Radiative Energy Transfer Model And High Frequency Vibration Analysis Of Curved Beam Structures

As a common structure in the field of aerospace engineering,the curved beam is widely used in arched structures of aircraft,rockets,and other flying devices.During service,flying vehicles often face complex and harsh flight environments,and the body structure may be subjected to high-frequency aerodynamic noise or engine noise excitation.This excitation could cause structural fatigue damage and could even produce structural strength problem,resulting in direct damage.Therefore,high-frequency response analysis of curved beams and their coupled structures has become an important issue to be addressed in engineering.Traditional deterministic analysis methods,such as the finite element method(FEM),the boundary element method(BEM),etc.,require fine meshes to describe the short-wavelength deformation of the structure under highfrequency modes,which increases computational costs and places high demands on modeling structural details.To address this issue,several energy-based analysis methods have been proposed,such as the statistical energy analysis(SEA),the energy finite element analysis(EFEA),and the radiative energy transfer method(RETM).Among them,RETM is analogous to geometric acoustics and can precisely estimate the local energy distribution and power flow direction of the analyzed structure.Currently,RETM has not yet been applied to the energy prediction of curved beams and their coupled structures,and thus this dissertation aims to extend RETM to high-frequency vibration analysis of curved beams and coupled curved beam structures.The main contents of the dissertation include:(1)High-frequency statistical characteristics analysis of curved beamsThe dissertation derives and calculates the control equations of the Euler-Bernoulli curved beam,and obtains high-frequency analysis parameters such as input power,modal density,internal damping factor,energy attenuation coefficient,modal overlap factor,and coupling loss factor between subsystems.The SEA and RETM models of the curved beam are presented,and their applicabilitye ranges on the damping-frequency plane are given.In numerical examples,the energies of SEA and the wave method are compared each other’s results,and it is found that SEA cannot present the non-uniform energy distribution of curved beams which shows its inapplicability under large damping conditions.(2)Radiative energy transfer model for curved beamsTaking carbon nanotube reinforced composite(CNTRC)curved beam as an example,the control equations of the curved beam ignoring the axial force effect are derived,and the RETM model of the curved beam under transverse point excitation is established.The accuracy of the model in calculating the high-frequency vibration response of the curved beam is verified by comparison with the theoretical solution.Furthermore,the differences in energy density of curved beams based on the Euler-Bernoulli beam theory and the Timoshenko beam theory under high-frequency excitation are discussed.Finally,the influence of the size of the curved beam structure,the distribution form of CNTRC,and the volume fraction of carbon nanotubes(CNTs)on the high-frequency energy response is studied.(3)Wave propagation and high-frequency vibration analysis of coupled curved beamsFurther derivation of the vibration control equations for Timoshenko curved beams,and the time-averaged powers generated by axial force,bending moment,and shear force in the curved beam are calculated for the two beam theories.Then,based on the semi-infinite assumption,the energy transfer coefficients of Euler-Bernoulli curved beams and Timoshenko curved beams coupled structures are derived.Finally,the RETM model of the coupled curved beam is established,and the energy responses of different waves are calculated.The accuracy of the proposed RETM model is validated by comparing it with the analytical solution.