A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

This study aimed at obtaining a semianalytical solution for nonlinear dynamic system of shallow arches. Taylor method was applied to find the analytical solution, and an investigation of their dynamic characteristic was carried out to verify the applicability of this methodology for the shallow arches under step or periodic excitation. A polynomial solution can be obtained from this multistep approach with respect to time, and direct buckling as well as indirect buckling of the shallow arches can be observed, also. The results indicated that the dynamic buckling load level was higher with higher shape factor. Additionally, a change of attractor in phase space was investigated. Coupling in symmetric mode as well as asymmetric mode was observed in case of indirect buckling, and a sensitive response was also manifested during sinusoidal and beating excitation. These results of applying multistep Taylor series for the investigation of displacement response and attractor change revealed that this analytical approach was valid in explaining the dynamic buckling behavior of shallow arches under direct and indirect snapping.