An investigation of transient vibrations of multistorey structures by the state-space approach and a comparison with mode superposition method

In this research, a comparative study of exact and approximate solution of transient and steady state vibrations in structural dynamics is presented. State-Space method provides the exact solution while Mode Superposition method presents an approximate solution. It is seen that the maximum responses obtained by different methods are not the same. It is discussed that how structural parameters must be adjusted to obtain the best approximation. Dynamic responses (displacement, velocity and acceleration) are computed and compared for simple structures. The maximum responses are obtained by square root of sum of the squares (SRSS) method. Sample comparisons are discussed for three, five, ten and twenty storey building. Calculations are programed in MATLAB platform. As a result of the study, the most suitable parameters for the approximate mode superposition method to render the results as close as possible to the exact solution are geiven.