【作者】 杨志国；

【导师】 韩广才； 闫培雷；

【作者基本信息】 哈尔滨工程大学 ， 工程硕士（专业学位）， 2017， 硕士

【摘要】 基于薄板振动的基本理论,采用半解析法研究了带有集中质量矩形薄板的振动问题,确定带集中质量薄板的固有频率及振型函数。研究了四边固支矩形薄板的振动问题,分析了四边固支板频率及振型的求解方法,可以确定四边固支矩形薄板的固有频率及振型。应用哈密顿原理与杜哈默积分得到带任意集中质量薄板在集中力、冲击力作用下动响应数值解。推导了移动载荷作用下薄板运动方程,采用Newmark逐步积分法求解移动载荷作用下矩形薄板动响应数值解。用MATLAB软件计算带集中质量薄板在集中质量的大小、作用位置、作用数量不同时薄板振动的固有频率,以及薄板的大小改变时板振动的固有频率。比较分析了带集中质量薄板与不带集中质量均匀薄板在四边简支、四边固支边界条件下的振型,分别作出了四边简支带集中质量矩形薄板在集中力、四边固支带集中质量矩形薄板在冲击力作用下的动响应图。对施加运动质量、移动力作用时矩形薄板的振动响应作了数值仿真,研究移动质量和移动力大小、移动质量和移动力速度大小、移动质量和移动力速度方向对薄板振动的影响。对比分析了带集中质量与无质量四边简支矩形薄板在移动载荷作用下的动响应,并对比分析了四边简支与四边固支矩形薄板在移动载荷作用下的动响应。对车-桥系统作了数值仿真,分析车在桥面上运动轨道的位置以及车速对桥面振动的影响。通过分析与数值仿真结果可以看出:在已知边界条件矩形薄板的频率及振型情况下,半解析法可以计算带有任意集中质量矩形薄板的固有频率及振型。基于四边固支板频率及振型的求解方法确定的频率及振型,可以计算四边固支板在集中质量作用下,四边固支带集中质量板在冲击力作用下,四边固支板在移动力作用下板的动响应。更多还原

【Abstract】 Basic theory of thin plate vibration,the vibration problem of rectangular plate with concentrated mass is studied by semi-analytical method,the natural frequency and the mode function of the concentrated mass sheet are determined.The vibration problem of rectangular plates with fixedly supported on four sides is studied,the method of solving the frequency and mode of the four-side fixed plate is analyzed,it can determine the natural frequency and vibration mode of rectangular plate with fixedly supported on four sides.In addition,using the Hamiltonian principle and Duhammer integral,the numerical solution of the dynamic response of the thin plate of concentrated mass with concentrated force and impact force is obtained.The motion equation of the thin plate under the action of moving load is deduced,numerical solution of dynamic response of rectangular thin plate under moving load is solved by using by Newmark step integral method.The natural frequency of thin plate vibration with lumped mass is calculated with MATLAB software when the size of concentrated mass,action position and number of action are different,and the natural frequency of the plate vibration when the plate size changes.The vibration modes of a thin plate with concentrated mass and a thin plate without concentrated mass are analyzed and compared under four edges simply supported and four clamped edges,The dynamic response diagram of rectangular thin plate with concentrated mass with four sides simply supported under the concentrated force and four clamped rectangular plates under impact force is presented.The numerical simulation of the vehicle bridge system is made,The numerical simulation of the vibration response of rectangular thin plate under the action of moving mass and moving force is carried out,the effects of moving mass and moving force size,moving mass and moving force velocity,velocity direction of moving mass and moving force on the vibration of thin plate are studied.The dynamic response of rectangular thin plate with lumped mass and massless quadrilateral simply supported under moving load is compared and analyzed,the dynamic responses of rectangular plates with simply supported edges and clamped edges under moving loads are compared and analyzed.The influence of the position of moving track on bridge deck and the vehicle speed on deck vibration are analyzed.It can be seen from the analysis and numerical simulation results:In the case of the frequency and mode of rectangular plates with known boundary conditions,semi-analytical method can be used to calculate the natural frequency and vibration mode of a rectangular plate with arbitrary concentrated mass.Determination of frequencies and modes based on the frequency and mode shapes of four clamped plates,the dynamic response can be calculated of the plates with fixedly supported on four sides under the effect of concentrated mass,and the four side fixed plates with concentrated mass under the impact force,and the four side fixed plates under the action of moving force.更多还原