Study Of Vibration Mechanism Of Plate And Stiffened Plate With Viscoelastic Damping Treatment

Theoretical analysis and numerical computation for dynamic problem of complex structures, which consist of elastic material and viscoelastic material, are presented in this paper. First, the finite element equations of motion of viscoelastic structures (which are only made of viscoelastic material) and complex structures are discussed. Possibility for the finite element equations of motion of viscoelastic structures that are represented by MCK model is investigated. The finite element equations of motion of complex structures concerned with outside viscous damping of the whole structure and inside viscous damping of elastic material are proposed by using the hypothesis of viscous damping. This paper analyzes the dynamic problem of viscoelastic structures and complex structures based on randomness of viscoelastic material. In the analysis resonant frequency, modal loss factor and harmonic response of structures are studied. In the vibration analysis of viscoelastic structures, model randomness and randomness of viscoelastic Poisson ratio are studied. In the model randomness, model with constantly complex modules, Kelvin-Voigt model, fractional derivative model with three parameters and standard rheologic model with three parameters are considered. The influence of material randomness on harmonic response of a single DOF system is studied. In the vibration analysis of unconstrained damped plate, the influences of real modulus, imaginary modulus, loss factor and Poisson ratio of viscoelastic material on the resonant frequency and the modal loss factor of structure with different thicknesses of damping layer are studied, and the influences of thickness of damping layer as random variable over the whole structure and within each element are also studied. The influences of real modulus, loss factor and Poisson ratio of viscoelastic material and thickness of damping layer on the amplitude and phase of structural steady-state harmonic response are studied. Numerical examples show that the randomness of material parameter and geometrical parameter of damped layer obviously influences the structural vibration. Therefore, the random analysis of viscoelastic damped structure is necessary. This paper proposes a simplified finite element method to analyze sandwich plate. The natural frequencies and modal loss factor of sandwich plate simplified as isotropic platebased on the equivalence principle are computed by using Mindlin plate finite element. The bending and shear modifying coefficients are derived according to distribution of the stress and strain of the sandwich plate along the direction of plate thickness. The solution of the complex eigenvalue is avoided for the sandwich plate with a viscoelastic core. A simplified analysis method is presented for the engineering application. The viscoelastic damping control of steady-state harmonic response of stiffened plate is studied by using modal superposition method. Three cases of stiffened plate with damping treatment are considered and compared: only with free damping layer and only with viscoelastic beam and with both damping treatments. Besides, the case of elastic beam as viscoelastic beam is also considered. The influences of material loss factor, thickness of free damping layer and section of viscoelastic beam are analyzed. Results indicate that the influences of different cases with damping treatment are different. The relational curves of structural response amplitude and load frequency show that the viscoelastic material is effective for control of structural resonant response.