Research On Transverse Vibration And Boundary Parameters Of Axially Travelling String Systems With Non-classical Boundaries

Satellites cable,elevators and conveyors,etc.which can be simplified as axially moving string systems,have attracted much attention due to their vibration problems.Currently,the research on axially moving strings mainly focuses on the classical boundary conditions.But there is a lack of research on non-classical boundary conditions.The movement of non-classical boundary and fixed boundary problems are closely linked to engineering practice and are also the key issues in boundaries vibration control of highspeed moving continuum.In this paper,an axially moving string system with a mixture of classical boundaries and non-classical boundaries is researched.Firstly,the model of commonly studied strings system is established,such as fixed-length and variable-length strings of nonclassical boundaries(damping?spring_damping?mass_spring_damping boundary).Then,the dynamics equation and the continuity condition of the non-classical boundaries are established by Hamilton's variational principle.The variation equation of incident wave and reflected wave of the axially moving string system with different boundaries is deduced according to the Traveling wave theory,which is the boundary reflection law equation.Secondly,based on the reflected wave on both sides,the expression of reflected wave is obtained by the initial conditions and the continuity condition of both sides.Then the reflection process is deduced in three stages,and the analytic expression of transverse vibration solution is obtained.Finally,the influence on the free vibration response with non-classical boundary fixed-length and variable-length string systems are analyzed by different boundary parameter,such as: spring,damping and mass.The relationship between the amplitude ratio of reflected wave and incident wave at the boundary of string system is taken as the control function.Damping coefficient is been taken as a variable to determine the optimal control effect and control the transverse vibration of the string system effectively.Through the research above,it can provide theoretical basis for the design and vibration control of the axially moving system in engineering.