Abstract: A resonator includes an anchor, an outer stiffener ring on an outer perimeter of the resonator, and a plurality of curved springs between the anchor and the outer stiffener ring.

Abstract: A resonator has a resonator body and a frame at least partially surrounding the resonator body, the resonator body being coupled to the frame by at least one tether. The resonator body, frame and at least one tether comprise silicon carbide. A plurality of interdigitated electrodes are disposed on the silicon carbide resonator body. The resonator body preferably comprises 6H silicon carbide and preferably has a crystalline c-axis oriented generally parallel to a thickness direction of the resonator body.

Abstract: A self-calibration method for an accelerometer having a proof mass separated by a gap from a drive electrode and a sense electrode includes initializing the accelerometer to resonate, applying a first bias voltage to the sense electrode and a second bias voltage to the drive electrode to obtain a first scale factor, measuring a first acceleration over a first time interval, swapping the first bias voltage on the sense electrode with the second bias voltage previously on the drive electrode and the second bias voltage on the drive electrode with the first bias voltage previously on the sense electrode so that a bias voltage on the sense electrode is set to the second bias voltage and a bias voltage on the drive electrode is set to the second bias voltage to obtain a second scale factor, measuring a second acceleration over a second time interval, and calculating a true acceleration.

Abstract: A method of making a SiC resonator includes forming a layer of an oxide material on a relatively thick wafer of SiC; bonding the layer of oxide material on the relatively thick wafer of SiC to a handle wafer having at least an oxide exterior surface, the resulting bond being substantially free of voids; planarizing the relatively thick wafer of SiC to a desired thickness; forming top and bottom electrodes on the wafer of SiC wafer to define a SiC wafer resonator portion; and forming a trench around the top and bottom electrodes, the tench completely penetrating the planarized wafer of SiC around a majority of a distance surrounding said top and bottom electrodes, except for one or more tether regions of the planarized wafer of SiC which remain physically coupled a remaining portion the SiC wafer resonator portion which defines a frame formed of the planarized wafer of SiC surrounding the SiC wafer resonator portion.

Abstract: An instrument package for use during the drilling a wellbore. The instrument package includes a plurality of instruments such as accelerometers, gyroscopes, and magnetometers; a computer is configured to determine the current position of the plurality of instruments from a set of measurements produced by the plurality of instruments; and wherein the plurality of instruments are mechanically isolated from a drill head assembly by one or more multi-degree of freedom vibration isolators. The computer preferably has at least two modes different analytical modes of analyzing the set of measurements produced by the plurality of instruments, including a continuous mode and a survey mode, the continuous mode being operational during times that active drilling is occurring and the survey mode being operational during times that the active drilling is not occurring.

Abstract: A resonant accelerometer includes a proof mass, one or more springs connecting the proof mass to an anchor, and one or more capacitive transduction gaps providing a void or space between the movable proof mass and a corresponding fixed electrode, wherein the static displacement of the proof mass in response to acceleration applied to the anchor modifies the electrostatic stiffness imparted by one or more of the capacitive transduction gaps on the proof mass, resulting in a corresponding change in the resonance frequency of the resonant accelerometer.

Abstract: A curved phononic waveguide. In some embodiments, the curved phononic waveguide includes a sheet including a plurality of standard reflectors and a plurality of divergent reflectors. Each of the standard reflectors is associated with a respective grid point of a grid defined by a plurality of intersecting lines, each grid point being a respective intersection of two of a plurality of intersecting lines, the grid being locally periodic to within 5%, and having a local grid spacing. Each of the standard reflectors has a center separated from the respective grid point of the standard reflector by at most 1% of the grid spacing. The divergent reflectors define a waveguide among the standard reflectors, each of the divergent reflectors being an absent reflector or a reflector that is smaller than one of the standard reflectors.

Abstract: A sensor comprising a resonator structure arranged for resonating along a first plane; and at least one sensing electrode arranged on a second plane parallel to said first plane at a predetermined distance of said resonator structure along a direction normal to said first plane.

Abstract: A resonant structure comprising at least two coaxial rings, wherein adjacent coaxial rings have adjacent peripheries and are attached together by a plurality of connection structures regularly arranged along said adjacent peripheries; and wherein a first ring has a first ring portion with a first radial thickness and a second ring, portion, in a vicinity of a first connection structure, with a second radial thickness smaller than said first radial thickness.

Abstract: A phononic coupler. In some embodiments, the phononic coupler includes a sheet, including a plurality of standard reflectors, and a plurality of divergent reflectors. The divergent reflectors define, among the standard reflectors, a first waveguide, and a second waveguide. The coupler has a first port, at a first end of the coupler, a second port, at the first end of the coupler, and a third port, at a second end of the coupler. The first waveguide has a first end at the first port. The second waveguide has a first end at the second port, and a second end at the third port. The coupler is configured to couple longitudinal sound waves to both the first port and the second port.

Abstract: Dimensions of a disk resonator gyroscope along the radial line of a resonator can be varied to engineer radial stiffness. An apparatus may comprise: a resonator comprising a plurality of concentric circumferential segments and a plurality of slots formed between the concentric circumferential segments; and at least one support supporting the resonator, wherein a width, in a radial direction, of each of the concentric circumferential segments is varied depending on a distance from the at least one support to the each of the concentric circumferential segments. The apparatus may further comprise radial segments connecting between the concentric circumferential segments. The concentric circumferential segments may have a ring shape.

Abstract: A resonator includes an anchor, an outer stiffener ring on an outer perimeter of the resonator, and a plurality of curved springs between the anchor and the outer stiffener ring.

Abstract: A resonator includes an anchor, an outer stiffener ring on an outer perimeter of the resonator, and a plurality of curved springs between the anchor and the outer stiffener ring.

Abstract: An angular sensor, comprising a Coriolis vibratory gyroscope (CVG) resonator, capable of oscillating along a first pair of normal n=1 modes comprising a first normal mode and a second normal mode; and a second pair of normal n=2 modes comprising a third normal mode and a fourth normal mode; the sensor further comprising one drive electrode and one sense electrode aligned along an anti-nodal axis of each mode; and a pair of bias tune electrodes aligned with an anti-nodal axis of each mode if no drive and sense electrode pair is aligned with said anti-nodal axis.

Abstract: A resonator has a resonator body and a frame at least partially surrounding the resonator body, the resonator body being coupled to the frame by at least one tether. The resonator body, frame and at least one tether comprise silicon carbide. A plurality of interdigitated electrodes are disposed on the silicon carbide resonator body. The resonator body preferably comprises 6H silicon carbide and preferably has a crystalline c-axis oriented generally parallel to a thickness direction of the resonator body.

Abstract: A method of making a SiC resonator includes forming a layer of an oxide material on a relatively thick wafer of SiC; bonding the layer of oxide material on the relatively thick wafer of SiC to a handle wafer having at least an oxide exterior surface, the resulting bond being substantially free of voids; planarizing the relatively thick wafer of SiC to a desired thickness; forming top and bottom electrodes on the wafer of SiC wafer to define a SiC wafer resonator portion; and forming a trench around the top and bottom electrodes, the tench completely penetrating the planarized wafer of SiC around a majority of a distance surrounding said top and bottom electrodes, except for one or more tether regions of the planarized wafer of SiC which remain physically coupled a remaining portion the SiC wafer resonator portion which defines a frame formed of the planarized wafer of SiC surrounding the SiC wafer resonator portion.

Abstract: An instrument package for use during the drilling a wellbore. The instrument package includes a plurality of instruments such as accelerometers, gyroscopes, and magnetometers; a computer is configured to determine the current position of the plurality of instruments from a set of measurements produced by the plurality of instruments; and wherein the plurality of instruments are mechanically isolated from a drill head assembly by one or more multi-degree of freedom vibration isolators. The computer preferably has at least two modes different analytical modes of analyzing the set of measurements produced by the plurality of instruments, including a continuous mode and a survey mode, the continuous mode being operational during times that active drilling is occurring and the survey mode being operational during times that the active drilling is not occurring.

Abstract: A phononic travelling wave gyroscope. The gyroscope includes a phononic waveguide including at least one loop. The phase change incurred by phonons propagating around the loop is compared to a reference phase, and utilized to form an estimate of the rotational rate of the gyroscope.

Abstract: A resonant structure comprising at least two coaxial rings, wherein adjacent coaxial rings have adjacent peripheries and are attached together by a plurality of connection structures regularly arranged along said adjacent peripheries; and wherein a first ring has a first ring portion with a first radial thickness and a second ring, portion, in a vicinity of a first connection structure, with a second radial thickness smaller than said first radial thickness.

Abstract: An angular sensor, comprising a Coriolis vibratory gyroscope (CVG) resonator, capable of oscillating along a first pair of normal n=1 modes comprising a first normal mode and a second normal mode; and a second pair of normal n=2 modes comprising a third normal mode and a fourth normal mode; the sensor further comprising one drive electrode and one sense electrode aligned along an anti-nodal axis of each mode; and a pair of bias tune electrodes aligned with an anti-nodal axis of each mode if no drive and sense electrode pair is aligned with said anti-nodal axis.