| Summary: | 碩士 === 國立臺灣科技大學 === 營建工程系 === 97 === Dynamic responses of bi-linear hysteretic systems under two-frequency excitations characterized by a frequency ratio, n, are studied in this thesis. The analytical results show markedly different response characteristics as the excitation parameter n increases from unity. The classical beat phenomenon can be found for most cases with an n smaller than 1.1. On the other hand, a two-mode superposition in displacement is obvious when n is closer to an even number. To further explore its engineering implication, the indicated response features are compared based on a steady-state amplitude parameter referring to the Response Amplitude Factor, . An analytical expression of the parameter is first derived for the linear system and is then compared with numerical solutions evaluated for the nonlinear systems. The spectra demonstrate a two-peak response feature that conforms to the external excitation frequencies. The effects of stiffness softening are also clear as evidenced by a left-switch trend in the response peaks as the degree of nonlinearity increases. However, the variation in the peak magnitude is difficult to quantify
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