| Composite material structure has the advantages of high specific strength,light weight,wear resistance,corrosion resistance,etc.,so it is widely used in large-scale engineering fields such as marine engineering and aerospace,thus making up for the vacancy of traditional singlephase materials with low strength and poor adaptability.Numerical analysis of the vibration of the system structure in the early stage of the structure design is essential for rationally optimizing the structure,reducing the sound and vibration level of the structure,and ensuring the durability of the equipment.At present,traditional numerical analysis methods have certain limitations in solving high-frequency vibration problems.Based on the classic laminated sheet theory,this paper establishes different energy flow analysis models for typical working conditions(thermal environment and fluid environment),typical materials(fiber type and damping type),and typical structures(single plate and coupling plate)to obtain the energy density under high frequency excitation.It provides strong theoretical support for the prediction of high-frequency vibration response of composite structures.For the laminate in thermal environment,the governing equation of wave number is derived by using the governing equation of vibration.The energy density control equation is deduced from the relationship between energy density and energy intensity and power balance,and its discretized form is obtained by conventional finite element,so as to obtain the energy density value of the board everywhere.The validity of the model is verified by comparing the energy finite element solution with the analytical solution,and the variation law of energy density is discussed in terms of different frequencies,structural damping,temperature difference and excitation value.For the laminate in the fluid environment,an energy flow analysis model is established from two aspects of one-side fluid action and fully immersed fluid action.Based on the fluidrelated assumptions and the boundary conditions of each plane,the fluid pressure of the plate under each working condition is deduced,thereby deriving the energy density control equation and realizing the calculation of the energy finite element.The effective mass and additional radiation damping effect are analyzed,and the influence of various factors(fluid density,flow velocity,etc.)on the energy density is analyzed.For the coupled plate structure,the control equations of longitudinal wave and shear wave energy density are derived by comprehensively considering the influence of out-of-plane and in-plane vibrations.The semi-infinite coupled plate structure is used instead of the finite structure,and the energy transfer coefficient is obtained by using the displacement solutions corresponding to different incident elastic waves and the conditions at the coupling boundary.A "virtual element" is introduced for the coupling boundary,and the coupled element stiffness matrix is obtained by using the energy flow transfer law at the coupling boundary,while other elements still use the derived four-node element stiffness matrix to realize the energy finite element calculation.Finally,the law of energy transfer coefficient and energy density law are discussed from the factors of frequency and damping.For the damped composite structure,based on the classical laminated plate theory and its related assumptions,the deformation and force analysis of the laminated structure is carried out,and its vibration control equation is obtained.In addition,the damping structure is treated equivalently,the position of the physical mid-plane is obtained by the principle of minimum strain energy,and the equivalent damping of the structure is obtained by the complex stiffness method.Still taking the coupling plate as the object,the damping structure is numerically analyzed from the aspects of damping characteristics,energy density and vibration reduction performance,and some requirements for the design of the damping structure are put forward. |
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