{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T14:20:09Z","timestamp":1761920409179,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T00:00:00Z","timestamp":1519689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["106112015CDJXY120007","106112017CDJQJ118846","106112017CDJXSJW0007","10611CDJXZ238826"],"award-info":[{"award-number":["106112015CDJXY120007","106112017CDJQJ118846","106112017CDJXSJW0007","10611CDJXZ238826"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFE0125200","2016YFC0101100"],"award-info":[{"award-number":["2016YFE0125200","2016YFC0101100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A dual-frequency ultrasound transducer (DFUT) is usually preferred for its numerous advantageous applications, especially in biomedical imaging and sensing. However, most of DFUTs are based on the combination of fundamental and harmonic operations, or integration of multiple different single-frequency ultrasound transducers, hindering perfect beam alignment and acoustic impedance matching. A novel single-element DFUT has been proposed in this paper. A small piezoelectric membrane is used as the high-frequency ultrasound transducer, which is stacked on a large non-piezoelectric elastic membrane with a groove used as the low-frequency capacitive ultrasound transducer. Such a capacitive-piezoelectric hybrid structure is theoretically analysed in details, based on the electrostatic attraction force and converse piezoelectric effect. Both the low and high resonance frequencies are independently derived, with a maximum deviation of less than 4% from the finite element simulations. Besides, a lumped-parameter equivalent circuit model of combining both the capacitive and piezoelectric ultrasound transducers was also described. Based on our dual-frequency structure design, a high-to-low frequency ratio of about 2 to more than 20 could be achieved, with easy and independent controllability of two frequencies, and the high-frequency operation shows at least an order-of-magnitude displacement sensitivity improvement compared with the conventional harmonic operations.<\/jats:p>","DOI":"10.3390\/s18030703","type":"journal-article","created":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T14:18:08Z","timestamp":1519741088000},"page":"703","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Numerical Study and Optimisation of a Novel Single-Element Dual-Frequency Ultrasound Transducer"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5156-033X","authenticated-orcid":false,"given":"Changhe","family":"Sun","sequence":"first","affiliation":[{"name":"Key Laboratory of Optoelectronic Technology &amp; Systems, Chongqing University, Ministry of Education, Chonqing 400044, China"},{"name":"Centre for Intelligent Sensing Technology, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Senlin","family":"Jiang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronic Technology &amp; Systems, Chongqing University, Ministry of Education, Chonqing 400044, China"},{"name":"Centre for Intelligent Sensing Technology, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2988-8843","authenticated-orcid":false,"given":"Yufei","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronic Technology &amp; Systems, Chongqing University, Ministry of Education, Chonqing 400044, China"},{"name":"Centre for Intelligent Sensing Technology, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Collaborative Innovation Center for Brain Science, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jconrel.2015.02.002","article-title":"Applicability and safety of dual-frequency ultrasonic treatment for the transdermal delivery of drugs","volume":"202","author":"Schoellhammer","year":"2015","journal-title":"J. Control Release"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.sna.2017.03.004","article-title":"Development of a flexible film electromagnetic acoustic transducer for nondestructive testing","volume":"258","author":"Pei","year":"2017","journal-title":"Sens. Actuators A Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1109\/TUFFC.2016.2620381","article-title":"Multifrequency interlaced CMUTs for photoacoustic imaging","volume":"64","author":"Chee","year":"2017","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.ultsonch.2010.07.005","article-title":"Enhancement and control of acoustic cavitation yield by low-level dual frequency sonication: A subharmonic analysis","volume":"18","author":"Hasanzadeh","year":"2011","journal-title":"Ultrason. Sonochem."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"20825","DOI":"10.3390\/s141120825","article-title":"Dual-frequency piezoelectric transducers for contrast enhanced ultrasound imaging","volume":"14","author":"Martin","year":"2014","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3943","DOI":"10.1088\/0031-9155\/53\/14\/014","article-title":"Efficient array design for sonotherapy","volume":"53","author":"Stephens","year":"2008","journal-title":"Phys. Med. Biol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kshirsagar, A., Chee, R., Sampaleanu, A., Forbrich, A., Rishi, D., Moussa, W., and Zemp, R.J. (2013, January 21\u201325). Multi-frequency CMUT arrays for imaging-therapy applications. Proceedings of the 2013 IEEE International Ultrasonics Symposium, Prague, Czech Republic.","DOI":"10.1109\/ULTSYM.2013.0508"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1109\/TUFFC.2014.006887","article-title":"A cMUT probe for ultrasound-guided focused ultrasound targeted therapy","volume":"62","author":"Gross","year":"2015","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2926","DOI":"10.1088\/0031-9155\/61\/7\/2926","article-title":"Real-time monitoring of focused ultrasound blood-brain barrier opening via subharmonic acoustic emission detection: implementation of confocal dual-frequency piezoelectric transducers","volume":"61","author":"Tsai","year":"2016","journal-title":"Phys. Med. Biol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1109\/TUFFC.2010.1534","article-title":"Dual-frequency ultrasound imaging and therapeutic bilaminar array using frequency selective isolation layer","volume":"57","author":"Azuma","year":"2010","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ma, J., Jiang, X., Martin, K.H., Dayton, P.A., Li, Y., and Zhou, Q. (2014, January 3\u20136). Dual frequency transducers for intravascular ultrasound super-harmonic imaging and acoustic angiography. Proceedings of the 2014 IEEE International Ultrasonics Symposium, Chicago, IL, USA.","DOI":"10.1109\/ULTSYM.2014.0166"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1049\/el.2015.3831","article-title":"High-frequency ultrasound transducer by using inversion layer technique for intravascular ultrasound imaging","volume":"52","author":"Sung","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Manh, T., Hoff, L., Eggen, T., Johansen, T.F., Lanteri, F., and Gelly, J.F. (2016, January 18\u201321). Dual frequency hybrid ultrasonic transducers\u2014Design and simulations. Proceedings of the 2016 IEEE International Ultrasonics Symposium, Tours, France.","DOI":"10.1109\/ULTSYM.2016.7728599"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sun, C., Dai, F., Jiang, S., and Liu, Y. (2017, January 6\u20139). A novel single-element dual-frequency ultrasound transducer for imaging-guided precision medicine. Proceedings of the 2016 IEEE International Ultrasonics Symposium, Washington, DC, USA.","DOI":"10.1109\/ULTSYM.2017.8091820"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hedegaard, T., Pedersen, T., Thomsen, E.V., Lou-Moeller, R., Hansen, K., and Zawada, T. (2008, January 2\u20135). Screen printed thick film based pMUT arrays. Proceedings of the 2008 IEEE International Ultrasonics Symposium, Beijing, China.","DOI":"10.1109\/ULTSYM.2008.0526"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.ultsonch.2008.08.009","article-title":"Single-transducer dual-frequency ultrasound generation to enhance acoustic cavitation","volume":"16","author":"Liu","year":"2009","journal-title":"Ultrason. Sonochem."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, T., and Lee, C. (2016, January 24\u201328). Electrically switchable multi-frequency piezoelectric micromachined ultrasound transducer (pMUT). Proceedings of the 2016 IEEE 29th International Conference on Micro Electro Mechanical Systems (MEMS), Shanghai, China.","DOI":"10.1109\/MEMSYS.2016.7421828"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6859","DOI":"10.1109\/JSEN.2017.2752229","article-title":"Dual-frequency ultrasound transducer using inversion layer technique for therapeutic ultrasound surgery","volume":"17","author":"Park","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1109\/TUFFC.2012.2383","article-title":"An improved lumped element nonlinear circuit model for a circular CMUT cell","volume":"59","author":"Koymen","year":"2012","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Canning, S., Walker, A.J., and Roach, P.A. (2016). A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer. Sensors, 16.","DOI":"10.3390\/s16122170"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1109\/TUFFC.2014.006725","article-title":"Experiment and simulation validated analytical equivalent circuit model for piezoelectric micromachined ultrasonic transducers","volume":"62","author":"Smyth","year":"2015","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.3390\/s17061381","article-title":"Design and Fabrication of Piezoelectric Micromachined Ultrasound Transducer (pMUT) with Partially-Etched ZnO Film","volume":"17","author":"Li","year":"2017","journal-title":"Sensors"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1109\/JMEMS.2014.2358991","article-title":"A High Fill-Factor Annular Array of High Frequency Piezoelectric Micromachined Ultrasonic Transducers","volume":"24","author":"Lu","year":"2015","journal-title":"J. Microelectromech. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1109\/TUFFC.2014.006553","article-title":"Electrostatic and Small-Signal Analysis, of CMUTs with Circular and Square, Anisotropic Plates","volume":"62","author":"Cour","year":"2015","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Bauchau, O.A., and Craig, J.I. (2009). Kirchhoff plate theory. Structrual Analysis: With Applications to Aerospace Structure, Springer. [1st ed.].","DOI":"10.1007\/978-90-481-2516-6_16"},{"key":"ref_26","unstructured":"Timoshenko, S., and Woinowsky-Krieger, S. (1959). Pure Bending of Plates. Theory of Plates and Shells, McGraw-Hill. [2nd ed.]."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Hwu, C. (2010). Plate Bending Analysis. Anisotropic Elastic Plates, Springer. [1st ed.].","DOI":"10.1007\/978-1-4419-5915-7"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hwu, C. (2010). Linear Anisotropic Elastic Materials. Anisotropic Elastic Plates, Springer. [1st ed.].","DOI":"10.1007\/978-1-4419-5915-7"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1109\/JMEMS.2015.2472958","article-title":"Zero-bending piezoelectric micromachined ultrasonic transducer (pMUT) with enhanced transmitting performance","volume":"24","author":"Wang","year":"2015","journal-title":"J. Microelectromech. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2276","DOI":"10.1109\/TUFFC.2005.1563270","article-title":"Piezoelectric micromachined ultrasonic transducers based on PZT thin films","volume":"52","author":"Muralt","year":"2005","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1109\/16.43810","article-title":"Micromachining for improvement of integrated ultrasonic transducer sensitivity","volume":"37","author":"Mo","year":"1990","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_32","unstructured":"Je, Y., Ahn, H., Been, K., Moon, W., and Lee, H. (2013, January 21\u201325). An advanced equivalent circuit for a piezoelectric micromachined ultrasonic transducer and its lumped parameter measurement. Proceedings of the 2013 IEEE International Ultrasonics Symposium, Prague, Czech Republic."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.sna.2016.01.054","article-title":"Modeling of plates with multiple anisotropic layers and residual stress","volume":"240","author":"Engholm","year":"2016","journal-title":"Sens. Actuators A Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.sna.2014.09.007","article-title":"Silicon as an anisotropic mechanical material: Deflection of thin crystalline plates","volume":"220","author":"Thomsen","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0045-7949(99)00217-5","article-title":"Bending of clamped orthotropic rectangular plates: a variational symbolic solution","volume":"77","author":"Mbakogu","year":"2000","journal-title":"Comput. Struct."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Shelton, S., Chan, M.L., Park, H., Horsley, D., Boser, B., Izyumin, I., Przybyla, R., Frey, T., Judy, M., and Nunan, K. (2009, January 20\u201323). CMOS-compatible AlN piezoelectric micromachined ultrasonic transducers. Proceedings of the 2009 IEEE International Ultrasonics Symposium, Rome, Italy.","DOI":"10.1109\/ULTSYM.2009.5441602"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1109\/58.677612","article-title":"Surface micromachined capacitive ultrasonic transducers","volume":"45","author":"Ladabaum","year":"1998","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.sna.2014.11.018","article-title":"A novel 6 \u00d7 6 element MEMS capacitive ultrasonic transducer with multiple moving membranes for high performance imaging applications","volume":"222","author":"Emadi","year":"2015","journal-title":"Sens. Actuators A Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"015012","DOI":"10.1088\/0960-1317\/25\/1\/015012","article-title":"PECVD low stress silicon nitride analysis and optimization for the fabrication of CMUT devices","volume":"25","author":"Bagolini","year":"2014","journal-title":"J. Micromech. Microeng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/3\/703\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:56:34Z","timestamp":1760194594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/3\/703"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,27]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["s18030703"],"URL":"https:\/\/doi.org\/10.3390\/s18030703","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,2,27]]}}}