Research On Vibration Characteristics And Excitation Responses Of Cracked Beams With Moving Effect

Beam structures are widely used in engineering fields,appearance of cracks may enormously affect the safety of the beam structures.At present,as a kind of integrated detection method,the crack detection technology based on structural vibration has gradually been widely applied and recognized.Meanwhile,the progress in such a crack detection technology and the expansion of its application depends on further study on dynamics theories of damage structural.For the vibration of cracked beams,current studies are mainly aimed at static beam structures.However,many actual engineering structures may be summarized as beam structures under moving state.To realize the online crack detection of such structure,it is necessary to develop the study on vibration characteristics and excitation responses of cracked beam with moving effect.In this paper,the continuous stiffness equivalent model is used to simulate the crack effect on beams,axial moving effect and rotational moving effect are also considered.The vibration characteristics and excitation responses of beams under the action of crack effect or moving effect are studied,and the co-action mechanisms of these two effects are investigated.By means of the continuous equivalent stiffness model of cracked beam,a cracked beam is modeled as an intact beam with its bending stiffness changes continuously along its length direction.The vibration control equation is establish,and transfer matrix method is adopted to solve the characteristic equations.Validlity and applicability of the continuous equivalent stiffness model is verified.The impacts of crack parameters on vibration frequencies of the cracked beams are discussed.In addition,the continuous equivalent stiffness model is extend applied to the cracked beams made of functionally graded material(FGM),feasibility of such a application is discussed,and the impacts of functional grade and crack depth on vibration frequency of the cracked FGM beams are analyzed.Considering the axially moving effect and crack effect simultaneously,vibration control equations of the beam is established.Matrix transfer method and Galerkin truncation method are respectively adopted to solve the characteristic equation.Natural frequency variation under the co-action of these two factors is analyzed.Result show:both crack effect and axial moving effect can result in frequency attenuation of a beam.Meanwhile,the impact of these two effects is not independent.Coupling effect can be found that increase of axial speed will accelerate frequency attenuation caused by cracks;and crack deepening will accelerate the frequency attenuation caused by speed increase.Green function method is adopted to solve the displacement response of the beams under lateral external excitation.The following conclusions can be obtained:when the external excitation frequency is lower than the initial fundamental frequency of the beam,both axial speed effect and crack effect are able to cause increase of displacement response amplitude of the beam;when the external excitation frequency is higher than the initial fundamental frequency of the beam,both the axial speed effect and crack effect are able to cause decrease of displacement response amplitude of the beam.Moreover the coupling effect is obvious when the two factors act together.The vibration control equation of cracked beam with rotational moving effect is established,matrix transfer method and assumed modes method are respectively adopted to solve the characteristic equation.Research shows that under the action of rotational moving effect,the vibration frequencies of beams increases.If crack effect and rotational moving effect are considered simultaneously,then increase of rotational speed will weaken the frequency attenuation caused by cracks,and crack deepening will accelerate the frequency increase caused by rotation effect.Green function method is also adopted to solve the displacement response.Results show:if crack effect and rotational effect exist simultaneously and the rotational speed is low,the displacement response of a beam under external excitation is mainly controlled by crack parameters.The deeper the crack,the larger the amplitude,and the amplitude difference is obvious under different crack depth.Under high rotational speed condition,rotational speed has gradually become the main control factor for displacement response of a beam,under such circumstance,even if a crack exists on the beam,the amplitude difference caused by the crack with different depths is not obvious.For multi-cracked beams,the continuous equivalent stiffness for beams with single crack is extendly applied to beams with multi-cracks.Beams with double cracks are used to analyze vibration characteristics and excitation responses of beams under the co-action of multi-crack beam effect,axial motion effect and rotational motion effect.Research shows that the change in crack spacing makes the natural frequencies of different orders under different boundary fluctuate.If axial motion effect exists the change range and fluctuation amplitude of the frequency will increase.If rotational motion effect is considered,the frequency fluctuation caused by change in crack spacing will be narrowed.