Study on Dynamic Response Evaluation through various Numerical Methods

Abstract

Response of structure subjected to various types of arbitrary dynamic forces like Pulse, Ramp, Unit Impulse, Earthquake is obtained by employing suitable Numerical Integration Method, since closed form solution of such problems are not evident. Mostly used numerical integration method includes Newmark’s Method and Runge-Kutta Method. Apart, many other numerical methods like Central Difference Method, Wilson Theta Method and Recursive Formula are also available. In the present study, dynamic response of linear Single Degree of Freedom (SDOF) system subject to dynamic force is obtained using various numerical methods. Dynamic forces considered are Harmonic Excitation (both at mass and base), Unit Impulsive Force and Earthquake Excitation. Convergence studies are carried out to arrive at appropriate time stepping interval for all numerical methods studied. Comparison among numerical solution obtained by various numerical methods is carried out. Apart, comparison is also carried out with closed form solution wherever possible. It is found that in case of Harmonic Excitation (at mass) and Unit Impulsive Force, Newmark’s Method (Linear Acceleration Method) converges to the closed form solution at large time stepping interval and hence best suited for them. Similarly, 4th Order Runge-Kutta Method proves the best suitable method for Harmonic Excitation (at base). In case of Earthquake Excitation time stepping size is very small, hence all methods are best suitable for Earthquake Excitation.