Lubricants are of key importance for mechanical processing, and exist in nearly every mechanical system. When the equipment is in operation, debris particles will be generated in mechanical lubricants. The detection of debris particles can indicate the wear degree of machinery components, and provide prognosis warning for the system before the fault occurs. In this work, a novel type of inductive debris sensor consisting of two excitation coils and two sensing coils is proposed for online debris monitoring. The developed sensor was proven to be of high sensitivity through experimental verification. The testing results show that, using the designed sensor, ferrous metal debris with a size of 115 μm and nonferrous metal debris with a size of 313 μm in a pipe with an inner diameter of 12.7 mm can be effectively detected. Moreover, the proposed inductive debris sensor structure has better sensitivity at higher throughput and its design provides a useful insight into the development of high-quality sensors with superior performances.

We studied mode couplings in thin film bulk acoustic wave resonators of a piezoelectric film on a dielectric layer operating with the fundamental thickness-extensional mode. A system of plate equations derived in our previous paper was used which includes the couplings to the unwanted in-plane extension, flexure, fundamental and second-order thickness shear modes. It was shown that the couplings depend strongly on the plate length/thickness ratio. For a relatively clean operating mode with weak couplings to unwanted modes, a series of discrete values of the plate length/thickness ratio should be avoided and these values were determined in the present paper. The results can be of great significance to the design and optimization of film bulk acoustic wave resonators.

Thin-film bulk acoustic wave resonators (FBARs) are of significant interest for wireless applications due to their good performance. To achieve excellent characteristics, the frame-like FBARs were previously invented by researchers in this field to suppress the resonances of spurious lateral modes (or spurious modes). Another aspect that has impact on the working performance of FBAR is the undesired coupling modes, which were rarely studied due to the lack of proper theoretical tools. In this paper, we thoroughly investigate the coupling modes and spurious modes in frame-like FBARs by two-dimensional theory, which was already derived in our previous work. The widely used state vector approach is applied here and both free and forced vibration problems are analyzed. Frequency spectra and mode shapes obtained from free vibration analysis show the coupling vibration characteristics in this structure. Moreover, the admittance resonance obtained from the forced vibration analysis show the efficiency of the designed structure on the suppression of both undesired coupling and spurious modes. Results in this paper provide a thorough understanding of the vibration in frame-like FBAR, and the method presented can work as an effective tool in engineering design process.

In this paper, a new Stroh formalism for gradient electro-mechanics is derived for the first time, which is both mathematically concise and numerically powerful, applicable to generally coupled anisotropic material systems. Based on this new formalism, the complicated Lamb wave in flexoelectric and piezoelectric plates is investigated. The dispersion equation is obtained by solving the eigenvalue problem along with the unconditionally stable dual-variable and position method. From the obtained dispersion equation, the dispersion curves and mode shapes of the Lamb wave are calculated by the 1D form of the multidimensional moduli ratio convergence method. Two important and interesting features are observed from our analysis: One is the difference in the mode shape symmetry between the piezoelectric and flexoelectric cases, and the other is the size-dependent property of the flexoelectric effect as observed by nondimensionalization. These features are further illustrated by comparing the dispersion curves and wave-mode shapes among the three different material models (purely piezoelectric, purely flexoelectric, and flexoelectric and piezoelectric coupled). The newly derived Stroh formalism offers a robust, concise, and unified approach for dealing with strain gradient electro-mechanic materials with crystal systems of general anisotropy. The present work also explains the physical mechanism of symmetry breaking observed, as induced by flexoelectric coupling in piezoelectric materials.

The shear mode film bulk acoustic wave resonators (FBARs) have been developed rapidly in recent years due to the increased interest in biosensors. In this article, the mode coupling effects that are unavoidable in real devices are theoretically analyzed and discussed. Mindlin's approximation method of expanding the displacement fields with power series along the plate thickness direction is employed, and a system of 2-D plate equations is obtained. The accuracy of the plate theory is validated through the comparison of dispersion curves with the results calculated by 3-D exact theory. Free coupling vibrations of the cross-sectional plane of finite-sized shear mode FBAR plates are further studied with the derived 2-D theory. The results in this article show that the presented plate theory is accurate and efficient for the structural analyses of shear mode FBARs. Besides, the selection of aspect ratios can be used to avoid strong mode couplings, which is helpful for device designs.