Determinated And Uncertain Dynamic Characteristics Of Quasi-periodic Supported Beam Structures With Damage

Railway track beam and periodic supported bridge beam are two typical periodic supported beam structures in engineering.Uncertainties in the process such as manufacturing,degradation and damage are unavoidable,the original periodic structure will be transformed into quasi-periodic structure,which will lead to the change of its dynamic characteristics.At present,the research mainly focuses on vibration localization of quasi-periodic structures,while the research on damage identification using the dynamic characteristics of quasi-periodic structures is relatively few.In this thesis,the dynamic characteristics of quasi-periodic track beam and quasi-periodic bridge beam are studied by theoretical methods.The main research work of this paper is as follows:(1)The frequency response characteristics of the track beam with detuning periodic support stiffness and damping and with detuning periodic support positions were studied.The partial differential equation of motion of the long sleeper buried track and track with track-sleeper coupling were derived by using Euler-Bernoulli beam model and Timoshenko beam model respectively.The frequency response function expression is obtained by using the Galerkin method,which is usable for non-periodic and periodic supports cases.The validity of the theory is verified by comparing the results with the finite element method.Numerical results on the frequency response and frequency response ratio characteristics of track beams under single support damage,support position offset and uncertain support damage and offset are calculated.It is found that the random uncertainties or quasi-periodicity of periodic support are reflected in the frequency response characteristics of track beams in different modes.The quasi-periodicity of support will lead to local resonance of track beams,and then the frequency response ratio will fluctuate.(2)The dynamic response characteristics of vehicle-track coupling system with quasi-periodic support and geometric irregularity on track were studied.The vehicle-track coupling model of single axle vehicle system was established,and the partial differential equations of vehicle-track coupling system vibration for two contact models were derived.Galerkin method was applied to expand the differential equations into ordinary differential equations.Newmark-beta method was used to solve the response of vehicle system under the conditions of quasi-periodic support,one-way loss of support stiffness and damping,and track irregularity.It is found that the wheel displacement could well reflect the change of track beam stiffness.A frequency domain analysis method for coupled system of periodic irregularity track was proposed.The amplitude of wheel-rail contact force fluctuation under different irregularity wave amplitude,wave length and vehicle speed were solved by this method.The wheel-rail contact state can be judged by comparing the amplitude of wheel-rail contact force fluctuation with the weight of vehicle system(3)The modal localization of a quasi-periodically multi-supported beam with weakly coupling was studied.Firstly,the analytical expressions of natural frequencies and modes of three-span periodically supported beams were deduced by modal superposition method,and the critical values of support stiffness of three-span periodically supported bridges when they reach weak coupling state were solved.It was found that the support damage under weak coupling would lead to frequency locus veering and mode localization.Taking a 7-span periodically supported viaduct as an example,the modal and natural frequencies of the Viaduct under damage condition were calculated.It is found that when the damage reaches the critical value,the modal localization and frequency loci veering would occur,and the modal localization position is near the damage support.