Theoretical modeling and vibration analysis of cylindrical shell carrying internal machine and metamaterial isolator with broadband bandgaps

The vibration control of the cylindrical shell carrying internal machine and isolator is of significant interest to underwater vehicles. The metamaterial isolator that combines Bragg bandgap and local resonant bandgap, namely periodic isolator with embedded absorber, is proposed to reduce the vibration transmission in the cylindrical shell carrying internal machine. For predicting the vibration behavior of the cylindrical shell with internal machine and periodic isolator with embedded absorber, a analytical method (AM) is proposed. The internal machine and the periodic isolator with embedded absorber are both modeled as one-dimension dynamic model using transfer matrix method. The exact three-dimensional modeling of the cylindrical shell is established based on Flügge shell theory. The accuracy of the proposed AM is validated by comparing to the finite element method (FEM). The vibration response of the cylindrical shell carrying internal machine and periodic isolator with embedded absorber is analyzed comparing with those of the continuous isolator and the periodic isolator. In addition, the wave propagation characteristics of those isolators are compared, which explains the bandgap characteristics. The parametric analysis are conducted for identifying the influence of dynamic parameters on bandgaps characteristic of the periodic isolator with embedded absorber.