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Abstract

The excessive stroke of semi-active variable stiffness-tuned mass damper (SATMD) which causes large distortion is common in practice. The effects of the geometrical nonlinearity of the semi-active variable stiffness (SAVIS) device have been investigated and are described in this paper. An expression which includes the stiffness nonlinearity of the device is obtained. A cubic polynomial model of the equivalent stiffness is approximately obtained using the least squares interpolation method. First, the simplified coupled nonlinear equations with no forcing and no damping are approximately solved using the multiple scale method. The results show that the vibration frequency of the primary system can be modulated by the nonlinearity of the SAVIS device, and the 1:1, 1:3 and 3:1 internal resonance may occur in some conditions. Second, using the Runge-Kutta method, the iteration results are obtained under a full period sine-wave pulse and under the El Centro seismic record. Standard deviation (STD) responses and peak responses of the system are calculated for different damping ratios and different local frequency ratios. The power spectra distribution (PSD) of the response of a nonlinear system shows that the local frequency will be shifted, and the effect on the vibration control of the main structure is much better for a nonlinear case than for a linear case as the frequency ratio is less than one under both the sine-wave pulse and the El Centro seismic excitation.

Keywords

duffing equation coupling multiple scale method internal resonance damping ratio SATMD power spectra distribution(PSD)seismic excitation

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