This study examined the dynamic characteristics of nonlinear electrostatic pull-in behavior for shaped actuators in micro-electro-mechanical systems (MEMS). The natural frequencies of a fixed-fixed shaped beam vibrating around its statically deflected position were calculated using the differential quadrature method (DQM). The proposed model included the nonlinear interaction between the curved electrostatic field force and the shaped micro-beam, as well as the mid-plane stretching, axial residual stress and electrical field fringing effect. Very good agreement existed between the results simulated using the proposed model and the measured data. This work also investigated the micro-beam and electrode shape effect on the natural frequencies of the actuator system. Analytical results indicate that the variation in the micro-beam and the electrode shapes might not only influence the electrostatic field distribution but also significantly alter the dynamic characteristics of the micro-actuator. Analytical results demonstrate that the shaped micro-beam with curved electrode can increase the working voltage range approximately six times compared to the rectangular micro-beam and flat electrode.

In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The wear prediction model proposed by Flodin et al. is used to simulate the tooth profile wear process. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.

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The effect of an insulated rail joint (IR J) on the contact stress variation near wheel±rail contact zones was simulated by employing three-dimensional ®nite element models. Three linear elastic IR J materials, i.e. epoxy-®breglass, polytetra¯uoroethylene (PTF E) and N ylon-66, were investigated. Contact elements were used to simu late the interaction between the wheel and rail contact points. N umerical results showed that the presence of IR J might signi®cantly affect the wheel±rail contact stress distrib utions. R esults also indicated that the traditional H ertzian contact theory is no longer available to predict the contact stress distribution around the rail joints.