ばねで連結された２層天井はりの振動解析

Abstract

This paper investigates the vibrations of two-layer ceiling beams (consisting of upper and lower beams) connected by a spring and dashpot when the upper beam is subjected to external harmonic excitation. In the theoretical analysis, the modal analysis approach is used to determine the natural frequencies and vibrational modes of the system, and frequency response curves of the two beams. In the numerical calculation, two cases are examined. One is the case A where the two beams have an identical material and dimension, and the other is the case B where the two beams have an identical material and different dimensions. As a result, in Case A, when the spring is connected at the middle of the beams, as its spring constant K increases, the natural frequencies corresponding to the vibrational modes with the two beams in phase are constant, and the natural frequencies corresponding to the vibrational modes with the two beams out of phase increase. When K reaches a threshold value Kc, two of the natural frequencies are identical, and a magnitude relationship of these two natural frequencies is switched. When the spring is attached at a position of a certain loop of the vibrational modes with the two beams out of phase, the natural frequencies become largest. The appearance of the vibrational mode depends on the position of the external excitation, and the lower beam does not always vibrate. In Case B, the resonance frequencies shift to the excitation frequency lower than in Case A. When the two beams vibrate out of phase, the amplitudes at the peaks of the response curves significantly decrease as the viscous damping coefficient of the dashpot increases.