Research Articles | Challenge Journal of Structural Mechanics

Determination of the exact mode frequencies of multi-storey structures by state-space method and a comparison with mode superposition method

Ahmad Yamin Rasa, Mehmet Hamit Özyazıcıoğlu



A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.


structural dynamics; state-space method; mode superposition method; transient vibration; mode frequency

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