Dynamic behaviour of commercial aircraft fuselage sections

Transcription

1 Dynamic behaviour of commercial aircraft fuselage sections Vincenzo Franzese 1, Alessandro Perazzo 1 Università degli Studi di Napoli Federico II, Naples, 80125, Italy This work is integrated in a research project aimed at cabin noise reduction for turbofan commercial aircraft. In order to understand the vibro-acoustic behaviour of a structure it is fundamental to find out its natural frequencies and mode shapes. Several numerical investigations were performed on different fuselage sections to predict the dynamic behaviour of these structures and the influence in the response of each single component. Then an experimental campaign was performed on the fuselage section available at CeSMA laboratory and experimental results were compared with numerical ones. Stiffened cylinders exhibit a dynamic behaviour which is the envelope of three simple structures: frame, shell between two frames and unstiffened cylinder. The envelope curve of the available structure and the NGTP model were obtained. Finally, experimental and numerical correlations of the frame were presented. KEYWORDS: modal analysis, vibro-acoustic testing r l t h f n d n h n s n f FEM E G ρ ν W ffff n EMA Δf S ff S xx S xf γ 2 MAC T H u f u e FRF Nomenclature = section radius of fuselage section = section length of fuselage section = average thickness = floor height = number of doors = number of portholes = number of stringers = number of frames = finite element method = Young s modulus = shear modulus = mass density = Poisson s ratio = width of the cross section = free-free condition on four edges = number of circumferential wave number = experimental modal analysis = percentage difference between FEM and EMA natural frequencies = power spectral density of the input signal = power spectral density of the output signal = cross spectral density of the input and output signal = coherence function = modal assurance criterion = transpose operator = hermitian operator = numerical eigenvector = experimental eigenvector = frequency response function 1 Graduate student, Industrial Engineering Department, via Claudio 21, Naples. 1

2 I. Introduction N airframe can be studied by development of numerical models, used to obtain modal parameters. In this case a AFEM approach was chosen, using many models which are successively described. Investigations on fuselage sections were made by some authors 1-6. A useful work was presented in 1979 by G. Sengupta 7. He studied the lowfrequency cabin noise reduction in commercial aircrafts and showed that structural response is influenced by stiffeners in different frequency bandwidths. The following work was based on this consideration and no complicating effects were considered, such as anisotropy, variable thickness, initial stress or shear deformation. The low-frequency behaviour of a periodic, frame-stiffened cylinder can be subdivided into three regions. In the first region, the cylinder dynamic is essentially dominated by the unstiffened cylinder dynamic, with the frame acting like attached mass. In the second region, the dynamic behaviour is influenced by the frame resonances, with the shells acting like attached masses. In the third region, the shell motion becomes much important than the frame one: in fact, the frequency approaches that of clamped-clamped shell segment. The main aim of this work was to verify and reproduce this envelope curve for two test structrures: the fuselage section located at the CeSMA laboratory and the central section of the New Generation TurboProp NGTP, a Leonardo Company project. : Figure 1. Natural frequencies of a periodic, frame stiffened cylinder. Figure 2. Aircraft fuselage section located at CeSMA laboratory. II. Description of the test structures The first test structure was a fuselage section of a commercial airplane that was placed in 2015 in the new CeSMA laboratory of Università degli Studi di Napoli Federico II, department of San Giovanni a Teduccio, see Fig. 2. In Table 1 there is a list of the geometric parameters of the fuselage section. The fuselage section was suspended by four coil springs attached to two portals, which are 4.5 m distant. The width of a portal is 4.5 m and the height is 7 m. The four springs were dimensioned using a 3 DOFs model of an empty cylinder, see Fig. 3. Table 1. Geometric parameters of the fuselage section of a commercial aircraft. r 2075 mm n d 2 l 4310 mm n h 10 t 2.2 mm n s 81 h f 1700 mm n f 7 Figure 3. Schematic model of the suspension system. 2

3 The second test structure was a fuselage section of the New Generation TurboProp, whose geometric parameters are summarised in Table 2 and the analysed section was the central one, see Fig. 5. Table 2. Geometric parameters of the NGTP fuselage section. r 1766 mm n h 24 l 6672 mm n s 52 t 1.05 mm n f 13 Figure 4. FEM model of the NGTP fuselage. Figure 5. FEM model of the NGTP fuselage section analysed. III. Numerical Modal Analysis The dynamic behaviour of the previous structures was described using the FEM approach, so some numerical models of increasing accuracy are presented 8. All the models were realized with MSC Patran and processed with MSC Nastran A. Fuselage section of a commercial aircraft The material used was Al 7075, whose features are shown in Table 3. In order to analyze the overall behaviour of the fuselage section, it was splitted into three parts: frame, shell between two frames and unstiffened cylinder. The frame was discretized with 80 CBAR elements and a Z section; the ring was in a free-free condition whereas the outof-plane DOFs were constrained. The shell between two frames was discretized with 320 CQUAD4 elements and a skin thickness of 2.2 mm; the shell edges were clamped. The unstiffened cylinder was modelized with 3840 CQUAD4 elements, a thickness of 2.2 mm and the in-plane translations of the circumferential edges were restrained (shear diaphragm condition). In the stiffened cylinder, the whole stringers, the frames and the panels were discretized with 3840 CROD, 720 CBAR and 3840 CQUAD4 elements, respectively. Table 3. Al 7075 properties. E 71 x 10 9 Pa G 26 x 10 9 Pa ρ 2795 Kg/m 3 ν 0.33 Table 4. Frame cross section data. W 18 mm 2 mm t f H 1 H 2 56 mm 60 mm Figure 6. Z section of the frame. 3

4 Figure 7. Frame, FEM model. Figure 8. Shell between two frames, FEM model. Figure 9. Stiffened cylinder, FEM model. A plot of the natural frequencies of the analysed cases versus the number of circumferential waves (n) is shown in Fig. 10. There is an increasing trend of the natural frequency with n in the frame model. As for the unstiffened cylinder, there is a minimum value of the f(n) curve, which is f = 14.4 Hz (n = 9); for n 9 it is a monotonically decreasing function whereas for n 9 it is a monotonically increasing function. A similar behaviour is observable for the shell between two frames, but the minimum value corresponds to f = Hz (n = 23). The frequency curve of the stiffened cylinder is the envelope of the three preceding cases; it is possible to identify three regions: Region I (1 n 4). In this region the dynamic behaviour is essentially dominated by the unstiffened cylinder and the frames act like attached masses, so there is a more important inertial effect, indeed the frequencies of the stiffened cylinder are lower than that of the unstiffened ones. Region II (4 n 8). In this region the dynamic behaviour is influenced by frame resonances, with the shell acting like attached mass, so the frames provide more effective stiffening. The natural frequencies of the stiffened cylinder are higher than the unstiffened cylinder, but lower than the frame frequencies. Region III (n 8). The frequencies approach the shell between two frames ones because the frame motion becomes small, compared to the shell panel one. Figure 10. Envelope curve of dynamic behavior for the turbofan aircraft. 4

5 B. Fuselage section of the NGTP The materials used were Aluminum alloys, which differ in E and ρ. In order to analyze the behaviour of the fuselage section of NGTP, three sub-structures were analyzed also in this case: frame, shell between two frames and unstiffened cylinder. The frame was discretized with 52 CBAR elements; the out-of-plane DOFs were constrained and only in plane flexural modes were considered. The shell between two frames was discretized with 156 CQUAD4 elements and a skin thickness of 1.05 mm; the shell edges were clamped. The unstiffened cylinder was modelized with 1664 CQUAD4 elements, a thickness of 1.05 mm and the shear diaphragm condition was used. In the stiffened cylinder, the whole stringers, the frames and the panels were discretized with 1836 CROD, 576 CBAR and 1728 CQUAD4 respectively. The curve trends of NGTP are similar to the previous case analysed, see Fig. 11. The frame curve is a monotonically increasing function whereas the shell curve has a minimum in n = 22 and a value of f = Hz. The same trend is evident in the case of the unstiffened cylinder, but the minimum value is f = 6.9 Hz in n = 8. The stiffened cylinder curve is the envelope of the three preceding ones: Region I (1 n 3) the dynamic behaviour is similar to the unstiffened cylinder one. Region II (3 n 7) the frames influences the structural mode shapes, causing an abrupt increment of natural frequencies. Region III (n 7) the envelope approaches the shell one. Figure 11. Envelope curve of dynamic behavior for the NGTP aircraft. Finally, an interesting comparison between the two studied envelopes was made, see Fig. 12. For 1 n 4 the natural frequencies of the NGTP are lower than that of the other section. This is due to the fact that in this region the frames act like attached masses. The NGTP has more frames than the turbofan aircraft, so its natural frequencies are lower, because there is more mass. For 4 n 9 the frames provide a stiffening behaviour, so NGTP frequencies are higher than the turbofan aircraft ones. For n 9 the behaviour is influenced by the shell portion between two adjacent frames. The turbofan aircraft shell has a bigger mass so its natural frequencies are lower than the NGTP. 5

6 Figure 12. Comparison between the turbofan and the NGTP envelope curve. IV. Experimental Modal Analysis Experimental modal analysis tests were made on a frame of the turbofan fuselage section, in order to compare the experimental results with the numerical ones and validate them The chosen fuselage frame is the central one, equidistant from the two couple of springs. Its diameter is 4150 mm and other geometric data are reported in Table 4. The instrumentation employed for all the campaign of experimental testing is itemized here: accelerometers and impedance head PCB Piezotronics, a Brüel & Kjær calibrator, an Endevco modal hammer, a Modal Shop shaker and an amplifier, a LMS SCADAS III acquisition frontend and a LMS Test.Lab 15A software. A. FEM model of the frame In order to have a more realistic numerical model, it was added the floor which properties are summarised in Table 5. The model was in a free free condition and the out-of-plane DOFs were constrained, and it was obtained with 212 CBAR elements. Table 5. Floor Cross Section Data. W 40 mm H 70 mm t 1 2 mm 2 mm t 2 Figure 13. Geometric model of the floor. Figure 14. Cross section of the floor. 6

7 B. Experimental setup The frame was discretized with 18 nodes and was excited by the shaker in one node which is marked with a red circle in Fig. 15. The frequency range adopted for the tests was Hz; a random signal was employed with a 0.25 Hz of resolution and 25 averages were used in every run to avoid FRF distortions near resonances. The random signal is a Gaussian-distributed random noise with a Hanning window and it allows to average out nonlinear response. Two accelerometers were applied for each run to a couple of different nodes to acquire data around the ring. Some test campaigns were made, changing the shaker position 15. The first one under the fuselage section and the second one on a side (using a support) didn t satisfy the expectations in term of Coherence and FRF functions. The optimal configuration was the one with the shaker in a ffff condition linking the trunnion of the shaker to a rigid support using four springs, as shown in Fig. 16; this kind of support was suitable to isolate the shaker from external vibrations. The shaker was attached to the fuselage, thanks to a two-component glue, as shown in detail in Fig. 17: using this linkage, it was provided a good excitation of the whole structure without misalignments between the stringer and the fuselage skin. Figure 15. Frame geometry model, LMS Test.Lab. The red circle indicates the excitation point. Figure 17. Particular of the linkage between shaker and fuselage. Figure 16. Test setup of the shaker. C. Results The campaign tests spent about 20 days and 160 hours, with the employment of three laboratory operators. At the end of the tests, there was a collection of about 100 FRFs from which was possible to extract the natural frequencies and mode shapes of the central frame of the fuselage. The Coherence function and the MAC are useful in order to examine the data quality 16. The Coherence formula is given in Eq. (1). γ 2 (f) = S xf 2 S xx S ff (1) The Coherence function of one test node is presented in Fig. 18. It is worth mentioning that the values of this function are close to unity; that implies a good accuracy of the data in the range Hz in which were included the natural frequencies of the frame. Figure 18. Coherence function. 7

8 A comparison between the measured FRF and the synthesized one of the whole structure is shown in Fig. 19. In this figure are indicated, with blue circles, the first four natural frequencies of the frame obtained by exciting the fuselage section with a random signal. In these FRFs there is also the presence of other peaks related to resonances of other subsctures of the fuselage section. The only aim of these experimental tests was to compare frame natural frequencies with the numerical ones and verify the level of the correlation. The MAC is graphically reported in Fig. 20. Figura 19. Measured and synthesized FRF, in Log scale. The Modal Assurance Criterion is a statistical indicator that is most sensitive to large differences and relatively insensitive to small differences in the mode shapes. This yields a good statistic indicator and a degree of consistency between mode Figura 20. MAC of four mode shapes. shapes. It is bounded between 0 and 100 (in percentage), with 100 indicating fully consistent mode shapes whereas a value near 0 indicates that the modes are not consistent. MAC = {u} e T {u}f H 2 {u} e T {u}e H {u}f T {u}f H (2) In Eq. (2) is presented the formula of MAC. To understand if there is a good correlation between the mode shapes it is helpful the main diagonal of the matrix in Table 6: its values are equal or higher than sixty per cent, so these modes shapes were enough consistent. A percentage comparison between first four EMA and FEM natural frequencies is reported in Table 7. It is possible to observe that the MAC value is high for the first and second resonances, even if the difference of EMA and FEM fundamental frequency is also high; maybe it is due to other complicating effects not considered in this experimental and numerical analysis. The MAC values for the third and fourth mode shapes are lower than the first ones, but these are acceptable values, so a good result was globally obtained from these experimental tests. It is worth mentioning a switch between the second and third resonances: the second EMA mode shape corresponded to the third FEM one while the third EMA mode shape corresponded to the second FEM one. Table 6. Frame MAC % table, FEM vs. EMA Table 7. Comparison of the natural frequencies of the frame between FEM and EMA. FEM EMA f % MAC %

9 A graphical correlation between the numerical and experimental mode shapes is shown in Fig. 21 and Fig. 22: the blue line represents the numerical mode shape and the red line with circles represents the experimental one. Figura 21. Mode shapes comparison, mode 1. MAC = Figura 22. Mode shapes comparison, mode 2. MAC = V. Conclusion This work was about the dynamic behaviour of fuselage sections. It was organised in two parts: numerical analysis of two commercial aircraft fuselage sections and an experimental one. In the first part, the dynamic behaviour of stiffened cylinders was studied using some FEM models: a frame, a shell between two frames and an unstiffened cylinder. The trend of the natural frequencies of a fuselage section was the envelope of their behaviours. In the second part two test campaigns were conducted on the fuselage section. After some proof tests, it was used the shaker in a free-free condition to excite the fuselage. EMA tests were carried out on the frame and the first four EMA modes were compared with the FEM ones. MAC was calculated to verify the consistency of the mode shapes analysed and a good correlation resulted. As an example, a good MAC value of 73% was reached for the first mode shape and almost 77% for the second one. As future developments, MIMO tests will be able to be performed using acoustic excitation and a shaker excitation in order to study the effects of combined loads on the behaviour of the whole structure. Finally, acoustic tests will be made to investigate the mid-frequency range of this turbofan fuselage section. Acknowledgments The authors greatfully acknowledge the valuable support of Prof. Francesco Marulo and Post P.h.D. Engineers Giuseppe Petrone and Tiziano Polito from the Università degli Studi di Napoli Federico II for providing the turbofan fuselage section and for help in performing vibro-acoustics experiments. A special thank to Gianfranco Tammaro, for his contribute with the authors in the development of this work. The work presented here was conducted in the course of the IMM project (Interiors with multi-functional materials) funded by the DAC (Aerospace Campania District). References 1 Arthur W. Leissa, Vibration of shells, Ohio State University, Columbus, Hu, W.C.L., Gromley, J.G., Lindholm, U.S., An analytical and experimental study of vibrations of ring-stiffened cylindrical shells, Tech.Rept. 9, Contract NASR-94(06), SwRI Project , Southwest Res.Inst.,

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