멀티스테이지 호모토피 섭동법을 이용한 얕은 정현형 아치의 근사-해석적 해

The purpose of this study is to investigate the applicability of multistage homotopy perturbation method (MHPM) to shallow sinusoidal 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. From the comparison results, it was found that the dynamic response by MHPM concurred with the numerical results. Besides, the pattern of the response and the attractor by semi-analytical solution could delineate the dynamic snapping of the arches under excitations, and the attraction of the model in consideration of damping reflected the convergence and asymptotic stability well.