This article focuses on characterizing the nonlinear nature of the piezoelectric actuators’ ‘33’-electromechanical coupling and ‘3’-directional elasticity. Vibrations of a cantilever aluminum beam, attached with a pair of $d_{33}$-mode surface bondable multilayer actuators, were studied to construct the required nonlinear constitutive equation. As both elasticity and electromechanical coupling were of equal interest, a sequential experimental procedure was followed to conduct an exclusive analysis of each of them. Accordingly, first, the actuators were short-circuited, and a set of displacement-frequency-response plots were obtained for the first and second bending modes. The profile of the backbone curve of the response plots revealed the presence and the nature of the nonlinearity in the elastic domain. Equipped with the knowledge of the nonlinear elastic behavior, nonlinearity in electromechanical coupling was then investigated from a set of response plots obtained through the piezoelectric actuation of beam. Here too, the profile of the backbone curves revealed the type of nonlinearity present in the electromechanical behavior. With the information obtained from these two steps, a final nonlinear constitutive equation was constructed to represent both the nonlinear elasticity and the nonlinear electromechanical coupling in the actuator.

本文重点介绍压电致动器“ 33”-机电耦合和“ 3”-方向弹性的非线性特性。悬臂铝梁的振动，并附有一对$d_{33}$模表面可粘接多层致动器进行了研究，以构造所需的非线性本构方程。由于弹性和机电耦合是同等重要的，因此遵循顺序实验程序对它们中的每一个进行排他性分析。因此，首先，使致动器短路，并且获得针对第一弯曲模式和第二弯曲模式的一组位移频率响应图。响应图的主干曲线的轮廓揭示了弹性域中非线性的存在和性质。配备了非线性弹性行为的知识，然后通过通过梁的压电驱动获得的一组响应图来研究机电耦合中的非线性。这里也，主干曲线的轮廓揭示了机电行为中存在的非线性类型。利用从这两个步骤获得的信息，构造了最终的非线性本构方程，以表示执行器中的非线性弹性和非线性机电耦合。