Research On Plate/Shell-Ccavity Vibro-Acoustical Coupling And Vibration Control Optimization

Structure-borne noise control is a common academic and engineering concern. Structure-acoustic coupling characteristics and the sound radiation characteristics are given particular attention. Above all, analytical model was established through structural dynamic equation of elastic plate-shell-cavity coupling structure, and then structure-acoustic coupling characteristics were analyzed. Based on this model, bilateral -coupling between plate and cavity was further studied. Considering multi-domain, Trefftz finite method and meshless method were utilized. About vibration and noise reduction, active force controlling method and damping control method were given. Especially to complex structure, an approximation method of topological optimization was given, which was simple and suitable for engineering applications.Better understand the structure-acoustic coupling theory,and realize optimal designing during the period of product design. This work includes the following sections:Chapter I: Summary of the research on structural-acoustic coupling and noise control technology, discusses the current main research methods applied to this field, which include analytical methods, numerical methods, statistical energy methods, and so on. The current method used in the field of noise control --Active noise control method and passive noise control methods were introduced. An overview of the current field of acoustic coupling, vibration and noise reduction status were also illustrated. Finally, main contents of this paper were given.Chapter II: According to the plate and shell theory, analytical method was used to derivate the coupling equation of the plate-shell-cavity structure. Spring system was exerted to simulate different hypothetical boundary conditions. Took into account the in-plane vibration and considered both the coupling between plate and shell and the coupling between structure and acoustics, a model was established. Examples show that the elastic plate- cavity coupling structure has clear structure-control modes and cavity-control modes.Chapter III: Using the mode superposition method to discuss bilateral coupling between plate and cavity. The structure-acoustic coupling of plate-cavity-plate and cavity-plate-cavity was discussed. Acoustic transfer characteristics were obtained through modal analysis. In the real engineering project the two-layer board, or the chamber board structure which is in fact bilateral coupling system are usual. Bilateral coupling analysis provides a theoretical basis for vibration and noise reduction of this type of structure.Chapter IV: About multi-domain problems, the key is to solve Helmholtz equation. Trefftz quadrilateral element of eight nodes formula is derived. Trefftz complete solution to Helmholtz equation within a multi-domain was derived. However considering more complex multi-domain, meshless method was more beneficial. In this paper, approximated functions were constructed based on the principle of reproducing kernel particle method and least-square collocation method. A least-square collocation formulation based on kernel reproducing particle method was established for solving multi-domain acoustic response. To verify the proposed method, several numerical examples of one and two-dimensional problems were analyzed. Examples show the results have good accuracy and convergence.Chapter V: According to the principle of point sources combination, sound radiation generated by the cylindrical shell and plate are derived. Sound pressure level (SPL) was analysised. Results show the elastic structure force impact on directly is the role to SPL. Based on the SPL formulation, modal force can be calculated, and then amplitude of the active force can be got easily. Application of active force control approach to vibration and noise reduction is feasible.Chapter VI: Laplace transform was utilized to solve the coupled equation of plate and acoustic cavity and analysis sensitivity of the vibro-acoustic system. Research on vibro-acoustic coupling system includes not only computation of the coupling frequencies, coupling modes and also sensitivities of the coupling system to design variables. Reducing displacement amplitude of the specified nodes on the plate is on the target of depressing sound pressure of the measured point. The sensitivity of the displacement amplitude with respect to size and shape design parameters for the coupled system is derived. The distribution of the damping material on the plate was then optimized by penalized density topology optimization theory. Filter method raised by Sigmund was developed to suppress the numerical instabilities such as checkerboards. Numerical example is given to show the validity and efficiency of the sensitivity analysis and design optimization method.Chapter VII: Commercial finite element software was used to obtain the finite element model of complex engineering structures. Nodes information, stiffness and mass matrix were read out by matlab program. Acoustic transfer vector was utilized to find the main modes which affect the sound pressure most. Fast damping layer topology optimization method was established on the base of energy-consuming. Only one eigenvalue calculating can approximate the optimal distribution of the damping layer. At the same time filter formula used effectively inhibit the checkerboard phenomenon. The approximation topology optimization method is simple and suitable for complex engineering applications.Chapter VIII: summarized the whole work and addressed some problems and prospects.