Based on the Donnell assumptions and linear viscoelastic theory, the constitutive relations for the multilayer passive constrained layer damping (PCLD) cylindrical shell are described. In terms of energy, the motion equations and boundary conditions of the cylindrical shell with multilayer PCLD treatment are derived by the Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equation in state space is established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor, and the frequency response of the multilayer PCLD cylindrical shell is obtained. The results show that with more layers, the more effective in suppressing vibration and noise, if the same amount of visco-elastic and constrained material is applied. It demonstrates a potential application of multilayer PCLD treatment in some critical structures, such as cabins of aircrafts, hulls of submarines, and bodies of rockets and missiles.
Transfer function method for frequency response and damping effect of multilayer PCLD on cylindrical shell
