质量-弹簧装置连接的双梁结构固有频率计算  

Natural frequency calculation of a double-beam system joined by a mass-spring device

作　　者：王静平[1] 葛仁余[1] 牛忠荣[2] 程长征[2] Wang Jingping;Ge Renyu;Niu Zhongrong;Cheng Changzheng(Key Laboratory for Mechanics,Anhui Polytechnic University,241000,Wuhu,China;School of Civil Engineering,Hefei University of Technology,230009,Hefei,China)

机构地区：[1]安徽工程大学力学重点实验室,芜湖241000 [2]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《应用力学学报》2020年第2期833-839,I0026,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11772114);安徽省自然科学基金(1808085ME147)。

摘　　要：双梁结构被用作一种新型的减振器来控制梁式结构的振动,在土木、机械和航空航天等工程中受到广泛应用。本文研究了两个平行的轴向功能梯度梁相互连接的双梁结构固有频率的计算问题,在这种双梁结构中,梁的端部受到平移和旋转两种弹性约束,同时,双梁结构通过质量-弹簧装置相互连接。基于Euler-Bernoulli梁的基本理论,将非经典边界条件下双梁结构自由振动固有频率的计算转化为一组常微分方程特征值问题,运用插值矩阵法可一次性计算出双梁结构的所有固有频率。数值算例表明,本文双梁结构量纲为一的固有频率的计算值与已有文献计算结果吻合良好。研究了弹簧刚度、质量系数和梯度参数对双梁系统的影响。数值计算结果表明,随着梯度系数?和悬挂物块的质量系数?的增大,第1阶固有频率?1逐渐减小。The double-beam system has been recently used as a new vibration absorber to control vibration of the beam-type structures.Therefore,it is used in many branches of engineering such as civil,mechanical and aerospace engineering.Natural frequency calculation of the double-beam systems is presented in this article,for the case of two parallel axially functionally graded beams are interconnected,the ends of beams are elastically restrained against translation and rotation.Besides,the beams are interconnected via a mass-spring system.Based on the Euler-Bernoulli beam theory,the governing equations of free transverse vibration analysis of double-beam system under the non-classical boundary conditions are transformed into a set of characteristic ordinary differential equations with all the natural frequencies.Then the interpolating matrix method is employed to solve numerically the governing equations of double-beam systems,all the natural frequencies of the double-beam system are calculated.It is shown that the dimensionless natural frequencies of double-beam system obtained by using interpolating matrix method are in excellent agreement with the existed results of numerical examples.Moreover,the effects of system parameters such as spring stiffness,suspended mass and gradient parameters are thoroughly examined.It is clearly seen that as the value of gradient index?and mass ratio?increases,the value of the first natural frequency?1 decreases.

关 键 词：双梁结构 固有频率 振型函数 功能梯度材料 

分 类 号：O326[理学—一般力学与力学基础]