粘弹性-弹性层合微悬臂梁的自由振动

发布时间：2018-03-29 20:03

本文选题：悬臂梁　切入点：层合结构　出处：《力学季刊》2017年02期

【摘要】：吸附膜的粘弹性性质对微梁生物传感器的固有频率有显著影响.首先,在欧拉梁假设下,采用线性粘弹性积分型本构关系和拉普拉斯变换方法,建立了动态识别技术中粘弹性-弹性层合微悬臂梁自由振动的基本方程;其次,采用空域分离变量法和时域微分求导法,获得了积分-偏微分系统的固有频率,并采用求解代数方程的卡尔丹公式和不等式的性质,在材料参数和几何参数张成的高维空间获得了齐次通解的结构;最后,研究了微梁的几何尺寸、吸附膜的粘弹性参数、膜基厚度比和模量比对微梁自由振动的影响.结果表明:吸附膜的粘弹性阻尼效应使得微梁的稳态固有频率低于瞬态固有频率;随着吸附膜松弛时间的减小,微梁瞬态固有频率漂移与稳态固有频率漂移之间的差别逐渐增大;通过控制膜基厚度比或模量比等参数可以使微梁振动进入弱阻尼振动区域.
[Abstract]:The viscoelastic properties of the adsorbed membrane have a significant effect on the natural frequencies of microbeam biosensors. Firstly, under the assumption of Euler beam, the linear viscoelastic integral constitutive relation and Laplace transformation method are used. The basic equations for the free vibration of viscoelastic laminated micro-cantilever beam in dynamic identification technique are established. Secondly, the natural frequencies of the integro-partial differential system are obtained by using the spatial separation variable method and the time-domain differential derivation method. By using the Kardan formula and the properties of inequality for solving algebraic equations, the homogeneous general solution structure is obtained in the high dimensional space of material parameter and geometric parameter Zhang Cheng. Finally, the geometric dimension of the microbeam and the viscoelastic parameter of the adsorbed film are studied. The results show that the viscoelastic damping effect of the adsorption membrane makes the steady natural frequency of the microbeam lower than the transient natural frequency, and with the decrease of the relaxation time of the adsorption membrane, The difference between the transient natural frequency drift and the steady state natural frequency drift of the microbeam is gradually increasing, and the vibration of the micro beam can enter the weakly damped vibration region by controlling the thickness ratio of the film base or the modulus ratio.
【作者单位】：上海大学上海市应用数学和力学研究所上海市力学在能源工程中的应用重点实验室;上海大学理学院力学系;
【基金】：国家自然科学基金(11272193) 上海市浦江人才计划项目(15PJD016)
【分类号】：O327

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