Analysis Of Vibration Characteristic And Nonlinear Of Vibration Response Of Damaged Cantilever Beam

Cantilever beam is a common beam structure in practical engineering applications.It is widely used in mechanical equipment,energy and chemical industry,civil construction and other fields.For example,aircraft wings in the aerospace field,solar stretching panels in the aerospace field,turbine blade structures in energy equipment,and load-bearing cantilever beams commonly used in civil buildings are typical cantilever beams.It will bear a variety of loads in service,and the beam structure will inevitably produce a variety of damage,which will cause the failure of the physical properties of the beam structure and even the fracture of the beam,thus causing a series of safety accidents.Therefore,the analysis of the vibration characteristics of cantilever beam structure and the timely and effective detection of its damage are the key problems to be faced and solved in engineering.Aiming at the bending deformation of cantilever beam,the equation of transverse bending vibration is derived based on Euler-Bernoulli beam theory.The single-crack cantilever beam is simplified as two-section beam connected by torsion spring,its dynamic differential equation is established,its natural frequency solution formula is deduced,the influence of crack depth and location on the natural frequency of the cracked cantilever beam is discussed,and the simulation modal analysis is carried out in ANSYS-workbench finite software to verify the accuracy of the derivation and analysis of the established dynamic differential equation.There are many cantilever beams with mounted contact surfaces in actual engineering structures.Because the influence of contact on the vibration characteristics of structures is very complex,it not only directly affects the dynamic service performance of structures,but also affects the amplitude,frequency and phase of structural vibration signals.In this paper,modal analysis of cantilever beam with mounted contact surface is carried out by using modal analysis technology from two factors of contact stiffness and friction coefficient of contact surface.The influence of contact stiffness and friction coefficient of contact surface on its natural frequency is studied.In addition,the non-linearity of structure damage and the non-linearity of the contact behavior of the joint surface are considered.Firstly,the cantilever beam is excited by a fixed frequency harmonic in the simulation environment,and the influence of damage degree,damage position,contact stiffness and friction coefficient on the high-order harmonic component of the response signal is analyzed.Secondly,the triangular beam excitation of the cantilever beam is studied.The degree of damage,contact stiffness and friction coefficient are used to analyze the nonlinearity of the cantilever beam structure system based on the nonlinear output frequency response functions.Finally,a simple cantilever beam experimental platform considering the installation of contact surface in practical engineering structure is built to carry out hammering experiments.The contact stiffness between two contact surfaces is simulated by flat springs with different stiffness coefficients.The influence of the contact stiffness of the joint on the natural frequency of the cantilever beam is analyzed approximately.In addition,the influence of damage degree and contact stiffness on the non-linear detection index based on the non-linear output frequency response functions is analyzed.