温度场下岛-桥结构屈曲薄膜的动力学分析

The island-interconnector type flexible electronic devices have been used in daily life, such as monitoring the blood pressure, heart rate, body temperature, and other biophysical and biochemical signals. Considering that these kinds of flexible electronic devices would work in a complex environment, their dynamic behaviours would be influenced. In this paper, the dynamic behaviours of the buckled interconnector, which is subjected to the temperature field, are studied. Firstly, based on the Euler-Bernoulli beam theory, the governing equation of the buckled interconnector is derived. Secondly, by introducing new variables, the second-order dynamic equation is transformed into one-order dynamic equations. Then, the symplectic Runge-Kutta method is used to solve the corresponding equations. From the numerical results, one can find that the results obtained by the symplectic Runge-Kutta method is more stable than that obtained by the classical Runge-Kutta method. Thus, in the following dynamic analysis, the symplectic Runge-Kutta method is adopted. In addition, from several numerical examples, the influences of the temperature change and pre-stain on the dynamic response of the buckled structure are discussed. Through these numerical examples, one can find that the natural frequency of the buckled interconnector is affected by the temperature change and pre-strain. When the thermal expansion coefficient is taken as a positive value, with the increase of the temperature change and pre-strain, the natural frequency of the buckled thin film increases. For the fixed temperature change, the higher the pre-strain, the higher the vibration amplitude; and for the fixed pre-strain, the higher the temperature change, the higher the vibration amplitude. When the thermal expansion coefficient is taken as a negative value, with the increase of the temperature change, the vibration amplitude of the buckled structure would decrease. The numerical results of this paper would be useful for the design of novel flexible electronic devices.