An efficient multi-point support-motion random vibration analysis technique

Random vibration analysis technique based on the mode superposition method requires computation of multiple static solutions for multi-point support-motion problems. These static solutions, known as quasi-static solutions, are utilized in the calculation of participation factors. For large practical problems, the quasi-static solutions may become expensive and time-consuming. The present paper shows that the needed participation factors can be computed from modal reactions, mode shapes and natural frequencies eliminating the need to solve for the quasi-static problem. It is also shown that a simple expression can be developed for the quasi-static solution in terms of modal reactions, mode shapes and natural frequencies, which can then be used in the expressions for the quasi-static and covariance components of the response power spectral densities. Thus, the need for quasi-static solution is completely eliminated without introducing any further assumption into the formulation.