{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T10:12:59Z","timestamp":1778667179487,"version":"3.51.4"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,22]],"date-time":"2017-03-22T00:00:00Z","timestamp":1490140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To accurately determine the dynamic response of a structure is of relevant interest in many engineering applications. Particularly, it is of paramount importance to determine the Frequency Response Function (FRF) for structures subjected to dynamic loads in order to avoid resonance and fatigue problems that can drastically reduce their useful life. One challenging case is the experimental determination of the FRF of submerged and confined structures, such as hydraulic turbines, which are greatly affected by dynamic problems as reported in many cases in the past. The utilization of classical and calibrated exciters such as instrumented hammers or shakers to determine the FRF in such structures can be very complex due to the confinement of the structure and because their use can disturb the boundary conditions affecting the experimental results. For such cases, Piezoelectric Patches (PZTs), which are very light, thin and small, could be a very good option. Nevertheless, the main drawback of these exciters is that the calibration as dynamic force transducers (relationship voltage\/force) has not been successfully obtained in the past. Therefore, in this paper, a method to accurately determine the FRF of submerged and confined structures by using PZTs is developed and validated. The method consists of experimentally determining some characteristic parameters that define the FRF, with an uncalibrated PZT exciting the structure. These parameters, which have been experimentally determined, are then introduced in a validated numerical model of the tested structure. In this way, the FRF of the structure can be estimated with good accuracy. With respect to previous studies, where only the natural frequencies and mode shapes were considered, this paper discuss and experimentally proves the best excitation characteristic to obtain also the damping ratios and proposes a procedure to fully determine the FRF. The method proposed here has been validated for the structure vibrating in air comparing the FRF experimentally obtained with a calibrated exciter (impact Hammer) and the FRF obtained with the described method. Finally, the same methodology has been applied for the structure submerged and close to a rigid wall, where it is extremely important to not modify the boundary conditions for an accurate determination of the FRF. As experimentally shown in this paper, in such cases, the use of PZTs combined with the proposed methodology gives much more accurate estimations of the FRF than other calibrated exciters typically used for the same purpose. Therefore, the validated methodology proposed in this paper can be used to obtain the FRF of a generic submerged and confined structure, without a previous calibration of the PZT.<\/jats:p>","DOI":"10.3390\/s17030660","type":"journal-article","created":{"date-parts":[[2017,3,22]],"date-time":"2017-03-22T12:04:00Z","timestamp":1490184240000},"page":"660","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":52,"title":["Accurate Determination of the Frequency Response Function of Submerged and Confined Structures by Using PZT-Patches\u2020"],"prefix":"10.3390","volume":"17","author":[{"given":"Alexandre","family":"Presas","sequence":"first","affiliation":[{"name":"CDIF (Centre de Diagn\u00f2stic Industrial I Fluidodin\u00e0mica), UPC (Universitat Polit\u00e8cnica de Catalunya), Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7125-0734","authenticated-orcid":false,"given":"David","family":"Valentin","sequence":"additional","affiliation":[{"name":"CDIF (Centre de Diagn\u00f2stic Industrial I Fluidodin\u00e0mica), UPC (Universitat Polit\u00e8cnica de Catalunya), Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduard","family":"Egusquiza","sequence":"additional","affiliation":[{"name":"CDIF (Centre de Diagn\u00f2stic Industrial I Fluidodin\u00e0mica), UPC (Universitat Polit\u00e8cnica de Catalunya), Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carme","family":"Valero","sequence":"additional","affiliation":[{"name":"CDIF (Centre de Diagn\u00f2stic Industrial I Fluidodin\u00e0mica), UPC (Universitat Polit\u00e8cnica de Catalunya), Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1777-1840","authenticated-orcid":false,"given":"M\u00f2nica","family":"Egusquiza","sequence":"additional","affiliation":[{"name":"CDIF (Centre de Diagn\u00f2stic Industrial I Fluidodin\u00e0mica), UPC (Universitat Polit\u00e8cnica de Catalunya), Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matias","family":"Bossio","sequence":"additional","affiliation":[{"name":"CDIF (Centre de Diagn\u00f2stic Industrial I Fluidodin\u00e0mica), UPC (Universitat Polit\u00e8cnica de Catalunya), Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,22]]},"reference":[{"key":"ref_1","unstructured":"Ewins, D.J. (1984). Modal Testing Theory and Practice, Research Studies Press."},{"key":"ref_2","unstructured":"Heylen, W. (2007). Modal Analysis Theory and Testing, Katholieke Universiteit Leuven."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3042","DOI":"10.1061\/(ASCE)0733-9445(1991)117:10(3042)","article-title":"Modal analysis for damage detection in structures","volume":"117","author":"Hearn","year":"1991","journal-title":"J. Struct. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1006\/mssp.1998.1211","article-title":"Modal testing and analysis of structures under operational conditions: Industrial applications","volume":"13","author":"Hermans","year":"1999","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.engfailanal.2012.01.012","article-title":"Failure investigation of a large pump-turbine runner","volume":"23","author":"Egusquiza","year":"2012","journal-title":"Eng. Fail. Anal."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1155\/S1023621X94000059","article-title":"Case Study of Pump Failure Due to Rotor-Stator Interaction","volume":"1","author":"Ohashi","year":"1994","journal-title":"Int. J. Rotat. Mach."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.ymssp.2013.02.010","article-title":"Elimination of transducer mass loading effects in shaker modal testing","volume":"38","author":"Bi","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"892","DOI":"10.2514\/1.18727","article-title":"Feedback Control and Optimization for Rotating Disk Flutter Suppression with Actuators Patches","volume":"44","author":"Wang","year":"2006","journal-title":"AIAA J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3094","DOI":"10.3390\/s110303094","article-title":"Optimization of Sensing and Feedback Control for Vibration\/Flutter of Rotating Disk by PZT Actuators via Air Coupled Pressure","volume":"11","author":"Yan","year":"2011","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.jsv.2008.09.032","article-title":"Electrically forced vibration of an elastic plate with a finite piezoelectric actuator","volume":"321","author":"Yang","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1016\/j.mechatronics.2004.04.003","article-title":"Modeling of a circular plate with piezoelectric actuators","volume":"14","author":"Sekouri","year":"2004","journal-title":"Mechatronics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/S0924-4247(04)00486-8","article-title":"An impedance approach for vibration response synthesis using multiple PZT actuators","volume":"118","author":"Cheng","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11919","DOI":"10.3390\/s140711919","article-title":"Feasibility of Using PZT Actuators to Study the Dynamic Behavior of a Rotating Disk due to Rotor-Stator Interaction","volume":"14","author":"Presas","year":"2014","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.jsv.2009.05.011","article-title":"Control of a piezoelectric actuator considering hysteresis","volume":"326","author":"Ikhouanne","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.jsv.2014.10.032","article-title":"Influence of the rotation on the natural frequencies of a submerged-confined disk in water","volume":"337","author":"Presas","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.ymssp.2015.01.013","article-title":"On the detection of natural frequencies and mode shapes of submerged rotating disk-like structures from the casing","volume":"60","author":"Presas","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Presas, A., Valero, C., Huang, X., Egusquiza, E., Farhat, M., and Avellan, F. (2012). Analysis of the Dynamic Response of Pump-Turbine Runners-Part I: Experiment, IOP Publishing.","DOI":"10.1088\/1755-1315\/15\/5\/052015"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.jfluidstructs.2013.01.008","article-title":"Experimental investigation of added mass effects on a hydrofoil under cavitation conditions","volume":"39","author":"Escaler","year":"2013","journal-title":"J. Fluids Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1016\/j.jfluidstructs.2015.02.001","article-title":"Dynamic modelling and active vibration control of a submerged rectangular plate equipped with piezoelectric sensors and actuators","volume":"54","author":"Kwak","year":"2015","journal-title":"J. Fluids Struct."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kwak, M.K., and Yang, D.-H. (2014, January 14\u201320). Active Vibration Control of a Hanged Rectangular Plate Partially Submerged Into Fluid by Using Piezoelectric Sensors and Actuators. Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, Montreal, QC, Canada.","DOI":"10.1115\/IMECE2014-37948"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Presas, A., Valentin, D., Egusquiza, E., Valero, C., Egusquiza, M., and Bossio, M. (2016, January 15\u201330). On the Use of PZT-Patches as Exciters in Modal Analysis: Application to Submerged Structures. Proceedings of the 3rd International Electronic Conference on Sensors and Applications, Available online: https:\/\/sciforum.net\/conference\/ecsa-3.","DOI":"10.3390\/ecsa-3-E010"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1006\/jfls.1996.0051","article-title":"Free vibrations of circular plates coupled with liquids: Revising the Lamb problem","volume":"10","author":"Amabili","year":"1996","journal-title":"J. Fluids Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1115\/1.2897209","article-title":"Vibration of circular plates in contact with water","volume":"58","author":"Kwak","year":"1991","journal-title":"J. Appl. Mech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"303","DOI":"10.5293\/IJFMS.2009.2.4.303","article-title":"Dynamic analysis of Francis runners-experiment and numerical simulation","volume":"2","author":"Lais","year":"2009","journal-title":"Int. J. Fluid Mach. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.compfluid.2012.09.016","article-title":"Numerical and experimental analysis of the dynamic response of large submerged trash-racks","volume":"71","author":"Huang","year":"2013","journal-title":"Comput. Fluids"},{"key":"ref_26","unstructured":"Blevins, R.D. (1990). Flow-Induced Vibration, Van Nostrand Reinhold Co., Inc."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1115\/1.3153712","article-title":"Formulas for natural frequency and mode shape","volume":"47","author":"Blevins","year":"1980","journal-title":"J. Appl. Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jfluidstructs.2014.06.006","article-title":"Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement","volume":"50","author":"Presas","year":"2014","journal-title":"J. Fluids Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.jfluidstructs.2016.02.003","article-title":"Dynamic response of a rotating disk submerged and confined. Influence of the axial gap","volume":"62","author":"Presas","year":"2016","journal-title":"J. Fluids Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1016\/j.sna.2006.06.023","article-title":"On the response of a resonating plate in a liquid near a solid wall","volume":"134","author":"Harrison","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1299\/kikaic.50.243","article-title":"Added Mass Effect on Disc Vibrating in Fluid","volume":"50","author":"Kubota","year":"1984","journal-title":"Trans. Jpn. Soc. Mech. Eng. C"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/S0924-4247(02)00398-9","article-title":"Dynamic response of a cantilever in liquid near a solid wall","volume":"102","author":"Naik","year":"2003","journal-title":"Sens. Actuators A Phys."},{"key":"ref_33","unstructured":"Preumont, A. (2006). Dynamics of Electromechanical and Piezoelectric Systems, Springer."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Preumont, A. (2011). Vibration Control of Active Structures: An Introduction, Springer.","DOI":"10.1007\/978-94-007-2033-6"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1121\/1.398788","article-title":"Theory of laminated piezoelectric plates for the design of distributed sensors\/actuators. Part I: Governing equations and reciprocal relationships","volume":"87","author":"Lee","year":"1990","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1006\/jsvi.1996.0158","article-title":"Free vibrations of annular plates coupled with fluids","volume":"191","author":"Amabili","year":"1996","journal-title":"J. Sound Vib."},{"key":"ref_37","unstructured":"White, F. (1979). Fluid Mechanics, McGraw-Hill."},{"key":"ref_38","unstructured":"Kubota, Y., and Ohashi, H. (1991, January 4\u20137). A study on the natural frequencies of hydraulic pumps. Proceedings of the 1st ASME Joint International Conference on Nuclear Engineering, Tokyo, Japan."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.jfluidstructs.2006.04.001","article-title":"Experimental investigation of added mass effects on a Francis turbine runner in still water","volume":"22","author":"Rodriguez","year":"2006","journal-title":"J. Fluids Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1016\/j.compfluid.2006.08.007","article-title":"Numerical simulation of fluid added mass effect on a francis turbine runner","volume":"36","author":"Liang","year":"2007","journal-title":"Comput. Fluids"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Madenci, E., and Guven, I. (2015). The Finite Element Method and Applications in Engineering Using ANSYS\u00ae, Springer.","DOI":"10.1007\/978-1-4899-7550-8"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Monette, C., Nennemann, B., Seeley, C., Coutu, A., and Marmont, H. (2014, January 22\u201326). Hydro-Dynamic Damping Theory in Flowing Water. Proceedings of the IOP Conference Series: Earth and Environmental Science, Montreal, QC, Canada.","DOI":"10.1088\/1755-1315\/22\/3\/032044"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.ymssp.2015.05.034","article-title":"Analysis of the dynamic response of pump-turbine impellers. Influence of the rotor","volume":"68","author":"Egusquiza","year":"2016","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/660\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:30:58Z","timestamp":1760207458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/660"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,22]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["s17030660"],"URL":"https:\/\/doi.org\/10.3390\/s17030660","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,22]]}}}