Mode superposition methods applied to linear mechanical systems under earthquake type excitations

Abstract

The determination of the maximum dynamic responses of a multidegree of freedom mechanical system under earthquake type excitation using mode superposition methods is the general problem considered. The experimental work was carried out using a special purpose electronic differential analyzer involving a three degree of freedom system, or a three mode approximation to a larger system. The results indicate that a suitably weighted average of the sum of the absolute values and the square root of the sum of the squares of the individual mode contributions gives a practical design criterion for the base shear forces. For critical designs this weighted average reduces to the absolute sum of the modes, which will be close to the true value for a significantly high percentage of the cases. The base moment may be more accurately approximated than the base shear by use of the first mode alone.