Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...

In this paper, vibration control of a nonlinear string system is considered. The system consists of a nonlinear string, two boundary supporting mechanisms, and a moving transporter at the base. To suppress the vibration, boundary control designs are carried out. A new robust and adaptive boundary controller is designed using the Lyapunov direct method. The proposed control is implemented at the...

Two robust nonlinear controllers along with a nonlinear observer have been developed in this study to control a 1D nonlinear flexible spacecraft. The first controller is based on dynamic inversion, while the second one is composed of dynamic inversion and µ-synthesis controllers. The extension of dynamic inversion approach to flexible spacecraft is impeded by the non-minimum phase characteristi...

A nonlinear optimal control method is developed for magnetostrictive actuators used to actively attenuate plate vibration. Significant improvements in vibration control can be achieved when the magnetostrictive actuators are driven at moderate to high field levels. This results in nonlinearity and hysteresis which cannot be effectively compensated using linear control theory. This issue is addr...

Graphene has received significant attention due to its excellent mechanical properties, which has resulted in the emergence of graphene-based nano-electro-mechanical system such as nanoresonators. The nonlinear vibration of a graphene resonator and its application to mass sensing (based on nonlinear oscillation) have been poorly studied, although a graphene resonator is able to easily reach the...

We consider the von Kármán nonlinearity and the Casimir force to first develop a reduced-order model for a prestressed clamped elliptic electrostatically actuated microplate, and then use it to study vibrations and pull-in instability. The reduced-order model is derived by taking a family of linearly independent kinematically admissible functions as basis functions for the transverse displaceme...