In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under the combined effects of electrostatic and intermolecular forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nano-cantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the distributed parameter model are compared with the lumped parameter model.

In this paper the two-point boundary value problem (BVP) of the cantilever deflection at nano-scale separations subjected to van der Waals and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. In the numerical method, the BVP is solved with the MATLAB BVP solver, which implements a collocation method for obtaining the solution of the BVP. The large deformation theory is applied in numerical simulations to study the effect of the finite kinematics on the pull-in parameters of cantilevers. The centerline of the beam under the effect of electrostatic and van der Waals forces at small deflections and at the point of instability is obtained numerically. In computing the centerline of the beam, the axial displacement due to the transverse deformation of the beam is taken into account, using the inextensibility condition. The pull-in parameters of the beam are computed analytically and numerically under the effects of electrostatic and/or van der Waals forces. The detachment length and the minimum initial gap of freestanding cantilevers, which are the basic design parameters, are determined. The results of the analytical study are compared with the numerical solutions of the BVP. The proposed methods are validated by the results published in the literature.

SUMMARYA new attitude control strategy for rotational manoeuvre of an elastic spacecraft is presented. Adaptive sliding mode control with hybrid sliding surface (HSS) is used to minimize the effects of uncertainties, disturbances and the difficulties arising from measurement of flexible dynamic co-ordinates. The model of the spacecraft considered as rigid central hub and two elastic appendages. Collocated actuators and sensors are placed on the rigid central hub. Stability proof of the overall closed-loop system is given via Lyapunov analysis. Numerical simulations show that the attitude manoeuvres can be performed precisely and the elastic deformations of the flexible substructures are suppressed as well.

In this paper, the tip tracking control problem of a Timoshenko micro-cantilever beam is investigated. The beam is actuated by a piezoelectric layer laminated on one side of the beam. Dynamic equations of the beam and piezoelectric layer are found using the Hamilton principle. By employing the Galerkin projection method, state space representation of the system is derived. Then, a cascade control loop is used for tracking control of the beam’s tip. The cascade control structure consists of an inner loop stabilizer and an outer loop proportional-integral-derivative controller. The stabilizer has a linear feedback form whose states are obtained through a linear observer which is based on the beam tip displacement measurement. Stability analysis of the inner loop stabilizer is performed to study the effects of higher un-controlled modes on performance of the controlled system. Simulation results show the effectiveness of the proposed control method.