INVESTIGATION ABOUT THE PVDF (POLYVINYLIDENE FLUORIDE) INFLUENCE ON A FLEXIBLE BEAM MODEL

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1 INVESTIGATION ABOUT THE PVDF (POLYVINYLIDENE FLUORIDE) INFLUENCE ON A FLEXIBLE BEAM MODEL Oliveira, É. L. 1, Maia, N. M. M. 1, Marto, A. G. 2, da Silva, R. G. A. 3, Afonso, F. J. 1, Suleman, A. 1 1 LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, , Lisboa, Portugal 2 Instituto de Aeronáutica e Espaço, Divisão de Aerodinâmica, Praça Marechal Eduardo Gomes, 50 - Vila das Acácias, , São José dos Campos - SP, Brazil 3 Instituto Tecnológico de Aeronáutica, Divisão de Engenharia Aeronáutica, Praça Marechal Eduardo Gomes, 50 - Vila das Acácias, , São José dos Campos - SP, Brazil Corresponding Author: eder.oliveira@tecnico.ulisboa.pt Keywords: instrumentation influence, experimental modal analysis, piezoelectric materials, PZT, PVDF Abstract The interest of applying piezoelectric materials for modal analysis has been growing in past the few decades. In piezoelectric materials, both electrical and mechanical domains are coupled, i.e., these materials are able to convert electrical energy in to mechanical energy and vice versa. Due to this very important characteristic, they can be used in several applications as actuators or sensors. Furthermore, some piezoelectric materials exhibit a predominant coupling, which make them more efficient when used for specific purposes/applications. In this sense, one widely used sensor is the PVDF (Polyvinylidene Fluoride). A possible advantage associated to the PVDF is the small influence on the results due to the thin thickness and high flexibility, which sometimes is neglected. The aim of this work is to evaluate the influence of a single PVDF film on a flexible beam model. This study proposes an efficient methodology to verify and identify the intrusiveness level. The proposed methodology consists in changing the sensor position (PVDF) and simultaneously acquiring the data by using a non-intrusive technique (laser vibrometer). The modal parameters (natural frequencies and damping factors) obtained by PVDF and laser vibrometer responses should be very close for each PVDF position. If this condition is satisfied, the variation of the modal parameters due to PVDF position will show the intrusiveness level imposed by PVDF instrumentation. This research emphasises the importance of verifying the influence of the instrumentation, even if it seems to have small influence. 1. Introduction The structure s dynamic behaviour can be affected not only by the excitation system but also by a force or response transducer [1]. The application of piezoelectric materials is increasing interest among researchers for experimental modal analysis, in the past few decades. In piezo-

2 electric materials 1 the electrical and mechanical domains are coupled. This means that these materials are able to convert mechanical energy into electrical energy and conversely. When a piezoelectric transducer is subject to a mechanical stress it produces an electrical displacement (direct effect), and produces a mechanical strain when an electric field is applied (converse piezoelectric effect) [2]. Therefore, they can be applied not only as sensors but also as actuators. Nevertheless, some materials are more efficient when applied to specific cases due to their predominant piezoelectric coupling. The PVDF (Polyvinylidene Fluoride) is an example of a widely used sensor. Due to the lower thickness and high flexibility, a possible advantage that can be attributed to the PVDF is the small influence which sometimes can be considered negligible (e.g. in [3]). Aiming to verify the influence of a single PVDF film introduced in a flexible beam model this study is conducted. The flexibility of a testing structure makes the model more susceptible to instrumentation influence, [4]. Thereby, a study to assess the instrumentation influence is required. The adopted strategy consists in extracting the modal parameters at different PVDF positions and comparing the results with laser doppler vibrometry. 2. Methodology This study was conducted aiming to verify the influence of a single PVDF in a flexible aluminun beam model. The adopted strategy consists in varying the PVDF positioning and estimating the modal parameters for each condition. The intrusiveness of the PVDF can be evaluated by comparing the obtained modal parameters at each condition. Nevertheless, the observed variation may be caused by due to only the identification capability of PVDF only that was affected by positioning change. In theory, if the PVDF does not influence the structure the modal parameters must be the same independently of positioning. By comparing the PVDF results for each position with the estimated results by laser doppler vibrometry (acquired always in the same points), it is possible to verify the intrusiveness level of the PVDF in the testing structure. The PVDF positioning was varied as illustrated in Fig. 1. Also in Fig. 1, are showed the dimensions of the tested model and instrumentations. This testing structure has a ballast mass on its tip, the ballast CG is positioned such that is m out of the CG model, (see Fig. 1). The PVDF was embedded in the structure by applying a double-side adhesive, as indicated by PVDF STD datasheet [5]. This adhesive is easy to apply for this work it is very important since it allows to removing and reapplying the PVDF without letting any residue. Other piezoelectric element was used to excite the structure (Fig. 1), a PZT (Lead Zirconate Titanate) type PSI-5H4E. This PZT was embedded using an epoxy adhesive, the 3M R Scotchweld R Structural Adhesive DP460 Off - White ([6]). This adhesive is widely applied for this purpose, as for example in [7]. The piezoelectric strain coefficients, d 13 and d 23 are equal for the used PZT element, which means that this PZT has both 31 and 32 operating modes. The piezoelectric strain coefficient d m j relates the applied electric field direction j with the correspondent direction of deformation m. Therefore, by applying an electric field in 3 direction ( j=3 ), the employed PZT will produce a stress and a strain in both 1 ( m=1 ) and 2 ( m=2 ) directions with the same intensity. 1 Piezoelectric materials also exhibit thermomechanical coupling, known as pyroelectric effect. It can be a problem if only electromechanical coupling is wanted, because higher temperature variations can produce an undesirable influence on piezoelectric elements.

3 Figure 1. Model Scheme - Instrumentation Positioning The excitation signal which supplies the PZT was also used to generate the Frequency Response Functions (FRFs) for the two techniques. The FRF achieved by a single PVDF response was calculated for each position using the excitation signal (volts) as reference signal and the direct PVDF response (volts), such that this FRF is dimensionless. This structural transfer function is not an usual FRF (receptance, mobility or accelerance), it is also subjected to the modal analysis foundation: the structure under test must be observable, linear, time invariant and obeys Maxwells theory of reciprocity [8]. The laser response was acquired using a Compact Laser Vibrometer (CLV) model Polytec c CLV ([9]) working with mobility FRF. Two CLV was used to measure simultaneously the points called point4 and point9 in Fig. 1 for each PVDF position. The clamped beam side is represented by point0 and point50 in Fig. 1. The estimation of the modal parameters through PVDF and CLV measurements was done using the same test parameters: excitation signal type Random with ± 25 (V) of intensity; H V (ω) estimator; and hanning window function used for response and reference signals. The excitation signal was defined based on several considerations presented in [10]. The H V (ω) estimator, also know as H 3 (ω), was defined by means of a preliminary investigation, where the presence of noise in the FRF and ordinary coherence were analysed. The hanning is the most commonly used window function for random excitation. Nonetheless, its application can cause amplitude distortions as high as 16 %, although this distortion is better than if no window was used, [11]. All the window functions cause an effect on the measured data, thus this is a evil in order to reduce the effects of leakage. The modal identification method PolyMAX R was applied to estimate the modal parameters for both PVDF and CLV instrumentations. One of the advantages of this method is the very clear stabilization diagram commonly achieved, [12]. The estimation was done by selecting the stable root s with lower model order which presented repeatable for each vibration mode. The default parameters were used for the stabilization diagram calculation and detailed informations can be found in [13].

4 3. Results The presented methodology which aims to verify the PVDF instrumentation influence is based on the modal parameters estimation for each PVDF position, such as previously described in section 2 and illustrated in Fig. 1. As expected, it was found a variation of the damping factors, due to the higher sensitivity. However, for each PVDF positioning was observed variation on the estimation of both modal parameters considered: natural frequencies and damping factors. The vibration modes more affected by PVDF position changing were the 6 th and 7 th modes in terms of frequency variation, therefore it was opted to show these results. As can be seen in the Fig. 2(a), the 7 th vibration mode show a considerable instrumentation influence of more than 10 Hz by varying the PVDF position according to the previously defined positions (P0, P1, P2, P3) in horizontal direction. The agreement between PVDF and CLV results states a very high instrumentation influence. Worth remembering that the CLV results were achieved using the same measured points and the same test parameters. The damping factor estimated for each position also show a high variation for the 7 th mode, around 0.55 % (in damping scale), Fig. 2(b). A small variation was observed between PVDF and CLV results, but the curve behaviour was well characterized. This variation is normal and expected considering that a single PVDF response was used, for instance a previous study [14] shown that the damping estimation also is very susceptible to the measured point position when a single laser doppler vibrometry response was used. (a) Freq. Variation (b) Damp. Variation Figure 2. Instrumentation Investigation - Horizontal The frequency evolution due to variation in vertical position also is large as can be seen in Fig. 3(a). For this case a lower damping variation was observed (Fig. 3(b)), although the 5 th mode shows a variation of 2.07 % by means of CLV results and 2.04 % in the PVDF results. A similar behaviour to the horizontal positioning in terms of modal parameters was found for the PVDF oriented in 45 (Fig. 4). Considering the CLV results, for the 7 th mode the natural frequency has a variation of Hz for 45 positioning and Hz for horizontal positioning. The achieved damping evolution for these cases is also similar behaviour as can be seen when comparing Fig. 2(b) and Fig. 4(b). A higher influence on structure s dynamic behaviour was found when changing the PVDF positioning in the horizontal direction. Results for the other position changing show that the 7 th vibration mode was always the most affected in terms of frequency estimation. However, the

5 (a) Freq. Variation (b) Damp. Variation Figure 3. Instrumentation Investigation - Vertical (a) Freq. Variation (b) Damp. Variation Figure 4. Instrumentation Investigation - 45 variation in the horizontal position produced the highest frequency changing which is interesting to note since the 7 th mode shape is the first pure torsional mode. Nonetheless, the most affected damping factor varies accordingly to each condition (horizontal, vertical and 45 ). 4. Conclusions The PVDF is a thin and flexible piezoelectric film which was applied to the testing structure by using a double-side adhesive. Despite the lower thickness and high flexibility, the results show that the PVDF can be highly intrusive if applied to a flexible model. Comparing the identification of natural frequencies between PVDF and CLV, it can be seen that these results are very close each other. All the identified vibration modes show variation for both modal parameters: natural frequencies and damping factors. The results for the more affected mode shapes (6 th and 7 th ) were presented in terms of frequency changing. For two positioning variation cases, horizontal and 45, the 7 th showed differences above 10 Hz. Despite being the 7 th mode, the natural frequency is lower than 200 Hz, so it is not considered a very high frequency. For some vibration modes, the changing of damping factor imposed by PVDF can achieve results of 2% (in damping factor scale). From the present study it is clear that the modal parameter variations is due to the PVDF influence, since the two CLV responses were always acquired in the same points and using the

6 same test parameters. Based on this study, one can conclude that the PVDF was very intrusive to the tested aluminum beam model. The results show the importance of investigating the instrumentation influence, even if it seems to have small impact on the results. Acknowledgements The authors acknowledge the support received from the Brazilian Research Agency CNPq through the INCT-EIE, the support provided by Fundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, CAPES, as well as the support received from Instituto Tecnológico de Aeronáutica, ITA. The authors also acknowledge the Portuguese Science Foundation FCT, through IDMEC, under LAETA. References [1] Maia, Silva, He, Lieven, Lin, Skingle, To, and Urgueira, Theoretical and Experimental Modal Analysis, John Wiley and Sons, Inc., New York, Chichester, Toronto, Brisbane, Singapore, [2] Moheimani, S. O. R. and Fleming, A. J., Piezoelectric Transducers for Vibration Control and Damping, Springer, [3] Ruggiero, E. J., Active Dynamic Analysis and Vibration Control of Gossamer Structures Using Smart Materials, Master s thesis, Faculty of the Virginia Polytechnic Institute and State University, [4] Oliveira, E. L., Marto, A. G., and da Silva R. G. A., Thin Aeroelastic Wing Finite Element Model Updating With Experimental Modal Analysis Results, 21st International Congress of Mechanical Engineering, [5] SDT Shielded Piezo Sensors, Technical Data, December, [6] 3M Scotch-Weld Epoxy Adhesives DP460 Off-White, Technical Data, Mach, [7] Bilgen, O., Wang, Y., and Inman, D. J., Electromechanical Comparison of Cantilevered beams with Multifunctional Piezoceramic Devices, Mechanical Systems and Signal Processing, Vol. 27, 2012, pp [8] Grosel, J., Sawicki, W., and Pakos, W., Application of Classical and Operational Modal Analysis for Examination of Engineering Structures, Procedia Engineering, Vol. 91, 2014, pp [9] Polytec Inc, CLV Compact Laser Vibrometer, User s Manual. [10] LMS International, The LMS Theory and Background Book, [11] Avitabile, P., Modal Space in our Little World, Modal Analysis and Controls Laboratory, Lowelll, Massachusetts USA, [12] Peeters, B., Vanhollebeke, F., and der Auweraer, H. V., Operational PolyMAX for Estimating the Dynamic Properties of a Stadium Structure During a Football Game, Shock and Vibration, Vol. 14, No. 4, 2007, pp

7 [13] LMS, The LMS Test.Lab Modal Analysis manual, LMS Test.Lab, Rev 11A. [14] Oliveira, Éder. L., Application of Piezoelectric Materials as Sensor and Actuator for Aeroelastic Investigation, Master s thesis, Aeronautics Institute of Technology, São José dos Campos, São Paulo, Brazil, 2014.