Vibration Behavior Analysis And Optimization Of The Double-layer Thin Revolutionary Shell Covered With Porous Materials

Porous materials have been widely used for passive control of the acoustic-vibration problem in many fields,such as the vehicle,aerospace,geophysics and civil engineering.Compared to the general plate and shell structures,the shell of revolution is of excellent structural strength,and its flow line shape can reduce the air flow resistance.According to this characteristic,the shell of revolution had been used in traffic engineering,such as the submarine,airplane,high-speed train and supersonic car.Laying the porous materials on the plates and shells can reduce the vibration and noise of the structures.But this type of structure is difficult to model.The solution method usually adopts the FEM and errors are easily produced in the high frequency.For this reason,this paper tries to analyze the dynamics of the thin revolutionary porous shell and the double-layer thin revolutionary shell covered with porous materials.The main research contents are divided into two parts: the first part is the establishment of the theoretical model of the thin revolutionary porous shell,and the analysis on its vibration characteristics.The second part proposed a model of a thin elastic revolutionary covered a thin porous layer based on the work of the first part.The third part discussed the influence of the porous layer on the vibration effect and optimized the parameters.In the existing modeling methods of fluid-saturated porous structure,three ways were usually used.In some of the literature,the porous models were developed by making assumptions for fluid displacement.In the some of the literature,the porous medium is equivalent to the rigid or flexible effective fluid model according to the bulk modulus of skeleton and fluid.Finally,in the other literature,an effective medium method was adopted.It also converted the porous medium into a kind of continuous medium.The numerical methods are the finite element method.However,in the high or intermediate frequency range,the calculation errors of the FEM are greater.In order to control its accuracy,number of elements would be increase,which may reduce the computational efficiency.Based on the Biot theory and the elastic theory of thin shell,a first order different equations of the revolutionary porous shell was established in this paper.This method can be applied to various boundary conditions.It makes no assumption of fluid displacement,and it also takes account for the relative action between the fluid and solid phase.A high precision numerical method,named novel extended homogeneous capacity high precision integration method,was proposed to solve this equation combined the boundary conditions.Numerical results were given and compared with experiment,equivalent effective fluid model and effective medium method for verifying the correctness.The influence of the geometric parameters and physical constants on the transverse vibrations had been discussed.In the work of the model for the double-layer thin revolutionary shell with porous materials,letting the porosity of the porous layer close to 0,the control equations of thebase shell were obtained by the model of the porous layer.The normal and tangential interaction between layers,and the eccentric torque caused by the tangential interaction were introduced into the inhomogeneity terms of the control equations of the single-layer shell by the force analysis.Under the superposition principle,he displacement function expressions with the unknown coefficients were derived.Combining the deformation coordination relationship and displacement continuous condition,the unknown coefficients are obtained,and the numerical model for analysis the vibration behaviors of double-layer thin revolutionary shell with porous materials was proposed.The influence of the porous medium on the dynamic response of the double-layer thin revolutionary shell with porous materials was discussed by response surface methodology.The Multi-Objective Optimization about vibration behavior of the double-layer thin revolutionary shell was finished by the ideal point method.The vibration behavior had been improved.Finally,the content,results and deficiencies of this article were summarized.And the paper gave prospects of the application and future research direction of the present theoretical model.