Modeling And Research On The Characteristics Of Three-dimensional Trapezoidal Cavities And Their Coupling With Plates Under Various Impedance Walls

The three-dimensional trapezoidal cavity with various impedance walls is widely used in the fields of national defense and civilian industry as a basic structure,such as aerospace,ship cabin,vehicle engineering and building.However,the main objects are rectangular and annular cavities in the existing methods,and rarely involves the acoustic characteristics of trapezoidal cavity.Based on this point,the modeling method and acoustic characteristics of the three-dimensional trapezoidal cavity and its coupling system with various impedance walls are studied in the thesis by using an improved Fourier series method and coordinate transformation.The research contents of the thesis are described as follows briefly:The unified analysis model for the acoustic characteristics of a closed three-dimensional trapezoidal cavity with various impedance walls is established.On the basis of the relationship of geometric parameters among triangle,rectangle and trapezoid,the energy functional of the three-dimensional cavity,which represented by trapezoidal cavity with various impedance walls,is constructed by the three-dimensional improved Fourier series and coordinate transformation.Natural frequency and sound pressure admissible function of the trapezoidal cavity are obtained by the Rayleigh-Ritz method.Then,the steady-state response of sound pressure in the cavity can be obtained by a sound source excitation.Numerical examples are used to obtain the effect of dimensional parameters,impedance walls and media on the acoustic characteristics of cavity.Based on the numerical comparison,the accuracy of modeling method for the three-dimensional trapezoidal cavity is verified.On the basis of the study of the single structure,the unified analysis model for the acoustic characteristics of a multi-three-dimensional trapezoidal cavity coupling system is built.The real performance of the coupling area is simulated by introducing the coupling potential energy.Then,bring the potential energy into the Lagrange function of each sub-cavity to form the energy functional of the coupling system.The energy equation of the coupling system can be solved by using the Rayleigh-Ritz method.The curves of sound pressure and energy with frequency in each sub-cavity are obtained by adding sound source excitation.The effect of excitation amplitude and impedance walls on frequency and energy curve of the coupling system are studied by numerical examples.Comparing the results of coupling systems with different shapes,the validity of the unified analysis model for the acoustic characteristics of the coupling system is verified.The unified analysis model of vibration and acoustic characteristics for trapezoidal cavity-plate-cavity coupling system composed of two three-dimensional trapezoidal cavity and one orthotropic trapezoidal plate is established.The three-dimensional modified Fourier series is compressed into a two-dimensional series to construct the energy functional of a trapezoidal plate with elastic boundary.The plate-cavity coupling potential energy is added to the energy functional of trapezoidal plate and cavity to ensure the continuity of the coupling area.The Rayleigh-Ritz method is used to solve the linearized equation of the coupled system.Through the corresponding relation between the coupling frequency and the sub-structure frequency,the difference between the strong coupling and the weak coupling is discussed.The effect of important factors such as boundary conditions and media on the steady-state response is studied by the external excitation.In addition,the effect of cavity depth and plate thickness on sound insulation are calculated,which providing ideas for vibration and noise reduction.The numerical comparison verifies the correctness of the trapezoidal cavity-plate-cavity coupling system.Experimental studies on the steady-state response of sound pressure in three-dimensional trapezoidal cavity,multi-three-dimensional trapezoidal cavity coupling system and trapezoidal cavity-plate-cavity coupling system are carried out.As the isotropic material is a special form of orthotropic material and it is easier to obtain,an isotropic plate is used in the experiment to verify the correctness of theoretical analysis of the trapezoidal plate and the trapezoidal cavity-plate-cavity coupling system.By comparing the results of experiment and numerical calculation,it can be found that there is a good agreement between them,so the effectiveness of the analytical model established in this thesis is validated.