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Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer

机译：用Terfenol-D层振动控制功能分级梁的差分正交解决方案

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摘要

The governing differential equation of motion for vibration control of a functionally graded material (FGM) beam using magnetostrictive layers is solved using differential quadrature method(DQM). It is known that, when differential quadrature is implemented directly for the solution of governing differential equation for vibration control of beam, it is required to convert the generalised eigenvalue problem into standard eigenvalue problem. However in the present work, the original differential equation of vibration control of beam is be separated into two simpler second and fourth order differential equations using the separation of variables in conjunction with the characteristics equation of damped single degree of freedom system. Solution of corresponding two simpler differential equation also yields damped natural frequency and damped factor comparable to that of the former approach. It is to be noted that using either of the solutions using differential quadrature method S point description of the physical domain at boundary is used to obtained the differential quadrature equations for the various boundary conditions of the beam. In order to assure the accuracy of formulation and solution using DQM, convergence behavior of natural frequencies is examined for five combinations of boundary conditions and comparison studies from the two solution approaches is presented. The effect of the location of the magnetostrictive layers, material properties and control parameters on the vibration suppression are investigated.
机译：使用差分正交方法（DQM）求解使用磁致伸缩层的功能上梯度材料（FGM）光束的控制差动方程。众所周知，当直接实施差分正交以用于控制光束的振动控制的控制微分方程的解决方案时，需要将广义的特征值问题转换为标准的特征值问题。然而，在本作本作中，使用变量的分离结合阻尼单一自由度系统的特性方程，将光束的原始差分方程分成两个更简单的第二和四阶微分方程。相应的两个更简单的微分方程的解决方案也产生阻尼的固有频率和阻尼因子与前一种方法相当。应注意，使用使用差分正交方法的任何一个解决方案，边界处的物理域的描述用于获得光束的各种边界条件的差分正交方程。为了确保使用DQM的配方和溶液的准确性，检查了自然频率的收敛行为进行了五种边界条件的组合，并提出了两种解决方案方法的比较研究。研究了磁致伸缩层的位置，材料特性和控制参数对振动抑制的影响。

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