In this paper, the method of electric analog synthesis is applied to design a piezo-electro-mechanical arch able to show the capacity of multimodal damping. An electric-analog circuit is designed by using a finite number of lumped elements representing the equivalent of a curved beam. Spatial and frequency coherence conditions are proven to be verified for the modes to be damped: in fact, lumped-element circuit can damp only a finite number of vibration modes. Analogous boundary conditions are ensured, so that natural frequencies and mode shapes of both the curved beam and the analog circuit are equal. The instance considered here is the vibration mitigation of a piezo-electro-mechanical arch. Having a view towards prototypical applications, all simulations consider values of physically feasible passive circuital elements. It is believed that the present results may represent a step towards the design of multi-physics metamaterials based on micro-structures exploiting the principle of multimodal damping.

在本文中，应用电模拟合成的方法设计了一种能够显示多模态阻尼能力的压电-机电拱。电模拟电路是通过使用有限数量的集总元件来设计的，这些元件代表弯曲梁的等效项。空间和频率相干条件已被证明可用于要衰减的模式：实际上，集总元件电路只能衰减有限数量的振动模式。保证了类似的边界条件，从而使弯曲梁和模拟电路的固有频率和模态振型相等。这里考虑的例子是压电机械拱的振动缓解。从原型应用的角度来看，所有模拟都考虑了物理上可行的无源电路元件的值。