Based on the theory of Donnell and Kirchhoff hypothesis and by using the complex constant model of viscoelastic materials, the vibration equations of five-layered constrained damping plate are established. The transfer matrix method (TMM) is improved and used to solve equations. The improved TMM is more effective to solve complex structural vibration. The influence of layer numbers, thickness of each layer, and arrangement of materials on vibration behavior are discussed. It is proved that multilayered plates can more effectively reduce natural frequency and obtain higher structural loss factor. The loss factor increases with the number of whole layers. Symmetrical structure can obtain higher structural loss factor than one-direction structure. Uniform arrangement of viscoelastic materials and constrained materials can obtain higher structural loss factor than nonuniform arrangement. There is different optimum frequency with different material thickness, and the optimum frequency is not dependent from layer numbers.
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.
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