On Dynamic Analysis Of The Closed Coupled Structure Based On The Energy Finite Element Analysis

The vibration of the structures usually cause the fatigue failure,which has a great influ-ence on the equipment's lifetime as well as the performance.In addition,the noise produced by the vibration affects the comfort of the people's daily life.With the development of the mechanical system towards the lightweight and high-speed,the source of the vibration is becoming stronger and a growing number of light-weighted structures have been applied,which make the middle-high frequency vibration problems a crucial issue in mechanical equipment manufacture and design.For the complex mechanical systems,if using some ac-curate and effective methods to predict the dynamic behavior of the mechanical systems at the design stage,the targeted measures can be taken to reduce the influence of the vibration on people's daily life,and therefore improves the design efficiency.For existing mechanical equipment,an accurate and effective dynamic prediction method can also help the people to optimize the structure and therefore improve the performance as well as reduce the noise.Energy Finite Element Analysis is an effective dynamic prediction method developed in recent years.This method is applicable in wide range frequencies and has a less computation cost.This method can also provide the response at anywhere inside the system and gives an intuitive results of the power flow in the system.This paper is supported by National Science Foundation project(Number:51275275 and 51675306)and studied the application of Energy Finite Element Analysis on the plates.Especially for the coupled plates in the engineering.The main points of this paper are listed as follows.Using the dispersion relationship of the waves in the thin plates,the wave solution of the flexural wave and in-plane wave are derived,which provides a foundation for the calculation of the energy transfer coefficients.Then the energy density governing equation for the flexural wave and in-plane wave are deduced based on the plane wave solution.The Energy Finite Element Analysis is performed on the single plate,and the Galerkin method is utilized to solve the energy density governing equation.The quadrilateral element is used to partition the regular plates and the triangular element is used to partition the plate with irregular plate.The compatibility of the different types of the element in Energy Finite Element Analysis is discussed.The introduction of the multiple types of element eliminates the limitation of the Energy Finite Element Analysis on the solving domain,and therefore enlarge the application range of the Energy Finite Element Analysis.On the basis of the wave solution,the equilibrant equations of the coupled plates with arbitrary coupling angle are established based on the force balance and geometry compatibil-ity of the coupling boundary.The energy transfer coefficients of the certain incident angle when different waves impinging are obtained.The energy transfer coefficients in Energy Finite Element Analysis are obtained by combining the reverbrant wave assumptions.The effects of the plate thickness,excitation frequency and coupling angle on the energy transfer coefficients are studied.Further,the energy transfer coefficients are introduced into coupled plate structure with the multiple plates coupling on a common edge,and energy transfer co-efficients of a three plates system are studied,energy transfer coefficients of both the flexural wave and in-plane wave are obtained.The energy coupling relationship is built based on the energy flow conservation princi-ple on the coupling edge and the energy coupling matrix is built based on the energy transfer coefficients with the consideration of all the three types of wave.The energy coupling matrix for the quadrilateral element,triangular element and hybrid elements are derived,providing a general method to process the coupling structures in Energy Finite Element Analysis.The Energy Finite Element Analysis is used to analyze closed cabs made up of coupled plates with all three types of wave,which lay a foundation for the acoustic analysis for the inside space of the closed structures such as driving room.