Viscoelastic Characteristics of Mechanically Assembled Three-Dimensional Structures Formed by Compressive Buckling

Vibrational microplatforms that exploit complex three-dimensional (3D) architectures assembled via the controlled compressive buckling technique represent promising candidates in 3D micro-electromechanical systems (MEMS), with a wide range of applications such as oscillators, actuators, energy harvesters, etc. However, the accuracy and efficiency of such 3D MEMS might be significantly reduced by the viscoelastic damping effect that arises from material viscosity. Therefore, a clear understanding and characterization of such effects are essential to progress in this area. Here, we present a study on the viscoelastic damping effect in complex 3D structures via an analytical model and finite element analysis (FEA). By adopting the Kelvin-Voigt model to characterize the material viscoelasticity, an analytical solution is derived for the vibration of a buckled ribbon. This solution then yields a scaling law for the half-band width or the quality factor of vibration that can be extended to other classes of complex 3D structures, as validated by FEA. The scaling law reveals the dependence of the half-band width on the geometries of 3D structures and the compressive strain. The results could serve as guidelines to design novel 3D vibrational microplatforms for applications in MEMS and other areas of technology.