Theoretical And Experimental Studies On The Vibration Characteristics Of Disordered Two- And Three-span Beams

Multi-span beam dynamics is always the hot issue in the fields of mechanical engineering,aerospace,high-speed trains,civil engineering and other engineering.The vibration characteristics of multi-span beams with different disordered ratios are especially needed to be studied.In order to facilitate the use of analytical or semi-analytical methods to study the above problems,it is necessary to carry out the dynamic modeling and studying the dynamic characteristics of the multi-span beams for different detuning degrees.The analytical results have important engineering application values for revealing the vibration characteristics of multi-span beams.Based on the theory of Euler-Bernoulli,two-and three-span beam models are established.Comparing the advantage and disadvantage of the existing methods for solving dynamic problems,such as modal the expansion method,the finite element method,the dynamic stiffness method,the transfer matrix method,the spectral element method and the reverberation-ray matrix method,according to the actual situation,the modal expansion method is used to solve the dynamic equilibrium equation.Substituting the vibration mode functions into the boundary conditions,the frequency equations of the two-and three-span beams are obtained,and the natural frequencies are also obtained.Moreover,the results are compared with the ANSYS results to verify the correctness of the analytical method.The Duhamel integral and Laplace transform are used to compute the time response curves and frequency response curves of the structures.Based on the theoretical calculations,the main work of this paper is as follows:(1)The vibration characteristics of disordered two span beams,including natural frequencies,modes of vibration,free vibration responses,forced vibration responses are researched.On the basis of the above analyses,the disorder ratio is defined and the vibration characteristics of the two-span beam under different detuning degrees are further studied.So the influence of disorder ratio on the vibration characteristics of the two-span beam is analyzed.(2)On the basis of the research results of the two-span beam,the vibration characteristics of three-span beams are studied,especially the changing trend of natural frequency with different disorder ratios need to be studied.The change curves of natural frequencies with disorder ratio are presented,which will be helpful for three-span beam design in engineering.(3)Utilizing the influence of disorder ratio on the vibration characteristics of the disordered two-and three-span beams,some engineering structures are redesigned by changing the disorder ratio.The time history response curves of two-and three-span beams before and after optimization are computed by ANSYS to verify the feasibility of this method.(4)Experimental verification.Based on the above analyses,the experiment model is designed and manufactured according to the model in Section 2.Then the time response curves and frequency response curves are tested by LMS spectrum analyzer and LK-Navigator laser displacement measurement device for further studying the vibration characteristics of the two-span beam and for verifying the correctness of the theoretical research results.