The Research On Vibration Characteristics Of Coupled Structures With Elastic Boundary Conditions

Boundary condition is such an important factor for coupled structures’ vibration that the dynamic analysis based on it will contribute to the noise and vibration control of coupled structures, which may bring about significant theoretical and practical effects. Surrounding the vibration theory’s modeling of coupled structures with elastic boundary restraints, following research work has been carried out in this thesis:An analytical method for vibration analysis of the multi-span beams with elastic boundary restraints is proposed. Different from before, the supplementary function of improved Fourier series are described trigonometric functions so that the work of formula derivation and programming becomes less complicated. By enforcing applicable continuity conditions and balance conditions between neighboring beams, coupled equations of multi-span beam system are established. Then the differential equations of multi-span beams system are converted into standard linear algebraic equations. Thus the main vibration characteristics of multi-span beams with elastic edge restraints can be determined conveniently, and then the present theory was verified by numerical simulation and experiment.Based on deformation compatibility condition of stiffened plate, elastic boundary conditions are introduced into the stiffened plate equations, and an analytical-numerical method for vibration of the rectangular stiffened plates with elastic boundary restraints is proposed. The displacement function is expressed as modified two-dimensional Fourier series, which converts the governing equations of stiffened plate into linear algebraic equations. Thus both free and forced vibration-sound of stiffened plate with elastic edge restraints can be determined conveniently. Results of the present method have good agreement both with those published and standard FEA results. Furthermore, Rayleigh’s proportional damping is introduced so that the damped forced vibration of stiffened plate with elastic edges can be determined.The elastic boundary theory is then generalized from the single plate structure to in-plane coupled plates. Based on the balance conditions and continuity conditions, boundary equations of coupling sides of four-palace type coupled plates are derived. The improved Fourier expansions are used to express the bending vibration displacement of these plates, and then these differential boundary equations and the governing equations are changed intosimple linear system equations. The present theoretical model and method are verified by numerical simulation and experiment. Using the present theoretical model, the effect of coupled boundary damping on sound-vibration response of coupled plates is considered. Results show that boundary damping of translational constraints may reduce resonance responses significantly, and boundary constraint dominates these effect. Afterwards, vibration power flow characteristics of coupled plates are studied. Simulation results show that increasing restraint stiffness of edges can effectively hinder the power flow through the edges, and the power tends to flow into plates that have the same material with the excited plate.Based on balance condition and continuity condition of displacement, motions of the in-plane longitudinal and tangential shears and transverse shears and bending moments on coupled boundaries are all incorporated. And then coupled equations of multi-span shells are established so that problem of expressing coupled boundary equations completely can be solved. The improved Fourier expansions are used to express bending vibration displacements of all shells, and differential governing and boundary equations are changed into equations of simple linear systems which can be solved conveniently. The present theoretical model was verified by FEA and experiment, and effect of elastic constraints on vibration response of coupled shells was examined. Results show that both circumferential and radial elastic constraints’ stiffness have more effect on vibrational response of coupled shells than axial and rotational elastic constraints.Furthermore, the present method of elastic boundary developed in this thesis is applied in the vibration study of cylindrical shells with water load, reinforcement and added damping layer considered. Using equivalent single layer theory and orthotropic theory, theoretical vibration models of free damping cylindrical shell and stiffened cylindrical shell are both established. With water load factor considered in the elastic boundary theory, the vibration study method of underwater free damping stiffened shell is approached. Experiment studies of stiffened cylindrical shell in laboratory and underwater damping stiffened cylindrical shell in outfield are carried out and the measured results and the theoretical results are in good agreement.