Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

Abstract

Since microplates are extensively used in MEMS devices such as microbumps, micromirrors, and microphones, this work aims to study nonlinear vibration of an electrically actuated microplate whose four edges are clamped. Based on the modified couple stress theory (MCST) and strain equivalent assumption, size effect and damage are taken into consideration in the present model. The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. Size effect and damage effect on nonlinear free vibration of the microplate under DC voltage are discussed using frequency-response curve. In the forced vibration analysis, the frequency-response curves were also employed for the purpose of highlighting the influence of different physical parameters such as external excitation, damping coefficient, material length scale parameter, and damage variable when the system is under AC voltage. The results presented in this study may be helpful and useful for the dynamic stability of a electrically actuated microplate system.

Size estimates for nanoplates

“…The demand for higher performances and small sizes (typical size around 1 ÷ 10 × 10 −4 m) have led to higher strain/stress states and very challenging operating conditions that can increase the probability of structural failure. Furthermore, defects such as cracks, internal voids, inhomogeneous material properties and abrasions can appear during the manufacturing process and can evolve during service, leading to the activation of mechanical device failure [12,20,31].…”

A sixth-order elliptic equation for nanoplates. Neumann problem and Unique Continuation in the interior

“…Albeit the detection of added mass is one of the most popular issues in applications [18,29,12], other notable inverse problems for nanoplates involve force or pressure sensing from dynamic data [21]. In addition, there has recently been growing interest in the development of diagnostic techniques for assessing the presence of defects in nanoplates, thus paving the way for the extension of methods hitherto designed for large-scale mechanical systems to the nanodimensional size as well [48].…”