Nonlinear vibro-acoustic behavior of cylindrical shell under primary resonances

Abstract

Abstract Nonlinear vibro-acoustic behavior of cylindrical shell excited by an oblique incident plane sound wave under primary resonances is analytically examined in this paper. Donnell’s nonlinear shallow shell theory is used to model the cylindrical shell. Coupled nonlinear differential equations of the system are analytically derived using Galerkin’s approach. The Multiple Scales Method is hence, employed to solve the corresponding nonlinear equations. Then, the effects of crucial design parameters including incident sound wave amplitude, damping ratio and thickness of the shell on the characteristics of the sound transmission loss are studied for different resonance cases. In addition, the effect of detuning parameter on the bifurcation and behavior of the limit cycle under primary resonance is examined. The results show that the detuning parameter is a bifurcation parameter and Neimark–Sacker, flip, and period-3 bifurcations occur when this parameter is varied. Also, according to the results, by getting away from the resonance frequencies, excitation level incorporates no significant effect on the transmission loss of the shell.