A rich variety of resonance scenarios induced in thin elastic plates by periodic axial strains is investigated to describe the morphing capability of flexible, ultra-lightweight panels. The strain-induced excitation is provided by embedded piezoelectric strips actuated by time-varying voltages. The study deals with plates characterized by geometric and mechanical symmetry entailing cylindrical motions so that an ad hoc approximate nonlinear model of elastic beams is adopted to formulate the incremental equation of motion about the nonlinear equilibrium under dead loads. An asymptotic approach based on the method of multiple scales is employed to study the plate dynamics and, primarily, to investigate the effect of the plate slenderness on the nonlinearity of the lowest normal modes. A bifurcation analysis is carried out to investigate the wide array of resonances induced by the harmonic axial excitation, acting in nontrivial equilibrium states, which include primary, super-harmonic, sub-harmonic, and principal parametric resonances, respectively. For selected slendernesses of the plate, corresponding to nonlinear softening, hardening and quasi-linear behaviors, respectively, comprehensive parametric studies on the effect of the PZT cross-sectional size, the plate damping, and the piezoelectric coupling coefficient are carried out to identify the threshold voltages triggering the different resonances.

研究了周期性轴向应变在薄弹性板中引起的多种共振情况，以描述柔性超轻型板的变形能力。应变引起的激励是由随时间变化的电压驱动的嵌入式压电条提供的。与板研究涉及其特征在于几何和机械对称将会导致筒状运动，使得特设采用弹性梁近似非线性模型，建立了恒载下非线性平衡运动的增量方程。采用基于多尺度方法的渐近方法来研究板的动力学，主要是研究板细长度对最低法线模态非线性的影响。进行了分叉分析，以研究由谐波轴向激励引起的各种谐振，这些谐振在非平凡的平衡状态下起作用，分别包括一次，超谐波，次谐波和主参数谐振。对于选定的细长板，分别对应于非线性软化，硬化和准线性行为，对PZT横截面尺寸的影响进行了全面的参数研究，