Analysis Of Vibration Characteristics Of Pre-Torsion Cantilever Beam And Variable Installation Angle Crack Beam

The cantilever beam structure is an important part of the cantilever machinery in the fields of hydraulic machinery and aeronautical engineering.It is widely used in axial flow turbine,aero-engine and turbine vane rotating machinery.Considering the unreasonable design of the beam structure and the existence of cracks and damage on the beam in reality,the integrity and stability of the beam system are often greatly affected.Therefore,this paper studies the cantilever beam model with variable section and the cracked beam model with equal section from two perspectives.The main contents and conclusions of this paper are as follows:(1)In the study of the variable section cantilever beam,the structural model of the variable section cantilever beam with pre-torsion angle is given.The variable of pre-torsion angle is introduced into the calculation of the moment of inertia of the section,and the variable of rotational speed is introduced into the calculation of centrifugal inertia force.Newmark-β integral method is used to solve the derived discrete equations of the beam in time,and the dynamic equations of the beam system are obtained by superposition of finite elements.(2)Based on the start and stop the two kinds of working conditions of beam dynamics analysis,by studying the variable cross-section cantilever beam of the pre-torsion angle changes from 0° to 45° and the change of beam length from 0.1m to 0.3m,found the end of the beam is moving parts would be affected by the changes of the two coupling,can make within the yoz plane perpendicular to the rotating flat end part of the increase,As a result,the end of the beam and the shell of the rotating machinery in the two working conditions have serious consequences such as rubbing.By comparing the effects of different rotating speeds and different pre-torsion angles under specific rotating speeds on the natural frequency of beams,this paper provides a reference for the selection and design of commonly used beam structures in engineering and the prevention of rubbing and collision.(3)In the study of cracked beam with equal cross-section,in order to avoid the influence of various variables on the crack parameters,the beam is simplified as a cantilever beam with equal cross-section,and the beam element is divided into two types:crack element and crack-free element.The local flexibility of the beam under bending moment and shear force is analyzed.The stiffness matrix of the crack element is obtained by superposition of the compliance of the crack element and the compliance of the crack-free element.(4)By studying the variation of the installation angle from 0° to 45° and the different combinations of crack parameters of the beam with equal cross-section,the frequency characteristics of the beam with different installation angles and crack parameters are discussed.The results show that the first three natural frequencies of the beam under different crack parameters decrease regularly with the increase of installation angle,and the crack parameters can still be quantitatively identified by frequency characteristics.This study is of reference value to crack identification,monitoring and crack propagation prevention.