Energy transmission through a double-wall structure with an acoustic enclosure: Rotational effect of mechanical links

This paper investigates the rotational effect of mechanical links on energy transmission of a double-wall structure with an enclosure. A criterion is proposed to identify energy transmission mechanisms and predict the dominant transmitting path. Studies in different frequency ranges show a more significant energy transmission due to the rotational effect of the link at higher frequencies compared with lower ones. Comparison between the translational effect and the rotational effect on energy transmission shows that although both effects are important for the transmission mechanism analysis, the rotational effect on energy transmission is more remarkable at high frequencies for a soft translational link; whereas is insensitive for a stiff one.     

Mechanisms of active control of sound transmission through a linked double-wall system into an acoustic cavity

The mechanism of active control on sound transmission through a mechanically linked double-wall structure into an acoustic cavity is investigated in this paper. Two control methods, i.e., structural control and acoustic control under two linkage cases (soft and hard) are investigated to analyze the effect of the links on the selection of control strategies and the corresponding control mechanisms. Simulations are performed to examine the dominant control mechanism (modal suppression or modal rearrangement) in different frequency ranges for each control case. The alteration in the structural-acoustic coupling is also analyzed so as to explain the mechanisms of sound attenuation. In addition, the dominance of the acoustic mode (0, 0, 0) in the energy transmission process as well as its use in designing a more effective sensor/actuator arrangement is discussed.     

Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong nonlinear stiffness at its free end.