Free vibration of functionally graded beam integrated with Terfenol-D layer on Winkler-two parameter and viscoelastic foundation are studied by means of differential quadrature method within the framework of classical beam theory. The material properties of functionally graded beam integrated Terfenol-D layer are estimated by using the rule of mixture. The applied kinematic boundary conditions are implemented using \(\delta \)-point and modified weighting coefficient approach. The solution of simply supported functionally graded material beam with Terfenol-D layer (FGMT) resting on the Winkler elastic foundation is obtained by using the technique of Navier. The numerical results obtained using differential quadrature method (DQM) and modified differential quadrature method (MDQM) are compared with exact results obtained from analytical formulation where excellent agreement is observed. The parametric study is carried out to encapsulate the influence of Winkler-two parameter and the viscoelastic foundation on the vibration characteristics of functionally graded beams integrated with Terfenol-D layer.

在经典梁理论的框架内，采用微分求积法研究了温克勒二参数和黏弹性地基上结合了Terfenol-D层的功能梯度梁的自由振动。通过使用混合法则来估算功能梯度束集成的Terfenol-D层的材料性能。应用的运动学边界条件是使用\（\ delta \）实现的点和改进的加权系数方法。利用Navier技术，获得了支撑在Winkler弹性地基上的带有Terfenol-D层（FGMT）的简支功能梯度材料梁的解决方案。将使用微分求积法（DQM）和改进的微分求积法（MDQM）获得的数值结果与从分析配方获得的精确结果进行比较，可以观察到极好的一致性。进行了参数化研究，以封装Winkler两个参数和粘弹性基础对集成了Terfenol-D层的功能梯度梁的振动特性的影响。