| Serving as an important factor, which can considerably influence the characteristics of structural vibration, enclosed sound field as well as its coupling system, boundary condition plays a crucial role in noise and vibration optimal design and improvement of the active/passive control effectiveness for related structural-acoustical system. Development of precise dynamic prediction model for structural-acoustical system with complicated boundary conditions can provide solid ground for fully understanding the influence nature of boundary conditions, and then exploiting its potentials as design and control space parameters, will be of great theoretical significance and applied value. Surrounding the modeling problem of structural vibration, enclosed sound space and its coupling system, the following research work has been carried out in this thesis:A two-dimensional improved Fourier series method is proposed to analyze the in-plane vibration of rectangular plates with elastically restrained boundary conditions, in which the in-plane vibration displacements along two directions are both expressed as the superposition of a double Fourier cosine series and four supplementary functions in the form of the product of a polynomial function and a single cosine series expansion. The use of these supplementary functions is to overcome the discontinuity problems encountered in the displacement partial differentials (normal and shear stresses) along the edges. All the frequency parameters can be easily obtained by solving a standard matrix eigenvalue problem. Numerical examples show that the proposed method can converge rapidly and give highly precise results. From the large amount of the literature survey, this work appears to be the first time to obtain the analytical solutions for such problem, and then enrich and develop the plate-shell theory. Subsequently, through the introduction of Dirac delta function, the current method is further extended to model the in-plane vibration of rectangular plates with arbitrary elastic point supports, in which the number of the edges point-supported, the number and locations of the supports along each edge, the stiffnesses of the supporting springs are all arbitrary. Calculated results verify the effectiveness of this method, and can also serve as the validation bench in the development of other solving approach in future.The dynamic prediction model of two elastically coupled rectangular plates with general boundary conditions is established, in which the bending and in-plane vibrations in each plate structure are both taken into account. Two sets of 2-D improved Fourier series are used to describe the flexural and in-plane displacement fields. Along the structural conjunction, four types of uniform coupling springs are introduced to completely model the coupling effects, namely bending moment, transverse shear, in-plane longitudinal and in-plane shear. Since the displacement functions can be expanded by the proposed 2-D improved Fourier series smoothly enough in the whole solving domain, then the Rayleigh-Ritz procedure based on energy principle description can give the precise solution which will be equivalent to solving the governing differential equations and boundary conditions directly. In the meantime, due to the advantages of the current displacement functions, all the internal force variables needed in the determination of power flow of the coupled plates can be obtained straightforwardly. In the numerical simulation, the comparisons with those reported in the literature as well as calculated from FEA (ANSYS) validates that the developed model can predict the modal characteristics, vibration response and vibrational energy transmission in the coupled plates structure with various boundary and coupling conditions. Different with most of the existing solution techniques, the coupled plate structure boundary and coupling conditions can be setted conveniently without any further modification of the theoretical formulations or calculation programs under the current solving framework, which represents the most general case attempted so far in the direction.A three-dimensional improved Fourier series method is proposed to predict the modal characteristics and pressure response of the rectangular acoustic cavity with arbitrary impedance walls, in which the sound field function is expressed as a standard 3-D Fourier cosine series supplemented by another six products of auxiliary polynomial function and 2-D Fourier cosine series expansion with the aim to attack the discontinuity problems encountered in the determination of pressure gradient on each impedance cavity surface. By setting the real or imaginary parts of the complex acoustic impedance into zero or infinity, the problem can degenerate into zero-velocity or pressure-release wall conditions. The current method successfully avoids solving a highly nonlinear characteristic equation iteratively, all the modal information can be obtained just by solving a standard matrix eigenvalue problem for one time. Numerical simulation analysis demonstrates that the calculated results can agree well with those from analytical solution and other solving methods, and the effectiveness of the current method is consequently verified. It is also found that this method possesses excellent accuracy and convergence.The dynamic analysis model of an acoustical cavity backed by a flexible panel structure with general elastically restrained boundaries, in which the transverse vibration displacement of the flexible panel is described by a 2-D improved Fourier series expansion to remove all the potential discontinuities involved in partial differentials of various order along the four edges. Subsequently, any classical boundary conditions as well as its combination can be easily realized by prescribing the boundary restraining spring stiffnesses into zero or infinity. In view of the position where the flexible panel is located and the acoustical characteristics on other surfaces, the supplementary functions are also introduced into the acoustic pressure expression to satisfy the pressure gradient continuity demanded in the Euler equation. The motion of the structural-acoustical coupling system is described by energy principle, and then solved by using Rayleigh-Ritz procedure to obtain all the unknown Fourier coefficients, which eventually leads to matrix formula of the system governing equation. By comparing the calculated results with those from other approaches in the literature, it is verified that the current method can give the precise natural frequencies and modal shape distributions of the structural-acoustical coupling system as well as the panel vibration and pressure response under the external excitation. The physical fact that the velocity continues on the fluid-structure internal interface is successfully realized. Moreover, there is also not any limit for the medium nature in the cavity, this method is applicable to arbitrary coupling extent.Finally, related experimental setups are designed and built up for in-plane vibration of rectangular plate, coupled plates vibration and flexible panel-cavity coupling system. And various experimental measurement works are performed. By comparing the measured results with the predicted results, the correctness of the modeling method proposed in this thesis is further validated, and various potential factors causing measuring error in the experiments are also discussed.The current method can be further extended to perform a series of study on modeling of structural-acoustical system with general boundary conditions in other solving domains, such as triangular, trapezoidal, conical and so on. It is hopeful that this will lead to a suit of mesh-free structural-acoustical analyzing technique with complete model assembly and high computation efficiency. At the same time, it will be also of reference significance for improvement of the current software calculation performance. |
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