A MODAL SUPERPOSITION METHOD FOR NON-LINEAR STRUCTURES

Abstract

The dynamic response of multi-degree of freedom (MDOF) non-linear structures is usually determined by the numerical integration of equations of motion. This is computationally very costly for steady state response analysis. In this study, a powerful and economical method is developed for the harmonic response analysis of non-linear structures. In this method, the equations of motion are first converted into a set of non-linear algebraic equations, and then the number of equations to be solved is reduced by employing linear modes of the system. The resulting coupled algebraic equations are solved iteratively. The concept of the pseudo-receptance matrix is introduced in calculating the steady state response. It is shown that the reduction in computational time can be considerable as very accurate results can be obtained by using only a limited number of modes. Several example problems are solved in order to illustrate the performance of the method. Effects of higher modes and higher harmonic components of the response are discussed in detail. In order to illustrate the accuracy and speed of the method suggested, the results obtained by applying the so called Iterative Modal Method are compared with those obtained by the Newmark method which is used as a classical time domain analysis technique.