Non- contact point excitation of ultra lightweight structures: membranes

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1 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference April 8-11, 2013, Boston, Massachusetts AIAA Non- contact point excitation of ultra lightweight structures: membranes Sriram V. V. N. Malladi, Ethan F. Robinson, Bryan Joyce 1, Nima Ameri 2 and Pablo A. Tarazaga 1 1Mechanical Engineering Dept., Virginia Tech, 309 Durham Hall, Blacksburg VA Aerospace Department, University of Bristol, Queens Building, University Walk BS8 1TR Abstract Given the lightweight and sensitive nature of gossamer structures, applying non- intrusive excitation and measurement techniques is beneficial during either the design stage or in operational conditions. The use of non- contact measurement techniques, such as laser vibrometry, has been extensively used in testing of lightweight structures and proven beneficial. The successful implementation of non- contact excitation techniques, however, is more difficult. Commonly used and seen in past literature, has been the implementation of boundary excitation and acoustics in order to generate a non- contact type of excitation source. Both these techniques distribute the excitation generated on the surface of the specimen as opposed to a point source. A SISO or SIMO type of approach cannot be used for system identification as the nature of these excitations are not single input. The implementation of a MIMO approach should not be used either, as the excitation cannot be measured directly nor are the inputs uncorrelated. The work here investigates the use of a pressurized solenoid valve with compressed air to generate a point excitation on an ultra- lightweight circular membrane. The experimental results are compared with a previously validated theoretical model of a membrane in air. An impedance- based model of a circular membrane is used which takes into account the energy loss due to radiation to the far field. This work also attempts to quantify in a general sense the errors induced when neglecting these differences using distributed type excitations versus single point. keywords: gossamer structures, laser vibrometry, testing, acoustic radiation, non- contact excitation. 1 INTRODUCTION The pursuit for larger space- based telescopes with larger apertures and space structures in general, has consequently led to what is now well known in literature as gossamer space structures [1]. For many large deployable space structure applications, space inflatable structures have several advantages over mechanically deployed systems. Some of these advantages include being lighter weight, having a higher packaging efficiency, a lower life- cycle cost, lower parts counts, and higher deployment reliability. The achievement of large space structures is now pursued through the use of innovative lightweight components that are able to meet the requirements currently sustained by more rigid metal- based and glass- based structures. This is important, as weight is one of the most crucial and limiting factors in the space industry.

2 In the odyssey of achieving further lightweight space structures and systems, optical- quality membrane mirrors are expected to replace the conventional, metal- based and glass- based, rigid mirrors. The proposition of using membranes as the optical component in telescopes and other imaging type devices was proposed by Yellin in 1976 in [2]. These thin film membranes offer an order of magnitude size increase in apertures and in weight reduction [3]. The replacement of rigid mirrors for optical quality membrane mirrors is still a large area of research with many questions thus far requiring further investigation. These areas include, but are not limited to: modeling, material properties, fabrication due to high tolerances required for imaging, characterization, storage, control, and deployability [4-8]. Given their lightweight nature and complexity, testing and characterization of such structures carries its set of challenges [9]. The use of sensors is fairly limited due to their mass loading effects on the structure, and conversely similar problems are also faced with excitation methods [10, 11]. Another challenge faced in testing such structures in laboratory conditions, or in operational conditions, is the amount of time available for testing. Due to high time constraints, fast testing techniques that do not compromise the quality of the data are favorable. The work here looks to describe an alternative technique with favorable characteristics such as non- contact excitation, single point and accurate. The work presented here is also compared to an impedance- based model of a membrane. 2 MODELLING A membrane model is presented in this section, which describes a circular membrane immersed in air. The model is fully developed in [12] and is briefly presented here for completeness. Lightweight membranes such as those found in optics can suffer significant changes in their dynamics due to air effects. The modeling is carried out using an impedance- based approach and is briefly described in the following sections. The analysis throughout this work assumes small displacement. It is worth noting that although the model described here has the ability to incorporate proportional damping, no damping is added to the model. The damping that results from the model of the circular membrane in air is due to the energy loss by means of sound radiation to the far field. 2.1 Circular membrane in air The system schematic described in Figure 1, is of an infinitely baffled membrane with air on both sides of the membrane. The subscript i indicates the i th discretized point with coordinates (ri, θi), area si and respective velocity vi. The system described at the i th discretized point has added dynamic contributions from the surrounding fluid, by way of sound radiation pressure on either side of the membrane described as PO and PI. In the same manner, the subscript j indicates the j th point where the actuation force is located, identified by coordinates (rj, θj), area sj and force fj.

3 Figure 1. Schematics of a circular membrane immersed in air. The coupled system described in Figure 1 consists of three subsystems. The first one is the subsystem described by the circular membrane. The second and third subsystems can be considered to be the air surrounding or immediately adjacent to both sides of the membrane. The sound radiation produced by the vibration of a continuous system can be assumed to be from a distributed number of elemental radiators, which in this case are equivalent to small piston sources on the surface of the membrane [13-15]. Now that the subsystems are understood, the coupled system illustrated in Figure 1 can be described as and V = Φ T A v Φ f S f f f + ΦSP O + ΦSP I (1) P O = ZV, P I = ZV (2) where S is a diagonal matrix of areas constructed from the individual discretized areas si and ΦSPO and ΦSPI are the contribution to the membrane dynamics from the surrounding air on either side of the membrane. The pressures produced as a consequence of the membrane vibration are assumed equal on each side, thus PO = PI = P and Z is taken originally from [14] and adapted to a circular membrane in [12]. Av is the resonance matrix where each diagonal term is described by the following equation A vn ( ω) = jω ( ω 2 n ω 2 ) + 2ζ n jω (3) where ω is the driving frequency, ωn is the n th natural frequency, ζn is the damping ratio of the n th mode, and j represents the square root of negative one.

4 Substituting equation (2) into equation (1) and solving for the velocity and pressure results in V( ω)= I 2Φ T 1 A v ( ω)φsz Φ T A v Φ f S f f f (4) P( ω)= Z I 2Φ T 1 A v ( ω)φsz Φ T A v Φ f S f f f (5) Given the frequency dependence of Av, the inverses shown in brackets in equation (4) and (5) need to be calculated for each frequency ω of interest. Thus, these equations describe the velocity and pressure of a membrane immersed in air being actuated by a point force at (rj, θj), for each frequency ω of interest. The vibration measurements of thin membranes can be very difficult to perform. Due to the fact that these structures are very sensitive to any source of environmental noise, special attention is taken when performing any vibration measurement. Further more, the only type of transducer suitable for measuring vibrations is one that does not have contact with the structure. Microphones and Laser Doppler Vibrometers (LDVs) are two non- contact transducers that can scan the surface and thus measure the vibration remotely. Any other type of contact transducer would be intrusive and unsuitable for this type of measurement. 3 EXPERIMENTS The following section develops the experimental part of this research in order to study and evaluate a non- contact method for point excitation. The results are analyzed and compared to a theoretical model in order to understand how these techniques can influence and alter the results. 3.1 General experimental setup As expressed earlier, due to the sensitivity of the experiment specimen, the test needs to take place in a controlled environment where ambient disturbances can be suppressed as much as possible in order to avoid interference. The membrane used can be observed in Figure 2. The membrane is made of polyolefin and has the dimensions and characteristics described in Table 1. The aluminum ring surrounding the membrane contains internal o- rings on the inside and outside boundary in order to clamp the membrane down with a very precise circumferential line. Circular membrane Diameter (mm) Density (kg/m 3 ) 1000 Thickness (µm) Tension (N) 22 Figure 2. Circular membrane Table 1. Properties of the circular membrane being analyzed.

5 A schematic of the experimental setup can be observed in Figure 3. The setup is comprised of a Scanning Laser Doppler Vibrometer (PSV 400) used to measure the out- of- plane vibrations of the membrane. It is positioned perpendicular to the membrane. Compressed air is feed to a solenoid valve (Marsh Bellofram type 3110), which is controlled in order to open and shut the valve at a very fast rate in order to generate a pulse of air. The output of the valve is split and sent to the membrane as an external excitation. The other end is feed to a microphone (PCB Piezotronics 130D21) in order to characterize the input. It is assumed here that the microphone is capable of reproducing or reading the same input that is feed to the membrane. In future work this assumption needs to be carefully verified, but at this point the work concentrates on the feasibility of the new method. The microphone reading is then feed back to the DSP system with the laser vibrometer output in order to generate a transfer function. This is all placed on top of a vibration isolation table in order to minimize disturbances. A portion of the actual experimental setup can be observed in Figure 4. Although not show in the picture the two pressure lines are split from the same solenoid valve not seen in the picture, just as seen in the schematic diagram. Figure 3. Schematic of the test setup. Figure 4. Test setup sits on a vibration isolation table with the membrane at right of the picture. 3.2 Non-contact approach for single point excitation As described in the previous section, the test setup consists of a non- contact laser vibrometer used to measure the out of plane velocity of the membrane. In this case, the membrane is excited using a solenoid valve with compressed air. A pulse of air is used to excite a small section of the membrane in order to generate an impulse type of excitation. The air is focused on a small enough area of the membrane in order to simulate a point excitation in the same manner an impulse hammer is used. The validity of this statement will be evaluated against theoretical data. 54th SDM AIAA Conference 2013, Boston, MA DRAFT

6 Since the air exiting the solenoid valve cannot be measured during a test, the line is split and feed to a microphone. The assumption that this is true needs further investigation but is considered acceptable here in the amount that the theory matches the experiment. Experimentally, this assumption has its limits, as the dynamics seen by the microphone are not the same as the ones experienced by a highly compliant membrane. This can be evaluated in a practical sense during testing by varying the pulse duration and air pressure. Much in the same way, stinger lengths connected to shakers are chosen such that consecutive lengths yield the same dynamical results [16]. Air pressure and pulse duration will be varied until consecutive changes yield no change in the dynamic response of the system. This can be taken as an indication that the actuation is not affecting the system s response. 4 RESULTS In the following section, results from the experiments in section 3 are presented and discussed. 4.1 Comparison of A preliminary modal test was performed using the scanning laser vibrometer over a discrete amount of points. A grid of measurement points were produced on the surface of the membrane, which was treated with baby powder so as to increase the Signal- to- Noise- Ratio (SNR) of the LDV output signal. The mass loading effect of the addition of the fine baby powder is negligible yet yields a substantial improvement on the SNR. The measured data was analyzed to obtain the modes of the specimen. Ten modes were identified and are listed in Table 2 and compared to the theoretical ones. As can be observed the theoretical modes follow very well the trend of the experimental observations. Modes 1 and 10 correlate very well with less than 1% error while anti- symmetric modes 2-3 and 4-5 reach errors of 6-7%. Table 2. Identified experimental membrane modes. Freq Exp (Hz) Freq Theory (Hz) Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode A plot of selected experimental operation deflection shapes are shown in Figure 5 and their theoretical counter parts can be observed in Figure 6. The shapes of the system correlate very well and assure the modes being compared are structurally the same.

7 Figure 5. Operation deflection shapes at selected modes of operation. Figure 6. Theoretical operation deflection shapes of coupled system.

8 5 SUMMARY AND PROPPOSED FINAL WORK The non- contact excitation technique described herein for the characterization and testing of ultra lightweight structures has proven to be a viable option for single point excitation method. This technique facilitates the system identification process and allows the use of well- established modal analysis techniques. More common methods such as speakers or boundary excitation have limits as their excitation cannot always be measured directly nor are the inputs uncorrelated, thus improperly using modal analysis techniques to evaluate the test data. Further investigation into this new non- contact single point technique should yield an accurate, consistent and practical alternative. Having said this, further analysis of the technique is need, especially in the characterization of the impulse provided by the air. Experimentally, this technique has its limits, as the dynamics seen by the microphone are not necessarily the same as the ones experienced by a highly compliant membrane and needs further study. It is expected that this is highly negligible but needs to be shown. The scalability of this technique also needs to be further analyzed for the case of large structures. Acknowledgments Dr. Tarazaga is thankful for the support of the AFOSR grant number FA

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