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首页> 外文期刊>Applied Mathematical Modelling >Modelling the dynamic response of a micro-cantilever excited at its base by an arbitrary thermal input using Laplace transformation
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Modelling the dynamic response of a micro-cantilever excited at its base by an arbitrary thermal input using Laplace transformation

机译：使用拉普拉斯变换，通过任意热输入在其底部激发的微悬臂梁的动态响应建模

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摘要

An analytical model for predicting the time-history response of a cantilever beam to arbitrary time-dependent thermal actuation is elaborated in this paper. Base excitation is investigated as a practical method for thermally exciting the micro-cantilever. The beam is considered to be mounted on a layer of material (actuator) that is thermally excited (e.g., by electric current). Thermal expansion/contraction of the base causes the micro-cantilever to vibrate. One-dimensional heat conduction equation is solved for the actuator, along with the Euler-Bernoulli continuous beam equation for the micro-cantilever. An arbitrary time dependant body heat generation is applied on the actuator as the excitation function for the latter equations. Laplace transformation is applied to tackle the time dependency of the partial differential equations. After solving the coupled ordinary differential equation, two methods based on Gaver-Stehfest algorithm and direct numerical integration are considered for the inverse transformation and discussion regarding results and procedures are presented. Moreover, a case study of a thermally actuated resonator with periodic input signal is investigated and conclusions on the practical design and implementation are demonstrated.
机译：阐述了一种预测悬臂梁对任意随时间变化的热激励的时程响应的分析模型。研究了基极激励作为热激励微悬臂梁的实用方法。认为束被安装在被热激发（例如，通过电流）的材料层（致动器）上。基座的热膨胀/收缩会导致微悬臂梁振动。求解了执行器的一维热传导方程式以及微悬臂梁的Euler-Bernoulli连续梁方程式。将随时间变化的任意体热生成作为后一方程式的激励函数应用于执行器。拉普拉斯变换用于解决偏微分方程的时间依赖性。在求解耦合常微分方程之后，考虑了基于Gaver-Stehfest算法和直接数值积分的两种方法进行逆变换，并讨论了结果和过程。此外，还研究了具有周期性输入信号的热激励谐振器的案例研究，并给出了有关实际设计和实现的结论。

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