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225 lines
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title = "Piezoelectric Actuators"
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author = ["Dehaeze Thomas"]
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draft = false
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category = "equipment"
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Tags
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: [Actuators]({{< relref "actuators.md" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}})
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## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
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### Manufacturers {#manufacturers}
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| Manufacturers | Country |
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|----------------------------------------------------------------------------------------------------------------------|-----------|
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| [Cedrat](http://www.cedrat-technologies.com/) | France |
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| [PI](https://www.physikinstrumente.com/en/) | USA |
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| [Piezo System](https://www.piezosystem.com/products/piezo_actuators/stacktypeactuators/) | Germany |
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| [Noliac](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark |
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| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8700) | USA |
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| [PiezoDrive](https://www.piezodrive.com/actuators/) | Australia |
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| [Mechano Transformer](http://www.mechano-transformer.com/en/products/10.html) | Japan |
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| [CoreMorrow](http://www.coremorrow.com/en/pro-9-1.html) | China |
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| [PiezoData](https://www.piezodata.com/piezo-stack-actuator-2/) | China |
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| [Queensgate](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) | UK |
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| [Matsusada Precision](https://www.matsusada.com/product/pz/) | Japan |
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| [Sinocera](http://www.china-yec.net/piezoelectric-ceramics/) | China |
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| [Fuji Ceramisc](http://www.fujicera.co.jp/en/) | Japan |
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### Model {#model}
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A model of a multi-layer monolithic piezoelectric stack actuator is described in (<a href="#citeproc_bib_item_2">Fleming 2010</a>) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb.md" >}})).
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Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
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The relation between the applied voltage \\(V\_a\\) to the generated force \\(F\_a\\) is:
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\\[ F\_a = g\_a V\_a, \quad g\_a = d\_{33} n k\_a \\]
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with:
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- \\(d\_{33}\\) is the piezoelectric strain constant [m/V]
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- \\(n\\) is the number of layers
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- \\(k\_a\\) is the actuator stiffness [N/m]
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## Piezoelectric Plate Actuators {#piezoelectric-plate-actuators}
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Some manufacturers propose "raw" plate actuators that can be used as actuator / sensors.
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| Manufacturers | Country |
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|---------------------------------------------------------------------|---------|
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| [Noliac](http://www.noliac.com/products/actuators/plate-actuators/) | Denmak |
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## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
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The Amplified Piezo Actuators principle is presented in (<a href="#citeproc_bib_item_1">Claeyssen et al. 2007</a>):
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> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
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> The flatter is the actuator, the higher is the amplification.
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A model of an amplified piezoelectric actuator is described in (<a href="#citeproc_bib_item_5">Lucinskis and Mangeot 2016</a>).
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Typical topology of mechanically amplified piezoelectric actuators are displayed in Figure [1](#figure--fig:ling16-topology-piezo-mechanism-types) (from (<a href="#citeproc_bib_item_3">Ling et al. 2016</a>)).
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<a id="figure--fig:ling16-topology-piezo-mechanism-types"></a>
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{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="<span class=\"figure-number\">Figure 1: </span>Topology of several types of compliant mechanisms" >}}
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| Manufacturers | Country |
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|----------------------------------------------------------------------------------------------------|-----------|
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| [Cedrat](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France |
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| [PiezoDrive](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia |
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| [Dynamic-Structures](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA |
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| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8700) | USA |
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| [Noliac](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark |
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| [Mechano Transformer](http://www.mechano-transformer.com/en/products/01a_actuator_5.html) | Japan |
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| [CoreMorrow](http://www.coremorrow.com/en/pro-13-1.html) | China |
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| [PiezoData](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
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## Specifications {#specifications}
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### Typical Specifications {#typical-specifications}
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Typical specifications of piezoelectric stack actuators are usually in terms of:
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- Displacement/ Travel range \\([\mu m]\\)
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- Blocked force \\([N]\\)
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- Stiffness \\([N/\mu m]\\)
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- Resolution \\([nm]\\)
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- Length \\([mm]\\)
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- Electrical Capacitance \\([nF]\\)
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### Displacement and Length {#displacement-and-length}
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The maximum displacement specified is the displacement of the actuator when the maximum voltage is applied without any load.
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Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\\%\\).
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The free displacement \\(\Delta L\_{f}\\) is then related to the length \\(L\\) of piezoelectric stack by:
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\begin{equation}
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\Delta L\_f \approx \frac{L}{1000}
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\end{equation}
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> A “free” actuator — one that experiences no resistance to movement — will produce its maximum displacement, often referred to as “free stroke,” and generate zero force.
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Note that this maximum displacement is only attainable at DC.
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For dynamical applications, the electrical capacitance of the piezoelectric actuator is an important factor (see bellow).
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### Blocked Force {#blocked-force}
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The blocked force \\(F\_b\\) is measured by first applying the maximum voltage to the piezoelectric stack without any load.
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Thus, the piezoelectric stack experiences its maximum displacement.
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A force is then applied to return the actuator to its original length.
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This force is measured and recorded as the blocking force.
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The blocking force is also the maximum force that can produce the piezoelectric stack in contact with an infinitely stiff environment.
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> When an actuator is blocked from moving, it will produce its maximum force, which is referred to as the blocked, or blocking, force.
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### Stiffness {#stiffness}
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The stiffness of the actuator is the ratio of the blocking force to the free stroke:
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\begin{equation}
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k\_p = \frac{F\_b}{\Delta L\_f}
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\end{equation}
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with:
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- \\(k\_p\\): stiffness of the piezo actuator
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- \\(F\_b\\): blocking force
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- \\(\Delta L\_f\\): free stroke
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### Resolution {#resolution}
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The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}).
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Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio.md" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
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Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
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\begin{equation}
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r \approx \frac{L}{10^5}
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\end{equation}
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For a piezoelectric stack with a displacement of \\(100\\,[\mu m]\\), the resolution will be \\(\approx 1\\,[nm]\\).
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### Electrical Capacitance {#electrical-capacitance}
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The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#figure--fig:piezoelectric-capacitance-voltage-max)).
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This is due to the fact that voltage amplifier has a limitation on the deliverable current.
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[Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
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<a id="figure--fig:piezoelectric-capacitance-voltage-max"></a>
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{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="<span class=\"figure-number\">Figure 2: </span>Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}}
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## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
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When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#figure--fig:piezoelectric-mass-load)).
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<a id="figure--fig:piezoelectric-mass-load"></a>
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{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="<span class=\"figure-number\">Figure 3: </span>Motion of a piezoelectric stack actuator under external constant force" >}}
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## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
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Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#figure--fig:piezoelectric-spring-load)):
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\begin{equation}
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\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
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\end{equation}
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<a id="figure--fig:piezoelectric-spring-load"></a>
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{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="<span class=\"figure-number\">Figure 4: </span>Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
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For piezo actuators, force and displacement are inversely related (Figure [5](#figure--fig:piezoelectric-force-displ-relation)).
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Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
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Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
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When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced.
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<a id="figure--fig:piezoelectric-force-displ-relation"></a>
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{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="<span class=\"figure-number\">Figure 5: </span>Relation between the maximum force and displacement" >}}
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## Piezoelectric stiffness - Electrical Boundaries {#piezoelectric-stiffness-electrical-boundaries}
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The stiffness of the piezoelectric stack varies a little bit whether it is open-circuited or short-circuited (<a href="#citeproc_bib_item_4">Liu et al. 2007</a>).
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This this experiment: <https://research.tdehaeze.xyz/test-bench-force-sensor/>.
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Therefore, if the piezoelectric actuator is driven by a charge amplifier (i.e. high input impedance), the stiffness will be a little bit higher than if it is driven with a voltage amplifier (i.e. small input impedance).
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## Driving Electronics {#driving-electronics}
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Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}).
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Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems]({{< relref "fleming14_desig_model_contr_nanop_system.md" >}}).
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## Bibliography {#bibliography}
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” <i>Ferroelectrics</i> 351 (1): 3–14. doi:<a href="https://doi.org/10.1080/00150190701351865">10.1080/00150190701351865</a>.</div>
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<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>Ieee/Asme Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
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<div class="csl-entry"><a id="citeproc_bib_item_3"></a>Ling, Mingxiang, Junyi Cao, Minghua Zeng, Jing Lin, and Daniel J Inman. 2016. “Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms.” <i>Smart Materials and Structures</i> 25 (7): 075022. doi:<a href="https://doi.org/10.1088/0964-1726/25/7/075022">10.1088/0964-1726/25/7/075022</a>.</div>
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<div class="csl-entry"><a id="citeproc_bib_item_4"></a>Liu, W. Q., Z. H. Feng, R. B. Liu, and J. Zhang. 2007. “The Influence of Preamplifiers on the Piezoelectric Sensor’s Dynamic Property.” <i>Review of Scientific Instruments</i> 78 (12): 125107. doi:<a href="https://doi.org/10.1063/1.2825404">10.1063/1.2825404</a>.</div>
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<div class="csl-entry"><a id="citeproc_bib_item_5"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”</div>
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</div>
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