Mode coupled vibrations in a thickness-shear (TSh) mode and laterally finite FBAR sensor with one face in contact with Newtonian (linearly viscous and compressional) liquid are investigated. With boundary conditions and interface continuity conditions, exact dispersion curves in FBAR sensor contacting with two kinds of liquids are obtained, and they are compared with the dispersion curves in a bare sensor without liquid contact. Frequency spectra, describing mode couplings between the main TSh modal branch and undesirable modal branches, are calculated by employing weak boundary conditions at lateral free edges constructed based on the variational principle. Mode shapes of mechanical displacements in both the sensor and liquid layer are presented, and mode transformations are observed due to the liquid contact and lateral edge effect. The effect of liquid thickness on frequency spectra is also studied. Numerical results reveal that the generation of shear wave in the liquid layer results in the shifts of spectrum curves along the frequency axis and hence it is the main factor of frequency shifts of FBAR sensors. The compressional wave causes the shifts of spectrum curves along the lateral aspect ratio axis. Then for a given FBAR sensor, the liquid thickness changes could also cause frequency shifts. Therefore, desirable vibration modes should be chosen based on the frequency spectra to avoid strong mode couplings and to eliminate frequency shifts induced by the liquid thickness changes in real applications.

Dielectric elastomers have attracted considerable attention both from academia and industry alike over the last two decades due to their superior mechanical properties. In parallel, research on the mechanical properties of dielectrics has been steadily advancing, including the theoretical, experimental, and numerical aspects. It has been recognized that the electromechanical coupling property of dielectric materials can be utilized to drive deformations in functional devices in a more controllable and intelligent manner. This paper reviews recent advances in the theory of dielectrics, with specific attention focused on the theory proposed by Dorfmann and Ogden. Additionally, we provide examples illustrating the application of this theory to analyze the electromechanical deformations and the associated bifurcations in soft dielectrics. We compared the bifurcations in elastic and dielectric materials and found that only compressive bifurcation modes exist in elastic structures, whereas both compressive and tensile modes coexist in dielectric structures. We summarize two proposed ways to suppress and prevent the tensile bifurcations in dielectric materials. We hope that this literature survey will foster further advancements in the field of the electroelastic theory of soft dielectrics.

Mode coupling between the operation mode and unwanted eigenmodes has a significant influence on the working performance of novel thin-film magnetoelectric (ME) devices operating at high frequencies. In this article, the extended frequency spectrum quantitative prediction (FSQP) method is used to investigate mode-coupling vibrations in high-frequency ME heterostructures. This method has three key procedures. First, wave propagation in ME heterostructures is studied to determine the wavenumber and frequency of the eigenmodes. Second, the variational formulation of a general ME heterostructure is constructed. Finally, frequency spectra for predicting the coupling strength among the eigenmodes are obtained by substituting the solutions consisting of all eigenmodes into the variational formulation. Two numerical examples are presented to validate the extended FSQP method. The mode shapes of the mechanical displacements are used to thoroughly describe the mode-coupling behavior in different vibration modes. The numerical results show that the mode-coupling strength is significantly affected by the structural size and number of layers in an ME heterostructure. Furthermore, structural symmetry along the thickness direction may cause specific mode-decoupling phenomena. Effective strategies for suppressing multimode-coupling vibrations in ME heterostructures by optimizing the lateral aspect ratios based on the frequency spectra are proposed to guide device design.

In this paper, an infinite circular ZnO thin film bulk acoustic resonator (FBAR) with a frame-like electrode operating at the thickness-extensional (TE) mode is studied. Two-dimensional scalar differential equations established for the problem in the Cartesian coordinate system are successfully solved by transforming them into normal Bessel equations and modified Bessel equations in the cylindrical coordinate system. Resonant frequencies and vibration distributions are obtained for this frame-like FBAR sensor. A nearly uniform mass sensitivity distribution in the active area is achieved by designing proper electrode size and mass ratio of the driving electrode to the ZnO film. Numerical results show that compared with the reported ring electrode FBAR sensor, the novel frame-like electrode FBAR can achieve a maximum optimization ratio (up to 97.90%) on the uniformity of the mass sensitivity distribution in the active area under the same structural parameters, which is also higher than the optimization ratio 77.63% obtained by the reported double-ring electrode design. Moreover, the mechanism to achieve a very uniform mass sensitivity distribution in the active area by the frame-like electrode is explained in detail according to dispersion curves. Namely, when the resonant frequency of the FBAR sensor is close to the cut-off frequency of the active region in the dispersion curve, the mass sensitivity distribution is nearly uniform. These conclusions provide a theoretical guidance for the design and optimization of ZnO FBAR mass sensors with high performance.