Damping is a difficult field in structural dynamic analysis. The proportional damping assumption used in dynamical analysis does not match the requirement of accuracy. It is difficult to design the structural modal damping ratio. Although (free) constrained damping layer is used to reduce the structural vibration, the topology optimization of (free) constrained damping layer is not researched yet. This paper focuses on damping research in structural dynamic analysis, include:(1)Developed the identification method for structural non-proportional damping matrix, By using Liang model of damping and Kronecker product method in structural dynamic analysis. The corresponding iterative algorithm was built for uncompleted experiment models. Compared with the identification method for proportional damping and simplified non-proportional damping, this method has the advantage of high accuracy. The damping matrixes obtained by the method are sparse-and-symmetry matrixes, which can seldom obtained by other method.(2)Developed the identification method for damping matrix of appended dampers. Firstly, the appended dampers are described as dashpots between degrees of freedom. Then, by using of the Kronecker product method and transforming a matrix to a long vector, the locations and damping coefficients of the dashpots are identified. For engineering applying, the corresponding iterative method is developed in this work for the incomplete test models. We can identify the damping coefficients with almost 100 percent precision in the condition of incomplete test models.(3)Develop the modal damping ratio optimization method for general damped structures. There are two aspects: (a) Maximizing the modal damping ratio with the given dampers. From the relation between the modal damping ratio and the structural parameter, by use of Kronecker product method, the sensitivity of modal damping ratio to the location where the damper attached was obtained. Then the optimal attached location was determined for maximal modal damping ratio. (b) Making the modal damping ratios of structure close to the given values. After the optimal attached locations were determined, the optimal damping coefficients of dampers were obtained by using of the iterative method of broyden. The advantage of the method is that it could be easily applied in engineering structures which can be discresized by finite-element-method.(4)Developed the topology optimization method for structures with free damping layer. Include: (a) By using principle of virtual work to constitutive equation of viscoelastical material, the finite element dynamical equation of free-damping-layer plate was obtained. The sensitivity of modal damping ratio to element can be calculated after solving the dynamic equation. Finally, the best viscoelastical material distribution was obtained by deleting the damping element with low sensitivity. (b)For engineering use, developed fast topology optimization method: Calculated the frequency and vibration shape of plate before attaching free damping layer. Then calculated the energy dissipation of the free damping element for every location where the damping element will be attached. Finally, free damping element is attached at the maximal energy-dissipation location to get the maximal modal damping ratio with the minimal damping material.( 5 ) Developed the topology optimization method for structures with constrained damping layer. Include:(a)Developed the vibration differential equation of constrained-damping-layer plate and worked out the analytical roots at the case of all edge were simply constrained. (b)By using principle of virtual work to constitutive equation of viscoelastical material, the finite element dynamical equation of constrained-damping-layer plate was obtained. The sensitivity of modal damping ratio to element can be calculated after solving the dynamic equation. Finally, the best viscoelastical material distribution was obtained by deleting the damping element with low sensitivity. (c)For engineering use, developed fast topology optimization method: At first calculated the frequency and vibration shape of plate before attaching constrained damping layer; and then calculated the energy dissipation of the constrained damping element for every location where the damping element will be attached; finally, constrained damping element is attached at the maximal energy-dissipation location to get the maximal modal damping ratio with the minimal damping material.