Influence of the Relationship Between Excitation Frequency and Natural Frequency on Formulating Structural Random Displacement Response

Abstract

Seismic action and wind excitation are the main sources of excitation to civil engineering structures. The analytical structural responses are similar for both cases, but the simplified formula in design codes on the displacement response under these excitations is quite different. This paper re-visits this difference from under stationary random excitation. The power spectrum density function of the above excitations contains several parameters which define the excitations in frequency domain. The simplified formulas of the displacement variance under different excitations are derived by adjusting these parameters. The responses from these formulas always include the resonance component of the response, whereas the presence of the background component depends on the ratio between the predominant frequency of excitation and the natural frequency of the structure. The influence of this ratio on the displacement covariance and the modal combination rules is then further discussed.