Approximate solutions for transient response of constrained damping laminated cantilever plate

The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work. By solving Lagrangeʹs equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly. The theoretical calculations are compared with the experimental data, the results show: both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results. Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.