Microelectromechanical systems (MEMS) based ring shaped resonators usually have a ring supported by spoke shaped springs. In this paper, we developed a general analytical model that can determine the natural frequency of any MEMS ring resonator considering effective mass and stiffness of spokes in both radial and tangential displacements. Our model is also able to determine the stiffness of the circular curved beam with arbitrary central angle. The well-known energy based Castigliano’s method was used to calculate the stiffness of a circular curved beam considering both flexural and axial rigidities. The stiffness of a circular curved beam with different central angles was determined and compared with the literature and finite element method (FEM). The results show that for the case of a central angle of the curved beam larger than 60 degrees, the deviation between the FEM and analytical approach is less than 1%. The potential energy and kinetic energy of the outside ring and spokes were determined based on the displacement function. The natural frequency of a ring resonator with different number of circular curved beams in the form of petals in modes n=2 and n=3 were determined and the results were compared with a numerical approach using FEM. The deviations between the analytical approach and numerical method are less than 4%.

With the development of wireless communication technology, active structural vibration control based on a wireless sensor network has tended to replace the traditional wired control method. However, the problem of time delay in a wireless control system is inevitable and requires serious attention. In this study, a wireless active vibration control scheme consisting of a cantilever beam with a piezoelectric actuator is proposed and implemented. Experimental results indicate that wireless control gives good control performance; however, because of the influence of time delay, the performance of wireless control is slightly worse than that of wired control. Therefore, a novel method for time delay compensation is presented in this study to resolve this problem. This approach takes advantage of the finite difference method to extend the state space of the cantilever beam. Additional time delay states are used to form the extended state space model for time delay compensation. Simulation and experimental results demonstrate that this method can effectively compensate for time delay and enables the wireless control system to exhibit excellent control performance that can be favorably compared with that of wired control.

No abstract

No abstract

The printing accuracy is one of the key factors affecting the final additively manufactured structures. As metamaterials for wave controlling, the printing accuracy caused in additive manufacturing can affect the band gap structures and the wave transmissions in phononic crystals (PnCs). Selective laser melting (SLM) was used to fabricate the designed PnCs. AlSi10Mg was used as the material for the fabrication. The distorted geometry of the additively manufactured PnCs by selective laser melting (SLM) was experimentally measured and then was re-built as finite element model. The band gap structures and the wave transmissions were calculated based on finite element method for the comparison of the structural performances of the theoretically designed and fabricated PnCs. Result indicated that the fabricated PnCs were thermally distorted from 0.298 mm to 1.664 mm depending on the designed geometries. The thermal distortion can lead to a deviation of central frequency in the range of -6.2%~3.7% in comparison with the theoretical design. Compared with the theoretical design, the band gap widths of the distorted PnCs vary from -7.4% to 5.6% due to the frequencies change of the eigenmodes at the upper and lower band edges which are directly affected by the thermal distortion. The further analysis shows that the change of the band structures of the distorted PnCs is due to the increase of the inertia moment of the distorted PnCs caused by the printing accuracy.