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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. [ABSTRACT FROM AUTHOR]

Mode-coupled vibrations in a thickness-shear (TSh) mode and laterally finite film bulk acoustic resonator (FBAR) 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 sensors 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. [ABSTRACT FROM AUTHOR]

Mode-coupled vibrations in an ultra-high frequency (UHF) ZnO thin film bulk acoustic resonator (FBAR) operating at thickness-extensional (TE) mode are studied by employing weak boundary conditions (WBCs), constructed based on Saint-Venant’s principle and mixed variational principle in the piezoelectric theory. The frequency spectra, describing the lateral size-dependence of mode couplings between the main mode (TE) and undesirable eigen-modes, for clamped lateral edges are compared with the existing frequency spectra for free lateral edges to illustrate the boundary influence. The displacement and stress variations in FBAR volume are also presented to intuitionally understand and distinguish the difference of frequency spectra between these two different lateral edges, and then we discuss how to select outstanding lateral sizes to weaken the mounting effect. The frequency spectra predicted from our approximate WBCs are also compared with and agree well with those predicted by the finite element method (FEM) using COMSOL, which proves the correctness and accuracy of our theoretical method. These results indicate that the WBCs could have potentials in the valid predictions of lateral size-dependence of mode couplings in piezoelectric acoustic wave devices. [ABSTRACT FROM AUTHOR]

Mode coupling vibration of a multilayered ZnO thin film bulk acoustic wave resonator (FBAR) with its c-axis along the wave propagation direction operating at the fundamental thickness-shear (TSh) mode is studied in this paper. The accurate dispersion curve from 3-D piezoelectric theory indicates that the operating TSh mode could couple to the flexural mode, which influences the performance of a sensing resonator and needs to be eliminated through the so-called frequency spectrum analysis. Frequency spectra of coupling vibration in this FBAR can be obtained by substituting the displacement solutions consisting of the mode branches in the dispersion curve into several weak boundary conditions, which gives the integral boundary conditions across the plate thickness at the side edge of FBARs. The results show that the content of mode couplings to spurious modes depends on the plate length/thickness ratios. The character of desirable values of plate aspect ratios under which the operating TSh mode dominates among all modes is stated specifically, which provides fundamental guidance to the design of structural parameters of FBARs. [ABSTRACT FROM AUTHOR]

Free and forced vibration analysis of ZnO thin-film resonator operating with trapped-energy thickness-extensional (TE) mode is performed based on the dispersion curves for both the unbounded fully electroded and unelectroded films. The thickness solutions to the free vibration problem consist of the mode branches of the dispersion curves for the electroded and the unelectroded regions, respectively. The mode branches in the unelectroded region that carry energy away from the vibration zone are neglected because this effective energy loss corresponds to a complex frequency in the frequency spectrum. Since the thickness solutions in each region have satisfied the differential equations and the boundary conditions on the major surfaces exactly, the substitution of the thickness solutions into the modified Hamilton variational principle derived by Tiersten gives an approximate continuity condition in the form of integral over the thickness of the resonator at the interface between the electroded and unelectroded regions. The stationary condition of the integral continuity condition leads to a system of homogeneous linear equations, which determines the frequency spectrum ranging from the first TE cutoff frequency of the fully electroded film to that of the unelectroded film where the conventional trapped-energy vibration occurs. Forced vibration analysis of ZnO thin film driven into TE mode by applying a voltage to the top and bottom electrodes is also performed, which further verifies the validity of the obtained results from the free vibration analysis. [ABSTRACT FROM AUTHOR]