Vibro-acoustic Characteristics Of Rectangular Plates

The structural vibration problems and acoustic radiation problems caused by structural vibrations have attracted much attention in engineering practice.The basic structure in projects can be accurately simulated by rectangular plates,such as the building's wall and floor,the car's shell and hull shell and so on.Therefore,rectangular plates are often used by scholars as the basic object for studying the acoustic radiation characteristics of structural vibrations.The principles and characteristics of vibration and acoustic radiation of the basic structure form of rectangular plates are thoroughly studied,which helps to understand the characteristics of more complex structures in essence.The problems of vibration and sound radiation are of great significance to the control of structural vibration and noise.Rectangular plates are often used as the basis for studying acoustic radiation in more complex plate-like structures.Most studies are based on the ideal condition of plates in an infinite baffle,including issues such as the radiation efficiency of multi-modal responses.For the structural vibration problem,the simple geometric form of the structure has analytical solutions under some particular boundary conditions.For complex structures and complex boundary conditions,finite element modeling is generally used,and then numerical calculations are performed.We choose to use the finite element method.For acoustic radiation problems,the common numerical methods are the finite element method and the boundary element method.The difference between the two is that the former has to mesh the entire acoustic domain,and the latter only meshes the surface of the acoustic domain.We choose to use the direct boundary element method,which regards boundary acoustic pressure and normal velocity as unknowns.In this paper,rectangular plates are used as the research object for structural vibration problems and structural acoustic radiation problems.Firstly,shell structures commonly used in engineering are modeled as Mindlin plates and membrane.Then,according to the basic theory,the acoustic Helmholtz equation is deduced.The boundary integral equations of the acoustic interior field problem and the external field problem are deduced using the weight function method.We use coordinate transformation to solve the problem of integral singularity,the CHIEF method is used to solve the non-uniqueness of the solution at the eigen frequency.The quadrilateral isoparametric element is used to discrete the structure and its surface,and the finite element and boundary element formulation is deduced.Finally,the acoustic radiation characteristics of structural vibrations are studied.The resonant modes and their sound radiation properties are discussed in wavenumber space.The radiation efficiency dependence on the parameters associated with the material properties and geometry of the plate is discussed.