光热激励下功能梯度梁在流体中的振动

Study on the vibration of functionally graded beam immersed in fluids under photothermal excitation

通过建立流体中功能梯度梁的光热振动模型,研究了在激光光热驱动下功能梯度梁在不同流体中的振动特性。将功能梯度材料的参数等效化处理得到了简化的热传导方程和振动控制方程,并求解得到了不同边界条件下功能梯度梁的温度场、光热驱动力和振动变形场的解析表达式。数值计算表明:对于本文选取的金和硅组成的功能梯度材料,梁的共振频率随梯度因子的增大而减小;梁在不同流体环境中振动时,共振频率会向低频漂移;梁的尺寸以及梯度因子会影响漂移程度,边界条件的影响较小;当梁的厚度减小时,频率漂移比增大,品质因子减小。

In this study,a mathematical model is presented for dynamic response of FGM(Functionally Graded Materials)beams immersed in fluids under high-frequency photothermal excitation.The temperature of FGM beams with different boundary conditions are obtained analytically using Fourier heat conduction theory.Using thermoelastic theory,photothermal driving force is given analytically.Based on the Euler-Bernoulli beam theory,effective bending modulus and effective density of the FGM beams,dynamical deflection fields are obtained using mode superposition method.Theoretical analysis show that the resonant frequency of the beam decreases with the increase of the gradient factor for the functionally graded materials composed of gold and silicon.By comparing the dynamic response of the beam in different environments,the resonant frequency of the beam in different fluid environments will drift to low frequency,and the quality factor of the beam will be reduced in different degrees and quality factor decrease significantly when the beams vibrated in liquids.The resonant frequency and frequency shift of the FG beams decrease with the increase of volume fraction.Also the results show that with the decrease of the thickness of beams,the volume fraction had a bigger impact on frequency shift,a smaller impact on quality factors.Boundary conditions had a little influence on frequency shift.This study can be valuable to users and designers of FGM structures in MEMS/NEMS.