Abstract

In this work, attempted has been made to analyze the nonlinear behavior of structures analytically. 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. Studying on nonlinear dynamics highlights the fact that essentially all dynamic systems encountered in the real world are to some extent nonlinear, meaning that their description as differential equations contains nonlinear terms. Such nonlinearities appear in different ways, such as through frictional terms, coriolis and centrifugal terms, large amplitude effects, or other structural nonlinearities. The nonlinearities make that standard linear dynamics unable to suffice to the analysis and understanding of nonlinear mechanical systems. 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; this is simulated by a damped nonlinear oscillator. In this paper, the nonlinear equation of oscillator with damping which 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.

Key words: Nonlinear oscillator equation, damping, nonlinearly dynamic structure.