Due to the excellent piezoelectric and ferroelectric properties of lead zirconate titanate (PZT), the buckled PZT ribbon-substrate structure has been widely used in the design of wearable electronic devices. However, wearable electronic devices must work in a complex vibration environment and are subjected to random excitations such as irregular human body motion. Hence, the reliability of the buckled piezoelectric ribbon-substrate structure in a dynamic context needs to be ensured. In this paper, Gaussian white noise is introduced to describe the broadband random environment. A voltage is applied to the PZT ribbon to realize the desired wavy configuration of the ribbon to influence the dynamic responses of this structure. Based on the Euler–Bernoulli beam theory and the Lagrange equation, the governing equation of the buckled piezoelectric ribbon-substrate structure is derived. By using a stochastic averaging method, the stationary probability density of stochastic responses of the buckled piezoelectric ribbon-substrate structure is obtained. Several numerical examples are analysed to reveal the effects of the intensity of the Gaussian white noise and the voltage applied to the PZT ribbon on the stochastic responses of this buckled structure. Through these numerical results, it can be found that when the applied voltage is above the critical voltage value, the piezoelectric ribbon would wrinkle into multiple small waves on top of the soft substrate. By increasing the applied voltage while keeping the intensity of noise excitation constant, the static buckling amplitude increases, and the number of transitions between two equilibrium positions decreases, which implies that the stretchability and stability of the ribbon-substrate structure would be improved. The results of this paper can be helpful for the design of robust piezoelectric ribbon-based stretchable electronics.

由于锆钛酸铅 (PZT) 优异的压电和铁电性能，屈曲 PZT 带状衬底结构已广泛应用于可穿戴电子设备的设计中。然而，可穿戴电子设备必须在复杂的振动环境中工作，并受到人体不规则运动等随机激励的影响。因此，需要确保弯曲压电带-基板结构在动态环境中的可靠性。本文引入高斯白噪声来描述宽带随机环境。将电压施加到 PZT 带上以实现带的所需波浪配置，从而影响该结构的动态响应。基于欧拉-伯努利梁理论和拉格朗日方程，推导出屈曲压电带-衬底结构的控制方程。通过使用随机平均方法，获得了屈曲压电带-衬底结构随机响应的平稳概率密度。分析了几个数值例子，以揭示高斯白噪声的强度和施加到 PZT 带上的电压对这种屈曲结构的随机响应的影响。通过这些数值结果可以发现，当外加电压高于临界电压值时，压电带会在软基片上皱缩成多个小波。通过增加施加电压同时保持噪声激励强度恒定，静态屈曲幅度增加，并且两个平衡位置之间的转变次数减少，这意味着带状衬底结构的拉伸性和稳定性将得到改善。本文的结果有助于设计坚固的基于压电带的可拉伸电子设备。