New approximation for steady-state response of general damped systems

A new approximation for steady-state dynamic displacements, which captures the nonlinearities associated with resonance, is presented. This approximation is based on modal analysis and is valid for general damped structures, which include the case of actively controlled structures. Intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximations. When these high-quality approximations are used within the context of the approximation concepts approach, the overall efficiency of the design synthesis process is improved by reducing the number of complete analyses required for convergence. Numerical results that illustrate the effectiveness of the method are presented.