Dynamic Characteristics And Random Response Analysis Of Beams And Plates

In recent years,with the development of viscoelastic damping technology and random vibration theory,many theoretical achievements are applied in aerospace engineering,mechanical engineering,structural engineering,civil engineering and vehicle engineering.The viscoelastic damping and the random excitation are considered in order to adapt to the objective reality.Dynamic characteristics and random response characteristics of the viscoelastic Timoshenko beams and thin circular plates are studied in this paper.(1)The dynamic characteristics of the viscoelastic Timoshenko beam under complicated boundary conditions are studied.The internal viscoelastic damping and the external viscoelastic damping are considered.The complicated boundary means that the end of the beam is connected to a supporting spring and a tip mass.Compared with the existing literature,one obvious progress of this work is that the technique of separating variables twice is used to solve the partial differential equations governing the transverse free vibration.The other evident improvement is that the effects of the spring stiffness,the tip mass,the rotary inertia of the tip mass and the span-depth ratio on the natural vibration characteristics are studied.In addition,the Bernoulli-Euler beam model can be considered as a special case of the Timoshenko beam model.The numerical results obtained from the theory presented are compares with those of the finite element method and a good agreement.(2)The dynamic characteristics of the viscoelastic thin circular plates under complicated boundary conditions are studied.The internal viscoelastic damping and the external viscoelastic damping are also considered.The boundary conditions involve the fixed support,the simple support and the free boundary.By using the method of separation of variables,the partial differential equation governing the free vibration of viscoelastic circular thin plates is solved.The effect of boundary conditions on the free vibration characteristics is studied.Finally,the numerical results obtained by finite element method are used to verify the theoretical analysis.(3)The random response characteristics of the Timoshenko beam and the thin circular plate are studied.The analytical solutions of the functions described by using Bessel function are obtained.The excitation form involves the distributed loading and the concentrated force.The random excitation is related to include the ideal white noise,the band-limited white noise and the colored noise.The functions involve mean value function,autocorrelation function and auto-spectral density function of the regular mode excitation,the cross correlation function and the cross power spectral density function between the regular modal excitations,mean value function,autocorrelation function and auto-spectral density function of the displacement response,and mean square transverse displacement,velocity and acceleration responses.The numerical results obtained from the theory presented are compares with those of the Monte Carlo method and a good agreement.In addition,the calculation formulas of mean square transverse displacement and velocity responses and auto-spectral density function of displacement and acceleration responses of the stationary random vibration of viscoelastic circular thin plates are got by using break-in operation,and they can meet the high calibration precision request.The effect of viscoelastic damping on random vibration is studied.