Analytical approximations to resonance response of harmonically forced strongly odd nonlinear oscillators

An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

“…To deal with such a case, two newly nonlinear systems with odd nonlinearity are introduced in Eqs. (34) and (35). 41 Both of them can be solved separately by the NHB method as described in Section 3.1.…”

“…where the subscripts "21" and "22" of ω, T and ) (t x denote the corresponding second-order analytical solutions for the systems (34) and (35), respectively.…”

“…Building upon the framework of the NHB approach, 31 we further consider the steady-state response of a harmonically forced odd nonlinear system near its first frequency. 35 The equation of motion is given by…”

“…To further refine the accuracy and flexibility of analytical approximation approaches, Wu et al 31 proposed the Newton harmonic balance (NHB) method that is capable of solving largeamplitude oscillation of strongly nonlinear systems. Subsequently, the NHB has been extended to deal with nonlinear conservative asymmetric oscillators 32,33 , strongly damped nonlinear oscillation problems 34 and harmonically forced oscillation systems 35 . In order to achieve a faster convergence rate, an improved version of the NHB method has recently been presented.…”