study on linear and nonlinear dynamically p-delta effects on frame structures under earthquake spectra, harmonic and stochastic excitations

In this research the effect of axial load on dynamic behavior of a simple frame, subjected to harmonic, seismic and earthquake excitation has been studied. the differential equations of motion have been considered for two types of small and large deformations. the method of multiple scales has been applied to solve the differential equations of motion with harmonic loading and for small and large deformations. then, the steady state response near one-to-one resonance condition has been studied and the effect of axial force in resonance and non-resonance conditions has been investigated, which has not been considered before. it is clear from the results that the dynamic behavior of the frame under axial load is completely different in resonance and non-resonance cases and the axial load has respectively descending and ascending effects on the responses in resonance and non-resonance conditions. the equations of motion under earthquake loading are also considered and the time history and the response spectrum of the model show that the axial load has increased the responses under earthquake excitation. although white noise as a stochastic loading is applied to the model and, the results are approximated using the method of stochastic differential equations so, the mean value and covariance are calculated and the effect of axial force on them is investigated.