effect.