Dynamic analysis of SDOF systems using modified energy method
In this research, a new numerical method is presented to evaluate the linear and especially the nonlinear dynamic response of single degree of freedom systems. This technique is based on the simultaneous usage of energy and force equilibrium equations which is called the Modified Energy Method. At first, a simple linear system is selected to illustrate the method in detail with harmonic and earthquake loading. Furthermore, several different nonlinear examples are studied such as: a-Coulomb Friction (nonlinear damping) b-Duffing Oscillator (material nonlinearity) and c-Large-angle Simple Pendulum (geometric nonlinearity). The results of the proposed method are compared with other methods, and it was found that this method is more accurate compared with the 4th order Runge-Kutta method for nonlinear analyses.