Vibration Absorption Effect Of Parallel Nonlinear Energy Sinks On Simply Supported Beam In Thermal Environment

Nonlinear energy sink(NES)is a kind of nonlinear vibration absorber,which has excellent vibration absorption performance,it can reduce the damage of the vibration to the structure effectively.However,the higher branch of the system will be produced when the harmonic excitation increases or/and the environment temperature increases,result in the NES part or total failure.At first,the vibration of the simply supported beam in the thermal environment are investigated,and then the effects of NES on vibration suppression and the elimination of higher branch of the simply supported beam are mainly studied under the different excitation and thermal effect.The first-order shear deformation theory used to describe the displacement fields of the beam,the nonlinear equation of motion for the simply supported beam in the thermal environment is derived by using Hamilton principle.The natural frequencies of the simply supported beam are calculated at different temperatures and compared with simulation results,the correctness of the theoretical model is proved.The analysis shows that the effect of thermal stress on structural stiffness is the main reason for decreasing the natural vibration frequency of structure.Finally,the nonlinear frequency responses of the simply supported beam under different excitation amplitudes and different temperatures are studied.Parallel NES is used to suppress the vibration of the primary structure.The vibration absorption efficiencies of the single and parallel NESs are comparatively investigated.The equation of motion for the system under harmonic excitation is derived and the dynamic responses are analyzed by using numerical method.Under normal temperature,through studying the influences of the installation locations and parameters of the single and parallel NESs respectively,it is found that the vibration absorption efficiency of the parallel NES is better than that of the single NES which having the equal mass with the former absorber.Under the consideration of the variation in the resonance frequency of the primary structure along with temperature,the stiffnesses of the single and parallel NESs are optimized under different temperatures.The results indicate that the parallel NES always has the higher vibration absorption efficiency than that of the single NES,and the advantage of the parallel NES is more obvious when the primary structure is under the higher temperature.The effects of nonlinear energy sinks on vibration suppression of a simply supported beam under different harmonic and shock loads are investigated.The numerical method mentioned above can not be used to study the higher branch responses of the system,so we need use analytic method for further analysis.The slow flow equations of the system are derived by using complexification-averaging method,and the validity of the derivation is verified.By comparing the vibration absorption of single and parallel NES of equal mass,it is found that the parallel NES can eliminate higher branch responses of the system to a certain extent under the harmonic load.Furthermore,it is found that parallel NES can eliminate the higher branches of the system more effectively by tuning nonlinear stiffness and damping.Moreover,the thermal effect on natural frequencies of the simply supported beam is considered,the influences of the parallel NES’s parameters on the energy dissipation rate under shock load are investigated,and the nonlinear response of the simply supported beam with parallel NES under harmonic load and with the increase of temperature is described.