Patent Description:
A resonant accelerometer is an oscillator whose output resonant frequency is a function of an input measurand. In other words, the output of a resonant accelerometer corresponds to the shift in resonant frequency of a mechanical microstructure that gets tuned in accordance to a change in a physical quantity to be measured.

There has been an increased interest over the past few years in the development of high precision micro-machined 'all-silicon' resonant micro-accelerometers. This interest has been triggered due to the recent growth in demand for miniature high precision motion accelerometers within the aerospace, automotive and even the consumer-electronics markets. Resonant micro-accelerometers fabricated using silicon micromachining techniques present a number of significant advantages, the biggest being economy. These silicon resonant micro-accelerometers not only boast improved sensitivity and resolution relative to their more traditional capacitive detection based counterparts with similar device footprints, but have also been shown to provide enhanced dynamic range making them ideal candidates for potential application in numerous motion sensing applications within the identified markets. One potential sensing application is gravimetry. Resonant accelerometers can be designed to provide a low-noise response for near-DC measurements (suitable for applications in gravimetry) and a wide dynamic range enabling measurements over the entire +/-<NUM> regime.

However, most of these accelerometers still remain uniaxial or biaxial, consequently restricting their functionality and practical applicability to those applications that do not demand sophisticated three dimensional (3D) motion control. Three uniaxial, orthogonally oriented resonant accelerometers can be employed for a precise three dimensional acceleration measurement. But such implementations correspondingly increase the cost, size and power requirements of the device. Also, such implementations require very precise alignment of the separate accelerometers relative to each other to provide accurate measurement.

It is an object of the present invention to provide a resonant accelerometer that allows for two and three dimensional acceleration read out in a single device package that is both small and provides for accurate measurement.

<CIT> discloses a dual-axis accelerometer. The dual-axis accelerometer comprises a single suspended silicon proof mass held within a dual-axis stage. The dual-axis stage comprises four platforms that are coupled to the proof mass at each corner of the proof mass, by flexures. The platforms are coupled to a surrounding frame by flexures. The platforms are each mechanically coupled to vibratory double ended tuning fork resonators. The acceleration of the proof mass results in strain on the resonators, altering their resonant frequency. <CIT> discloses an integrated MEMS inertial sensor device. The device is a two proof-mass design with concentrically configured proof masses and frame structures. A first proof mass is connected to a first frame by springs configured to allow translation along an X-axis. The first frame is coupled to a second frame by springs configured to allow translation along a Y-axis. The second frame is coupled to anchors. The device further discloses a second proof mass, which is disclosed to be a Z proof mass and is coupled by springs to the anchors. The springs can allow rotational translation about the X-axis, allowing displacement of the second proof mass in a Z direction.

The invention is defined in the appended independent claims, to which reference should be made.

In a first aspect of the invention, there is provided an accelerometer comprising:.

An accelerometer in accordance with the invention has the advantage of providing for two axes of acceleration measurement in a single, compact device. The sensitive axes can be aligned at the chip level if the accelerometer is fabricated from a single piece of semiconductor material. The two sensitive axes are mechanically decoupled from one another so that cross talk between two axes of measurement is minimised.

Advantageously, a centre of mass of the first proof mass is substantially coincident with a centre of mass of the second proof mass. This ensures that both masses respond to inertial forces acting at the same effective location.

Advantageously, the accelerometer is fabricated so that the first proof mass and the second proof mass are coplanar and lie in a plane defined by the first and second axes. This allows for straightforward fabrication of the accelerometer using a layered structure but with few layers, resulting in a compact accelerometer.

The first and second axes may be orthogonal to one another. It is typically desirable to provide orthogonal measurement axes as this simplifies the processing of the accelerometer outputs.

Advantageously, the first proof mass and second proof mass are of substantially equal mass. This provides for equal sensitivity along the first and second axes.

The accelerometer may be a micro electrical mechanical systems (MEMS) device. The frame, first proof mass, second proof mass and flexures may be formed from a single piece of semiconductor material, such as silicon. This allows for small and robust accelerometers to manufactured using well established fabrication techniques.

The first and second resonant element assemblies may be different to another. In particular the first and second resonant elements may be constructed to have significantly different resonant frequencies to one another. This reduces the potential for cross-talk between the outputs from the first and second resonant elements. The resonant element assemblies may be formed from the single piece of semiconductor material.

The accelerometer may comprise a third resonant element assembly fixed between the frame and the first proof mass, wherein movement of the proof mass along the first axis relative to the frame exerts a strain on the third resonant element that affects the resonant behaviour of the third resonant element assembly.

The third resonant element assembly may be substantially identical to the first resonant element assembly and is fixed on an opposite side of the first proof mass to the first resonant assembly in the direction of the first axis. The provision of a third resonant element in this way allows for common mode rejection of changes in the output due to effects such as variation in temperature or pressure.

The accelerometer may comprise a fourth resonant element assembly fixed between the frame and the second proof mass, wherein movement of the proof mass along the second axis relative to the frame exerts a strain on the fourth resonant element that affects the resonant behaviour of the fourth resonant element assembly.

The fourth resonant element assembly may be substantially identical to the second resonant element assembly and is fixed on an opposite side of the second proof mass to the second resonant assembly in the direction of the second axis. This again allows for common mode rejection.

One or more of the resonant element assemblies may comprise one or more resonant elements. The one or more resonant elements may be double ended tuning fork (DETF) resonant elements, for example. One or more of the resonant element assemblies may comprise a pair of weakly coupled resonant elements. Mode localisation in weakly coupled resonant elements can be used to provide a highly sensitive measure of acceleration.

The one or more of the resonant element assemblies may comprise a drive electrode though which a drive signal is applied to the resonant element assembly. At least one resonant element is driven into resonance by the drive signal.

The one or more resonant element assemblies may comprise one or more sense electrodes, through which a frequency of vibration or an amplitude of vibration of at least one resonant element can be detected. A control loop comprising both the drive electrode and the sense electrode may be used to maintain a resonant element assembly vibrating in resonance. Changes in the resonant frequency, or in the case of coupled resonant elements, a change in the relative amplitude of vibration of the couple resonant elements, can be used to provide a measure of acceleration.

The accelerometer may further comprise at least one lever linking the first proof mass or second proof mass to at least one of the resonant elements. The lever can be used to amplify the strain modulation experienced by the at least one resonant element as a result of movement of the first proof mass or second proof mass. This can improve the sensitivity of the accelerometer.

The accelerometer may comprise one or more electrodes adjacent the first proof mass or second proof mass and spaced from the first proof mass or the second proof mass along a third axis orthogonal to the first axis and the second axis. The flexures suspending the first proof mass or second proof mass from the frame may allow the first proof mass or second proof mass to move relative to the frame along the third axis. In other words, the first proof mass or second proof mass may be moveable towards or away from the one or more electrodes. This has the advantage of providing a third axis of acceleration measurement in a single, compact device.

The one or more electrodes may be used to indicate the proximity of the first proof mass or the second proof to the respective electrode to indicate the acceleration in the third axis. For example, the accelerometer may be configured to measure capacitance wherein the capacitance is dependent on the gap between the respective electrode and proof mass.

Alternatively, the one or more electrodes may be configured to drive the first or second proof mass to oscillate in the third axis. The acceleration in third axis may be determined by the accelerometer based on the oscillatory behaviour of the first or second proof mass. In particular, changes in the resonant frequency of the proof mass or masses can be measured based on signals from the one or more electrodes to allow acceleration along the third axis to be determined.

The one or more electrodes may be configured to calibrate the accelerometer. It may be advantageous to align the proof mass with a field in the third axis. The one or more electrodes may be configured to apply forces on the first or second proof mass to maintain this alignment.

The flexures that suspend the first proof mass from the frame may be positioned inside first proof mass. Similarly, the flexures that suspend the second proof mass from the frame may be positioned inside second proof mass. This may provide a compact accelerometer design.

In another aspect of the invention, there is provided a gravimeter comprising an accelerometer according to the first aspect of the invention.

<FIG> is a schematic illustration of a top view of an accelerometer in accordance with the present invention. The accelerometer is advantageously fabricated entirely from a single semiconductor wafer, such as a silicon-on-insulator (SOI) wafer.

The accelerometer comprises a first proof mass <NUM> and a second proof mass <NUM>. The second proof mass <NUM> surrounds the first proof mass <NUM> on all sides. The center of mass of the first proof <NUM> is coincident with the centre of mass of the second proof mass <NUM>. The first proof mass <NUM> and the second proof <NUM> mass have equal mass.

The first proof mass <NUM> and second proof mass <NUM> are coplanar and lie in a plane defining an X axis and a Y axis. The X and Y axes are shown in <FIG> and are orthogonal to one another. Orthogonal to both the X and Y axis is a Z axis. The Z axis is in a direction out of the page with respect to <FIG>.

Flexures <NUM> couple the first proof mass <NUM> to fixed anchors <NUM> such that the first proof mass <NUM> is suspended from the fixed anchors <NUM>. The fixed anchors are all part of the same frame.

A first resonator <NUM> of a first resonant assembly is connected between an anchor <NUM> on the frame and one side of the first proof mass <NUM> through amplifying levers <NUM>. In operation, the first resonant element is driven to resonance by the application of an alternating current to a drive electrode <NUM> adjacent to the resonant element.

The second proof mass <NUM> is similarly suspended from fixed anchors <NUM> on the frame by flexures <NUM>. A second resonator <NUM> of a second resonant element assembly is connected between the frame and one side of the second proof mass <NUM> through amplifying levers <NUM>. In operation, the second resonant element is driven to resonance by the application of an alternating current to electrodes adjacent to the second resonant element.

<FIG> is an enlarged view of the second resonant element assembly of <FIG>, including the drive and sense electrodes. The second resonator <NUM> is connected to the frame at anchor <NUM> and to the second proof mass <NUM> (not shown) through levers <NUM>. The resonator is driven into resonance by the application of a voltage to drive electrode <NUM>, which is adjacent to the resonator. The frequency or amplitude, or both the frequency and amplitude, of vibration of the second resonator <NUM> is detected by monitoring the voltage on readout electrode <NUM>.

By providing both a first and a second proof mass <NUM> and <NUM>, the accelerometer of <FIG> can provide a measure of acceleration in two axes, the X axis and the Y axis.

The accelerometer is sensitive to acceleration along the X axis as a result of acceleration of the first proof mass <NUM> along the X axis. The first resonant element experiences a force as a result of acceleration of the proof mass along the X axis. Amplifying levers <NUM>, also referred to as a micro-levers, amplify the force applied to the first resonant element as a result of the displacement of the first proof mass along the X axis. In this way, any displacement of the proof mass along the X axis results in a strain on the first resonant element. The strain induced on the first resonant element results in a change in the resonant behaviour of the first resonant element.

The accelerometer is sensitive to acceleration along the Y axis as a result of displacement of the second proof mass <NUM> along the Y axis. The second resonant element experiences a force as a result of acceleration of the proof mass along the Y axis. Amplifying levers <NUM>, also referred to as micro-levers, amplify the inertial force applied to the second resonant element as a result of the displacement of the second proof mass <NUM> along the Y axis. Any displacement of the proof mass along the Y axis results in a strain on the second resonant element. The strain induced on the second resonant element results in a change in the resonant behaviour of the second resonant element.

With the arrangement shown in <FIG>, the first proof mass <NUM> is mechanically decoupled from the second proof mass <NUM>. Therefore, cross talk between two axes of measurement is minimised.

In the embodiment illustrated in <FIG>, identical resonator assemblies are attached at diametrically opposite sides of the first proof mass <NUM> along the X axis. In other words, a third resonator assembly <NUM> is positioned diametrically opposite the first resonator assembly and connected to the frame and to the first proof mass <NUM> through amplifying levers <NUM>. Any motion of the first proof mass <NUM> consequently gets translated into an equal magnitude of strain on each of the oppositely positioned resonators, but of opposite polarity. By taking the difference between the output from the first resonant element assembly and the output from the third resonant element assembly, common mode effects can be rejected.

Similarly, identical resonator assemblies are attached at diametrically opposite sides of the second proof mass <NUM>. In other words, a fourth resonator assembly <NUM> is positioned diametrically opposite the second resonator assembly and connected to the second proof mass <NUM> through amplifier levers <NUM>. This again allows variations due to common mode effects to be rejected.

While the first and third resonator assemblies are advantageously identical to one another, the second resonant element assembly is advantageously different to the first resonator assembly. In particular the first and second resonant elements are designed to have significantly different resonant frequencies to one another. This reduces the potential for cross-talk between the outputs from the first and second resonant elements <NUM> and <NUM>.

The flexures <NUM> and <NUM> that are used to suspend each of the first and second proof masses from the frame may be single beam flexures. These offer good cross-axis decoupling of the acceleration in the X axis or the Y axis respectively. However the stiffness of single beam flexures can exhibit early onset of mechanical nonlinearity (the spring hardening effect). This means that the displacement of the proof mass will not be linear with increasing acceleration at high acceleration levels and the inertial force on the resonant elements will be relatively reduced at large displacements. To improve the sensitivity of the accelerometer, folded flexure beams can be used. However, conventional folded beam designs provide limited cross-axis decoupling, making them undesirable for a single axis accelerometer. So, to improve sensitivity of the accelerometer, it is advantageous to use serpentine flexures <NUM>, <NUM> to suspend the proof mass from the frame, as illustrated in <FIG>. A serpentine shape can minimise the spring hardening effect but still maintain good cross-axis decoupling. Serpentine flexures are described in more detail in <CIT>.

As described, the accelerometer is advantageously fabricated entirely from a single semiconductor wafer, such as a silicon-on-insulator (SOI) wafer and can be fabricated using conventional MEMS fabrication techniques, such as surface micromachining and etching. By fabricating the accelerometer from a single piece of semiconductor material, the sensitive axes can be aligned at the chip level.

<FIG> is a schematic illustration of the basic elements and principle of operation of the accelerometer for measuring acceleration based on changes in the resonant frequency of a resonator element. The principle of operation is described with respect to the first proof mass <NUM> and for measuring an acceleration in the X axis, but equally applies for measuring an acceleration in the Y axis with the second proof mass based on changes in the resonant frequency of a resonator element.

An acceleration acts on the first proof mass <NUM> to generate an inertial force along the X axis. The inertial force is amplified by the levers <NUM> to act on the resonant element of the first and third resonant element assemblies. A frequency tracking oscillator, represented in <FIG> by amplifier <NUM> is used to maintain the resonant elements at a resonant frequency. Any change in resonant frequency is measured by frequency measurement unit <NUM> and processed using a data processing unit <NUM> to provide an output measured acceleration signal.

<FIG> illustrates an example of a resonant element that can be used in the accelerometer of <FIG>. The resonant element of the resonant element assembly is a double-ended tuning fork (DETF) resonator and comprises first and second tines <NUM>, <NUM> connected between a fixed anchor <NUM> on the frame and a floating anchor <NUM> which is connected to the first proof mass through the levers <NUM> (not shown in <FIG>). Elements <NUM> are connections to the amplifying levers. First and second electrodes <NUM> and <NUM> are connected to the first second tines <NUM> and <NUM> and are used to drive and sense the motion of tines. As described above, the embodiment illustrated in <FIG> comprises identical resonator assemblies attached at diametrically opposite sides of the first proof mass <NUM> along the X axis and diametrically opposite sides of the second proof mass <NUM> along the Y axis. Any motion of the first proof mass <NUM> consequently gets translated into an equal magnitude of strain on each of the oppositely positioned resonators, but of opposite polarity. In other words, one resonator undergoes an axial tensile stress while the other undergoes an axial compressive stress. This arrangement allows for a differential measurement from the two diametrically opposed resonators which can then be used to provide for common mode cancellation.

In order to obtain the maximum common-mode rejection of the influence of temperature, residual stress, and cross-axis vibrations, it is advantageous for the resonant elements of the first and third (or second and fourth) resonant element assemblies to have identical geometry to one another. However, if both the first and third resonant elements are driven in the same mode of vibration, then problems can arise. In particular, manufacturing tolerances means that the two resonant elements will never have exactly the same resonant frequency for a given mode of vibration. The resulting currents signals from the two resonant elements have very similar but not identical frequencies. When used together in a differential output scheme this can lead to issues such as mode-shape distortion, injection locking and signal cross-talk because of unavoidable mechanical and electrical coupling effects in the accelerometer.

To address this issue, the accelerometer of <FIG> is configured to drive the resonant element of the first resonant element assembly in a different mode to the resonant element of the third resonant element assembly, the different modes having different resonant frequencies, but using the same electrode arrangement for both resonant elements. This preserves the symmetry of the mechanical structure and removes any restriction on which of the resonant elements should operate in which mode.

In one embodiment, one of the first and third resonant elements is driven to vibrate in a fundamental mode and the other of the first and third resonant elements is driven to vibrate in a second order mode. <FIG> illustrates in an exaggerated form, the shape of the fundamental mode of vibration <NUM> and a second order mode of vibration <NUM>. The two modes have different resonant frequencies but both can be excited independently by a single pair of adjacent drive electrodes.

Modes other than the modes illustrated in <FIG> can be used, and different forms of resonant element can be used. However, there is an advantage to an arrangement which preserves the symmetry of the physical structure of the accelerometer. Different modes will give rise to different scale factors. In other words, for a given input acceleration the frequency shift of the resonant frequency will be greater for one mode than the other. The overall scale factor for the accelerometer along that axis will be the average of the two. The use of higher order modes can be advantageous because they will typically give rise to higher scale factors.

<FIG> illustrates in more detail the drive and sense circuitry used to produce output signals that are measures of acceleration along the X and Y axes. As described with reference to <FIG> and <FIG>, each resonant element is driven by a drive electrode and the vibratory response sensed by a sense electrode. A frequency tracking oscillator is used for each resonant element to provide feedback control in order to maintain each resonant element at resonance. The resonant frequency of each resonant element, which will vary depending on the strain experienced by that resonant element, and the amplitude of vibration of each resonant element is provided as an output from each frequency tracking oscillator. As shown in <FIG> the first resonant element <NUM> is driven by drive electrode <NUM>, and the response sensed by sense electrode <NUM>. The oscillator <NUM> maintains the first resonator in resonance and outputs the resonant frequency to the multi-axis processing circuit <NUM>. An identical arrangement is used for the third resonator assembly <NUM>, with the oscillator <NUM> maintaining the third resonator in resonance and outputting the resonant frequency to the multi-axis processing circuit <NUM>. The multi-axis processing circuit <NUM> uses the difference between the output from the oscillator <NUM> and the output from the oscillator <NUM>, having adjusted for any scale factor difference, to provide a measure of acceleration Ax along the X axis.

The same arrangement is used for second and fourth resonator assemblies. The second resonant element <NUM> is driven by drive electrode <NUM>, and the response sensed by sense electrode <NUM>. The oscillator <NUM> maintains the second resonator in resonance and outputs the resonant frequency to the multi-axis processing circuit <NUM>. The oscillator <NUM> maintains the fourth resonator assembly <NUM> in resonance and outputs the resonant frequency to the multi-axis processing circuit <NUM>. The multi-axis processing circuit <NUM> uses the difference between the output from the oscillator <NUM> and the output from the oscillator <NUM>, having adjusted for any scale factor difference, to provide a measure of acceleration Ay along the Y axis.

A measure of acceleration in the Z-axis can also be obtained using an arrangement described below, with reference to <FIG>. An output from the Z-axis electrode or electrodes can be provided to the multi-axis processing circuit <NUM>.

<FIG> illustrates an alternative example of a resonant element assembly. Rather than relying on frequency shift of the resonant frequency to measure acceleration, the resonant element assembly of <FIG> exploits the phenomenon of mode localization in two weakly coupled resonant elements.

As described above, an acceleration acts on the first proof mass <NUM> to generate an inertial force along the X axis. However, in this arrangement, each resonant element assembly comprises two resonant elements. A first resonator element <NUM> is connected between a fixed anchor <NUM> on the frame and a floating anchor <NUM> which is connected to the first proof mass through the one of the levers <NUM> (not shown in <FIG>). A second resonant element <NUM>, identical to the first resonant element <NUM>, is coupled to the first resonant element <NUM> by a mechanical coupling <NUM>. The second resonant element is connected on one end to the fixed anchor <NUM> and at the other end to the other amplifying lever <NUM>, identical to the other amplifying lever <NUM>, but not to the proof mass. This provides structural symmetry between the first and second resonant elements.

In operation, the resonant elements <NUM>, <NUM> are driven to resonance by the application of an alternating voltage to the drive electrodes. The mechanical coupling between the resonant elements in each pair is only a weak coupling. When two vibrating resonant elements are weakly coupled in this way, any change in stiffness of one resonant element relative to the other leads to significant changes in the relative amplitude of vibration of the two coupled resonators. By monitoring the ratio of the amplitude of vibration of the resonant elements <NUM>, <NUM>, a measure of acceleration of the proof mass can be obtained. This can be achieved either by measuring the amplitudes of both the resonant elements and comparing the two, or by controlling the amplitude of vibration of one of the resonant elements to be constant using feedback control, and measuring the amplitude of vibration of the other. This phenomenon is called mode localization and is explained in detail in <CIT>.

While <FIG> shows a mechanical coupling between the two vibrating resonant elements, the means for coupling may instead by an electrostatic coupling means.

As described, an accelerometer in accordance with the invention may advantageously be made from a single silicon wafer. <FIG> illustrates four layers of a silicon accelerometer having a layout as shown in <FIG>. Each layer extends in the plane defined by the X and Y direction, as already described.

Base layer <NUM> forms the base of the accelerometer. This base layer comprises a frame <NUM> in which the fixed anchors <NUM> and <NUM> are defined.

Layers <NUM> and <NUM> are lower and upper intermediate layers of the accelerometer. The fixed anchors <NUM> and <NUM> are defined in both layer <NUM> and layer <NUM>. The lower intermediate layer <NUM> has voids around the areas defining the first proof mass <NUM> and the second proof mass <NUM>. Each of the proof masses is shaped around the fixed anchors. Furthermore, there are spaces provided to allow for movement of the flexures, resonant element assemblies and levers in the upper intermediate layer, as well as spaces allowing for displacement of the proof masses in response to acceleration in either the X direction or the Y direction.

The upper intermediate layer <NUM> provides the flexures, resonant element assemblies and levers, which are connected to the first and second proof masses <NUM> and <NUM>. The flexures are connected to the proof masses at one end and to the fixed anchors at the other. The first and second proof masses can move relative to the frame. A comparison of the lower intermediate layer <NUM> with the upper intermediate layer <NUM> illustrates the relative thickness of the proof masses <NUM> and <NUM> compared to other features such as the flexures. This is so that the proof masses have as large a mass as possible within the confines of the device. Larger proof masses provide for greater device sensitivity.

The top layer <NUM> is a cap layer of the accelerometer and seals the moving parts from the environment.

<FIG> illustrates an arrangement for detecting acceleration in a third axis using the first or second proof mass of the embodiment of <FIG>. <FIG> is a schematic cross-section through an accelerometer, showing the proof mass <NUM> suspended from a frame <NUM> by flexures <NUM>. A Z-axis drive and sense electrode <NUM> is provided in the cap layer of the frame <NUM>, above the proof mass <NUM>. The proof mass is able to move along the Z-axis on the flexures <NUM>, as illustrated by the dotted line in response to an applied acceleration along the z-axis. As the distance between the proof mass <NUM> and the electrode <NUM> varies, so will the capacitance between the proof mass <NUM> and the electrode <NUM>.

In one arrangement, the value of the variable capacitance between the proof mass <NUM> and the electrode <NUM> is used as a measure of acceleration. In another embodiment, the electrode <NUM> may be used to drive the proof mass and flexure assembly into a resonant vibration along the z-axis by the application of a drive voltage. Any external acceleration in the Z-axis direction will result in an additional strain on the flexures <NUM>, altering the resonant frequency of the proof mass and flexure assembly. As with the X and Y axis readouts, a frequency tracking oscillator can be used to provide an output signal to the multi-axis processing circuit <NUM>, shown in <FIG>. A measure of acceleration in the Z-axis direction can thus be obtained.

As well as providing a measure of acceleration in the Z-axis direction, one or more electrodes in the cap layer can be used to correct small tilts of the device relative to the gravity field. By applying electrostatic forces on the first and second proof masses, the accelerometer can be correctly aligned.

Claim 1:
An accelerometer comprising:
a frame (<NUM>);
a first proof mass (<NUM>) suspended from the frame by one or more flexures (<NUM>) to move relative to the frame along a first axis;
a first resonant element assembly fixed between the frame and the first proof mass, wherein movement of the proof mass along the first axis relative to the frame exerts a strain on the first resonant element (<NUM>) that affects the resonant behaviour of the first resonant element assembly; characterised in
a second proof mass (<NUM>) suspended from the frame by one or more flexures (<NUM>) to move relative to the frame along a second axis,
a second resonant element assembly fixed between the frame and the second proof mass, wherein movement of the proof mass along the second axis relative to the frame exerts a strain on the second resonant element (<NUM>) that affects the resonant behaviour of the second resonant element assembly;
wherein the second proof mass surrounds the first proof mass and the first resonant element assembly.