部分浸入水中弹性支承Timoshenko梁动力特性

Dynamic Characteristics of Timoshenko Beam Partly Immersed in Water on Coupled Elastic Foundation

研究了部分浸入流体中自由端具有集中质量块的等截面弹性支承Timoshenko悬臂梁横向振动的固有频率和振型特征.考虑梁横截面转动和剪切变形以及集中质量块引起轴向压力的影响,建立了支承处弹性水平位移约束和转动约束耦合情形下悬臂梁横向自由振动的数学模型.由于集中质量块的惯性力和惯性矩,此模型的边界条件与振动频率相关.推导了Timoshenko梁的频率方程和振动模态的广义正交条件.数值研究了集中质量块质量、转动惯量、质心距以及弹簧刚度系数等参数对Timoshenko悬臂梁固有频率的影响.数值结果表明:由于横截面转动和剪切变形效应的影响,相比于Eu ler-Bernou lli梁模型,Timoshenko梁的固有频率减小,对高阶频率的影响尤为显著;弹簧刚度耦合项的增大将减小梁的固有频率;轴向力的增加将减小梁的低阶固有频率,但对高阶固有频率的影响不大.

Natural frequencies and the corresponding modes of an elastically supported cantilever Timoshenko beam carrying a tip mass partly immersed in water are investigated.Taking into account the effects of the cross-section rotation,shear distortion and compression axial force due to the tip mass,the mathematical model for free vibration of a cantilever beam is presented,in which constraints of the elastic horizontal displacement and elastic rotation are coupled.Due to the inertial force and inertial moment of the tip mass,boundary conditions of the mathematical model are frequency dependent.The frequency equation and the generalized orthogonal condition for the vibration modes are established.Influences of tip mass,moment of inertia,location of tip mass and coupled spring-stiffness coefficient,etc.,on the natural frequencies are presented numerically and discussed.It is shown that,compared with the model of Euler-Bernoulli beam,due to the cross-section rotation and shear distortion of the beam,the natural frequencies of the Timoshenko beam decrease,especially for the higher order natural frequencies.The addition of coupled spring-stiffness coefficient will reduce the natural frequencies to different extent,and the axial force reduces the lower order natural frequencies while has a negligible influence on the higher order ones.