Analysis of Dynamic Model of a Structure with Nonlinear Damped Behavior

In this work, it has been attempted to analytically treat the nonlinear behavior of structures. Since analysing nonlinear problems is of great difficulty, different numerical methods and software are advised to treat such problems. Despite the increasing expenses of building structures to maintain their linear behavior, nonlinearity has been inevitable, and therefore, nonlinear analysis has been of great importance to the scientists in the field. As structures confront lateral forces and intense earthquakes especially near fault regions, a part of the structure remains linear, but some part of it behaves nonlinearly for example dampers, columns and beams. This is simulated by a damped in nonlinear oscillator. In this paper, the nonlinear equation of oscillator with damping which has nonlinear behavior is representative of the dynamic behavior of a structure has been solved analytically. In the end, the obtained results are compared with numerical ones and shown in graphs and in tables; analytical solutions are in good agreement with those of the numerical method.