IP Library › Granted Patent US 12,631,516
Granted Patent B2
US 12,631,516 · App. 18/133,135 · Granted May 19, 2026

Systems and methods for tuning resonators for enhanced sensitivity

Inventors: Xiaopeng Li (Ann Arbor, MI); Taehwa Lee (Ann Arbor, MI); Ziqi Yu (Ann Arbor, MI); Yuyang Song (Ann Arbor, MI)
Assignees: TOYOTA MOTOR ENGINEERING & MANUFACTURING NORTH AMERICA, INC.; TOYOTA JIDOSHA KABUSHIKI KAISHA
G01M7/025G01L9/0022G01L9/06G01L9/08G01L17/00
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Quick Facts
Patent No.
US 12,631,516
App. No.
18/133,135
Granted
May 19, 2026
Kind
B2
Abstract

System, methods, and other embodiments described herein relate to tuning a mechanical resonator for detecting a significant value using an electrical resonator that enhances sensitivity. In one embodiment, a system includes a mechanical resonator having a beam coupled to a body. The system also includes an electrical resonator coupled through a patch to the mechanical resonator, the electrical resonator operating as a shunt and having an inductor and a resistor (LR) circuit in series. The system also includes the electrical resonator that detects, associated with a perturbation of the body, an exceptional point (EP) of the mechanical resonator by varying the LR circuit according to a model.

Claims (29)

1 . A system comprising:

a mechanical resonator having a beam coupled to a body;

an electrical resonator coupled through a patch to the mechanical resonator, the electrical resonator operating as a shunt and having an inductor and a resistor that form an LR circuit in series; and

the electrical resonator detects a signal caused by a perturbation of the body and a processor is configured to compute an exceptional point (EP) of the mechanical resonator by varying the LR circuit according to a model, and the EP represents an intersection of eigen parameters associated with values of the inductor and the resistor.

2 . The system of claim 1 further comprising the electrical resonator causes tuning to the EP using the model, wherein the model follows a square-root dependence on a resistance of the resistor from the electrical resonator, and the square-root dependence is associated with the perturbation and a splitting frequency.

3 . The system of claim 2 , wherein the EP represents an intersection and coalescence of the eigen parameters, and the eigen parameters include eigenfrequencies and eigenvalues associated with the values of the inductor and the resistor.

4 . The system of claim 2 , wherein a peak of the splitting frequency is derived from the square-root dependence and the splitting frequency represents a frequency response of the mechanical resonator associated with the perturbation that is resistance.

5 . The system of claim 4 , wherein the splitting frequency is associated with scaling as a square-root of a strength associated with the perturbation.

6 . The system of claim 5 , wherein the values are correlated with a temperature or a crack associated with the electrical resonator.

7 . The system of claim 2 further comprising the electrical resonator measures resistance values for the resistance at the EP.

8 . The system of claim 1 , wherein the model is a complex-square-root function that derives the EP associated with the perturbation of the mechanical resonator and the perturbation causes frequency splitting of a frequency response.

9 . The system of claim 1 , wherein the mechanical resonator and the electrical resonator are associated with one of a sensor, an ultrasonic sensor, and a waveguide.

10 . The system of claim 1 , wherein the patch is a piezoelectric material and the EP is associated with the perturbation of a shunting impedance.

11 . The system of claim 1 , wherein the beam is one of an elastic material, aluminum, a micro-structure resonator, and a nano-structure resonator.

12 . A system comprising:

a mechanical resonator having a flexible beam coupled to a body;

an electrical resonator coupled through a patch to the mechanical resonator, the electrical resonator shunting the mechanical resonator and having an inductor and a resistor that form an LR circuit in series; and

the electrical resonator controls frequency detuning near an exceptional point (EP) of the mechanical resonator by controlling the LR circuit according to a model using a signal, and the EP represents an intersection of eigen parameters associated with values of the inductor and the resistor.

13 . The system of claim 12 further comprising the electrical resonator causes tuning to the EP using the model, wherein the model follows a square-root dependence for a resistance of the resistor from the electrical resonator, and the square-root dependence is associated a splitting frequency.

14 . The system of claim 13 , wherein the EP represents a crossing of eigenfrequencies associated with the values of the inductor and the resistor, and the eigen parameters include the eigenfrequencies.

15 . The system of claim 13 , wherein a peak of the splitting frequency is derived from the square-root dependence and the splitting frequency represents a frequency response of the mechanical resonator.

16 . The system of claim 13 further comprising the electrical resonator measures resistance values for the resistance at the EP.

17 . The system of claim 16 , wherein the resistance values are correlated with a temperature or a crack from a structure coupled to the electrical resonator.

18 . The system of claim 12 , wherein the model is a complex-square-root function that derives the EP associated with a perturbation of the mechanical resonator and the perturbation causes frequency splitting of a frequency response.

19 . A sensor comprising:

a mechanical resonator having a flexible beam coupled to a body;

an electrical resonator coupled through a piezoelectric device to the mechanical resonator, the electrical resonator shunting the mechanical resonator through an inductor and a resistor that form an LR circuit in series; and

the electrical resonator is configured to measure, associated with a shock of the body, frequency detuning near an exceptional point (EP) of the mechanical resonator by controlling the LR circuit according to a non-linear model and a signal, and the EP represents an intersection of eigen parameters associated with values of the inductor and the resistor.

20 . The sensor of claim 19 further comprising the electrical resonator causes tuning to the EP using the non-linear model, wherein the non-linear model follows a square-root dependence for a resistance of the resistor from the electrical resonator, and the square-root dependence is associated with a splitting frequency.

Assignments (2)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Jun 17, 2026
From: TOYOTA MOTOR ENGINEERING & MANUFACTURING NORTH AMERICA, INC.
To: TOYOTA JIDOSHA KABUSHIKI KAISHA
Reel/Frame 074994/0828 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded May 12, 2023
From: LI, XIAOPENG; LEE, TAEHWA; YU, ZIQI; SONG, YUYANG
To: TOYOTA MOTOR ENGINEERING & MANUFACTURING NORTH AMERICA, INC.; TOYOTA JIDOSHA KABUSHIKI KAISHA
Reel/Frame 063626/0460 →
Continuity (2)
Provisional Application 63447489 · Feb 22, 2023
Related Publication 20240280432A1 · Aug 22, 2024
References Cited (113)
US 3609593A · Boll · 1971 [cited by examiner]
US 4492246A · Prescott et al. · 1985 [cited by applicant]
US 5499526A · Muro · 1996 [cited by applicant]
US 6134964A · Jaenker · 2000 [cited by examiner]
US 6954686B2 · Aubourg · 2005 [cited by examiner]
US 7358503B2 · Fellerman et al. · 2008 [cited by applicant]
US 7551058B1 · Johnson et al. · 2009 [cited by applicant]
US 8354778B2 · Arnold · 2013 [cited by examiner]
US 9411029B2 · Pirkl · 2016 [cited by applicant]
US 9601266B2 · Karalis · 2017 [cited by examiner]
US 9933503B2 · Vernickel et al. · 2018 [cited by applicant]
US 10284176B1 · Solal · 2019 [cited by applicant]
US 10717672B2 · Loh et al. · 2020 [cited by applicant]
US 10724994B2 · Van Tooren et al. · 2020 [cited by applicant]
US 11022561B2 · Ziehl · 2021 [cited by applicant]
US 11162972B2 · Abdolvand et al. · 2021 [cited by applicant]
US 20090301176A1 · Rowe · 2009 [cited by examiner]
US 20110107838A1 · Suijlen et al. · 2011 [cited by applicant]
US 20140053651A1 · Besling et al. · 2014 [cited by applicant]
US 20140062256A1 · Buss · 2014 [cited by examiner]
US 20150308911A1 · Pechstedt et al. · 2015 [cited by applicant]
US 20150338380A1 · Ziehl et al. · 2015 [cited by applicant]
US 20170115382A1 · Koudar et al. · 2017 [cited by applicant]
US 20180062062A1 · de Bonfim Gripp · 2018 [cited by examiner]
US 20180107015A1 · Dümpelmann et al. · 2018 [cited by applicant]
US 20190028084A1 · Yoon · 2019 [cited by examiner]
US 20220051650A1 · Lee et al. · 2022 [cited by applicant]
US 20220057440A1 · Capolino · 2022 [cited by examiner]
US 20220190231A1 · Li et al. · 2022 [cited by applicant]
US 20220214312A1 · Lee et al. · 2022 [cited by applicant]
US 20220285604A1 · Li et al. · 2022 [cited by applicant]
US 20240371349A1 · Li et al. · 2024 [cited by applicant]
US 20240371350A1 · Li et al. · 2024 [cited by applicant]
US 20240372530A1 · Li · 2024 [cited by examiner]
CN 208254930U · 2018 [cited by examiner]
DE 102016105803A1 · 2017 [cited by examiner]
EP 1531372A1 · 2005 [cited by examiner]
EP 4477915A1 · 2024 [cited by examiner]
JP 2002070933A · 2002 [cited by examiner]
WO 2013076270A1 · 2013 [cited by applicant]
WO 2016081915A1 · 2016 [cited by applicant]
Translate_JP2002070933 (Year: 2002). [cited by examiner]
Wang et al., “Multi-resonant piezoelectric shunting induced by digital controllers for subwavelength elastic wave attenuation in smart metamaterial,” Smart Materials and Structures, vol. 26, No. 2, 2017, pp. 1-20. [cited by applicant]
Li et al., “A self-adaptive metamaterial beam with digitally controlled resonators for subwavelength broadband flexural wave attenuation,” Smart Materials and Structures, vol. 27, No. 4, 2018, pp. 1-13. [cited by applicant]
Gripp et al., “Vibration and noise control using shunted piezoelectric transducers: A review,” Mechanical Systems and Signal Processing, vol. 112, Nov. 2018, pp. 359-383. [cited by applicant]
Chen et al., “Elastic-electro-mechanical modeling and analysis of piezoelectric metamaterial plate with a self powered synchronized charge extraction circuit for vibration energy harvesting,” Mechanical Systems and Sign… [cited by applicant]
Nassar et al., “Nonreciprocity in acoustic and elastic materials,” Nature Reviews Materials, vol. 5, Iss. 9, 2020, pp. 667-685. [cited by applicant]
Sugino et al., “Nonreciprocal piezoelectric metamaterial framework and circuit strategies,” Physical Review B 102 (1), 2020, 7 pages. [cited by applicant]
Wu et al., “Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam,” The Journal of the Acoustical Society of America, vol. 146, Iss. 1, 2019, pp. 850-862. [cited by applicant]
Doppler et al., “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature, vol. 537, 2016, pp. 76-79. [cited by applicant]
Zhang et al., “Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point,” Physical Review X, vol. 8, Iss. 2, Apr. 2018, pp. 1-18. [cited by applicant]
A. Preumont et al., “Vibration control of active structures: an introduction,” 3rd edition, vol. 246, Springer, 2018, 202 pages. [cited by applicant]
Tang et al., “Active-passive hybrid piezoelectric networks for vibration control: comparisons and improvement,” Smart Materials and Structures, vol. 10, No. 4, 2001, pp. 794-806. [cited by applicant]
Neubauer et al., “Vibration damping with shunted piezoceramics: fundamentals and technical applications,” Mechanical Systems and Signal Processing, vol. 36, Iss. 1, 2013, pp. 36-52. [cited by applicant]
Haus et al., “Waves and fields in optoelectronics,” Prentice-Hall, Inc., Englewood Cliffs, NJ, 1984, 402. [cited by applicant]
Fan et al., “Temporal coupled-mode theory for the fano resonance in optical resonators,” JOSA A, vol. 20, Iss. 3, 2003, pp. 569-572. [cited by applicant]
Zhang et al., “A metamaterial beam with inverse nonlinearity for broadband micro-vibration attenuation,” Mechanical Systems and Signal Processing, vol. 159, Oct. 2021, pp. 1-13. [cited by applicant]
Allik et al., “Finite element method for piezoelectric vibration,” International journal for numerical methods in engineering, vol. 2, Iss. 2, 1970, pp. 151-157. [cited by applicant]
Leng et al., “Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems,” New Journal of Physics, vol. 21, May 2019, pp. 1-11. [cited by applicant]
Li et al., “An active meta-layer for optimal flexural wave absorption and cloaking,” Mechanical Systems and Signal Processing, vol. 149, Feb. 15, 2021, pp. 1-35. [cited by applicant]
Hsu et al., “Bound states in the continuum,” Nature Reviews Materials 1, article No. 16048, 2016, pp. 1-13. [cited by applicant]
Li et al. “Observation of an exceptional point with an LR-shunted resonator,” Mechanical Systems and Signal Processing, vol. 196, Aug. 1, 2023, pp. 1-25. [cited by applicant]
Li et al. “Experimental study of a tunable perfect flexural wave absorber with a piezoelectric shunted resonator,” Frontiers in Physics, vol. 10, Dec. 13, 2022, pp. 1-7. [cited by applicant]
Wu et al., “Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam,” The Journal of the Acoustical Society of America, vol. 146, 2019, pp. 850-862. [cited by applicant]
Schipf et al., “Tunable piezoelectric metamaterial for Lamb waves using periodic shunted circuits,” arXiv:2207.07845v1, Jul. 16, 2022, pp. 1-30. [cited by applicant]
Zhao et al., “Numerical analysis of effective refractive index ultrasonic sensor based on Cantilever arm structure slot-based dual-micro-ring resonator,” International Journal of Modern Physics B, vol. 35, No. 4, 2021, … [cited by applicant]
Durdaut et al., “Phase Sensitivity and Phase Noise of Cantilever-Type Magnetoelastic Sensors Based on the ΔE Effect,” arXiv:2003.01085v1, Mar. 2, 2020, pp. 1-15. [cited by applicant]
Casadei et al., “Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials,” Journal of Applied Physics, vol. 112, 2012, pp. 1-6. [cited by applicant]
Casadei et al., “Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates,” Smart Materials and Structures, vol. 19, No. 1, 2010, pp. 1-13. [cited by applicant]
Cardella et al., “Manipulating waves by distilling frequencies: a tunable shunt-enabled rainbow trap,” Smart Materials and Structures, vol. 25, 2016, pp. 1-15. [cited by applicant]
Jain et al., “Emerging Ideas in Nanocantilever based Biological Sensors,” arXiv:1305.5729, 2013, pp. 1-17. [cited by applicant]
Airoldi et al., “Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos,” New Journal of Physics, vol. 13, Nov. 2011, pp. 1-21. [cited by applicant]
Chen et al., “Exceptional points enhance sensing in an optical microcavity,” Nature, vol. 548, 2017, pp. 192-196. [cited by applicant]
Su et al., “Research on damage visualization of concrete structures based on electrical resistance tomography,” Frontiers in Physics, 2022, pp. 1-12. [cited by applicant]
Ashida et al., “Non-Hermitian physics,” Advances in Physics 69 (3) (2020), pp. 249-435. [cited by applicant]
Guo et al., “Observation of PT-symmetry breaking in complex optical potentials,” Physical review letters, vol. 103, Iss. 9, 2009, 4 pages. [cited by applicant]
Lee et al., “Topolectrical circuits,” Communications Physics 1 (1), 2018, pp. 1-9. [cited by applicant]
Yoshida et al., “Exceptional rings protected by emergent symmetry for mechanical systems,” Physical Review B, vol. 100, Iss. 5, 2019, pp. 1-17. [cited by applicant]
Fleury et al., “An invisible acoustic sensor based on parity-time symmetry,” Nature communications 6 (1), 2015, pp. 1-7. [cited by applicant]
Zangeneh-Nejad et al., “Active times for acoustic metamaterials,” Reviews in Physics, vol. 4, Nov. 2019, pp. 1-17. [cited by applicant]
Ding et al., “Emergence, coalescence, and topological properties of multiple exceptional points and their experimental realization,” Physical Review X, vol. 6, Iss. 2, 2016, 13 pages. [cited by applicant]
Gear et al., “Unidirectional zero reflection as gauged parity-time symmetry,” New Journal of Physics, vol. 19, Iss. 12, 2017, pp. 1-10. [cited by applicant]
Lin et al., “Unidirectional invisibility induced by p t-symmetric periodic structures,” Physical Review Letters, vol. 106, Iss. 21, 2011, pp. 1-4. [cited by applicant]
Li et al., “Experimental demonstration of extremely asymmetric flexural wave absorption at the exceptional point,” Extreme Mechanics Letters, vol. 52, Apr. 2022, pp. 1-6. [cited by applicant]
Wang et al., “Extremely asymmetrical acoustic metasurface mirror at the exceptional point,” Physical review letters, vol. 123, Iss. 21, Nov. 2019, pp. 1-5. [cited by applicant]
Hodaei et al., “Enhanced sensitivity at higher-order exceptional points,” Nature, vol. 548 (7666), Aug. 2017, pp. 187-191. [cited by applicant]
Assawaworrarit et al., “Robust wireless power transfer using a nonlinear parity-time-symmetric circuit,” Nature, vol. 546 (7658), Jun. 2017, pp. 387-390. [cited by applicant]
Peng et al., “Parity-time-symmetric whispering-gallery microcavities,” Nature Physics, vol. 10, Iss. 5, May 2014, pp. 394-398. [cited by applicant]
Yi et al., “Asymmetric viscoelastic metamaterials for broad bandgap design and unidirectional zero reflection,” Mechanical Systems and Signal Processing, vol. 162, Jan. 2022, pp. 1-15. [cited by applicant]
Wang et al., “Coherent perfect absorption at an exceptional point,” Science, vol. 373, Iss. 6560, Sep. 2021, pp. 1261-1265. [cited by applicant]
Sweeney et al., “Perfectly absorbing exceptional points and chiral absorbers,” Physical review letters, vol. 122, Iss. 9, Mar. 2019, pp. 1-6. [cited by applicant]
Zhu et al., “Simultaneous observation of a topological edge state and exceptional point in an open and non-Hermitian acoustic system,” Physical review letters, vol. 121, Iss. 12, Sep. 2018, pp. 1-14. [cited by applicant]
Liu et al., Willis metamaterial on a structured beam, Physical Review X, vol. 9, Iss. 1, 2019, pp. 1-21. [cited by applicant]
Domínguez-Rocha et al., “Environmentally induced exceptional points in elastodynamics,” Physical Review Applied 13 (1), 2020, pp. 1-8. [cited by applicant]
Cummer et al., “Controlling sound with acoustic metamaterials,” Nature Reviews Materials, vol. 1, Iss. 3, Mar. 2016, pp. 1-13. [cited by applicant]
Chen et al., “A review of tunable acoustic metamaterials,” Applied Sciences, vol. 8, Iss. 9, 2018, pp. 1-21. [cited by applicant]
Ji et al., “Recent progress in acoustic metamaterials and active piezoelectric acoustic metamaterials—a review,” Applied Materials Today, vol. 26, Mar. 2022, pp. 1-28. [cited by applicant]
Popa et al., “Non-reciprocal and highly nonlinear active acoustic metamaterials,” Nature communications, vol. 5, Iss. 1, 2014, pp. 1-5. [cited by applicant]
Popa et al., “Active acoustic metamaterials reconfigurable in real time,” Physical Review B, vol. 91, Iss. 22, 2015, pp. 1-7. [cited by applicant]
Akl et al., “Analysis and experimental demonstration of an active acoustic metamaterial cell,” Journal of Applied Physics, vol. 111, Iss. 4, 2012, 9 pages. [cited by applicant]
Chen et al., “An active mechanical willis meta-layer with asymmetric polarizabilities,” Nature communications, vol. 11 Iss. 1, 2020, pp. 1-8. [cited by applicant]
Li et al., “Shaping elastic wave mode conversion with a piezoelectric-based programmable meta-boundary,” Extreme Mechanics Letters, vol. 39, Sep. 2020, pp. 1-18. [cited by applicant]
Li et al., “An active meta-layer for optimal flexural wave absorption and cloaking,” Mechanical Systems and Signal Processing, vol. 149, Feb. 2021, pp. 1-35. [cited by applicant]
Chen et al., “Realization of active metamaterials with odd micropolar elasticity,” Nature communications, vol. 12, Iss. 1, 2021, pp. 1-12. [cited by applicant]
Li et al., “Acoustic metamaterials capable of both sound insulation and energy harvesting,” Smart Materials and Structures, vol. 25, No. 4, 2016, pp. 1-5. [cited by applicant]
Airoldi et al., “Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos,” New Journal of Physics, vol. 13, Iss. 11, Nov. 2011, pp. 1-21. [cited by applicant]
Thomes et al., “Space-time wave localization in electromechanical metamaterial beams with programmable defects,” Mechanical Systems and Signal Processing, vol. 167, Part B, Mar. 2022, pp. 1-16. [cited by applicant]
Trainiti et al., “Time-periodic stiffness modulation in elastic metamaterials for selective wave filtering: theory and experiment,” Physical review letters, vol. 122, Iss. 12, Mar. 2019, 17 pages. [cited by applicant]
Chen et al., “Enhanced flexural wave sensing by adaptive gradient-index metamaterials,” Scientific reports, vol. 6, Iss. 1, 2016, pp. 1-11. [cited by applicant]
Zhu et al., “Experimental study of an adaptive elastic metamaterial controlled by electric circuits,” Applied Physics Letters, vol. 108, Iss. 1, 2016, 6 pages. [cited by applicant]
Hu et al., “Metamaterial beam with graded local resonators for broadband vibration suppression,” Mechanical Systems and Signal Processing, vol. 146, Jan. 2021, pp. 1-20. [cited by applicant]
Yi et al., “Programmable metamaterials with digital synthetic impedance circuits for vibration control,” Smart Materials and Structures, vol. 29, No. 3, 2020, pp. 1-21. [cited by applicant]
Sugino et al., “Digitally programmable resonant elastic metamaterials,” Physical Review Applied, vol. 13, Iss. 6, 2020, 5 pages. [cited by applicant]