Free Vibration Analysis of Pyroshock-Loaded Hardened Structures

Transcription

1 Proceedings of the IMAC-XXVIII February 1 4, 21, Jacksonville, Florida USA 21 Society for Experimental Mechanics Inc. Free Vibration Analysis of Pyroshock-Loaded Hardened Structures Jason R. Foley *, Lashaun M. Watkins, Brian W. Plunkett, and Janet C. Wolfson Air Force Research Laboratory * AFRL/RWMF; 36 W. Eglin Blvd., Bldg. 432; Eglin AFB, FL , jason.foley@eglin.af.mil Preston C. Gillespie Jacobs Engineering, Inc. Jeffrey C. Van Karsen LMS Americas, Inc. Alain L. Beliveau Applied Research Associates, Inc. ABSTRACT The free vibration response of a high stiffness, high strength (hardened) structural member is characterized under a variety of energetic and simulated pyroshock system inputs. The hardened structure studied is a structural pipe which includes a reinforcing material, e.g., a composite potting, with threaded end caps. Impulsive loads are imparted on the structure using bulk explosives and non-energetic impacts. The free vibration response of the structure is measured using a variety of sensors (accelerometers and strain gages); the observed experimental modes are compared with computationally estimated and experimentally observed principle modes up to approximately 5 khz. The operating (output-only) response of the system is also compared to show the effects of damaged reinforcing materials on the vibration frequencies and observed damping. The operating mode shapes also exhibit nonlinearities which are discussed, with possible explanations including rate- and amplitudedependent damping. NOMENCLATURE c E f n n L Elastic wave speed Elastic modulus Density Natural frequency Mode number Length INTRODUCTION Impulsive (high frequency and high amplitude) mechanical loads are an extremely severe environment found in impact, blast, and penetration applications. However, fully reproducing these environments is sometimes impossible due to safety concerns, unique test items, or prohibitive cost. It is therefore desirable to develop testing techniques that can reproduce a particular aspect of the dynamic environment experienced by a test article. The high frequency components of impulsive loads are especially damaging to sensitive electronic components used to sense and record the in situ environment. One of the experimental methods used to test the survivability of electronic systems to high-frequency input is pyroshock [1]. A significant body of literature exists on pyroshock testing methods for aerospace and defense applications [2, 3]. However, there many methods to simulate pyroshock in laboratory settings using impact tests [4] and resonating structures [5]. Pyroshock is generally defined by the proximity of the test article to an energetic input with a corresponding change in the dynamic environment. Near-field pyroshock generally includes higher frequency excitation (>1 khz) and appears impulsive in nature, with an output shock response spectrum that rises at approximately 1

2 db/decade [1]. Far-field pyroshock includes system response, and correspondingly has a knee in the shock response spectrum (SRS) and power spectral density (PSD) curves. This paper details both pyroshock and simulated pyroshock experiments to measure the dynamic reseponse of a stiffened structure. The structure is an 8 ft. long right cylindrical pipe of hardened steel (434 alloy) with 15 in. diameter and 1 in. wall thickness. The pipe is machined from a forged bar, leaving one end of the pipe closed with 6 in. thickness. This reinforced front section is designed to transfer the input loads and not participate in the overall dynamic response of the pipe. The pipe is filled with a composite of 64 ± 3% dead burned gypsum, 31 ± 3% wax (glycerol ester of 12-hydrox stearic acid), and 5 ± 3% wood rosin. The inside of the cylinder is prepared with a thin lining of tar and the potting material is then cast in situ. Finally, a bulkhead (or cap) is threaded into the open end of the pipe, confining the internal filler. A sensor and instrumentation package is mounted to the bulkhead. A schematic of the system is shown below in Figure 1. Impact v Hardened steel structural pipe Sensor & instrumentation package Striker bar Transfer bar Input Composite fill Pyroshock Reinforced front Threaded Bulkhead Figure 1. Experimental configuration using impact (top) or pyroshock (bottom) inputs. The basic approach taken is to provide mechanical input to the pipe by either impacting the structure with a hardened striker bar (for simulated pyroshock) or explosively loading a transfer bar that transmits this load to the structure. The transfer bar in this configuration functions similar to a Hopkinson bar, a widely-used apparatus for measuring elastic wave propagation [6]. Mechanical properties of the bar conceptually allow inference of the applied pyrotechnic force profile. However, the difficulties of quantifying the energy input to the system lead to an output-only, or operational, analysis in this paper. ANALYSIS The observed dynamic output of each sensor is evaluated using linear signal processing methods, including power spectral densities and short-time Fourier transforms (spectrograms). Although the modal behavior of the tube is not emphasized in the subsequent analysis, a one-dimensional approximation [7] is used as a first order check of the free vibration measurements. The longitudinal elastic wave speed (c) in a bar is c E /, (1) where E is the elastic modulus and is the density of the bar material. Equation (2) gives c ~ 5 m/s for high strength steel alloys; the corresponding frequency for the n th mode of a bar is f nc n. (2) 2L For a L = 2.5 m, the first axial or longitudinal mode (n = 1) is approximately 1 khz with higher harmonics at the corresponding multiples (n = 2, 3, ). SIMULATION Simulations of the structure under impact and pyrotechnic loading were run using two explicit finite element analysis codes, EPIC [8] and LS-DYNA [9]. The bar impact uses a 1 long, 3 diameter 434 steel bar with an incident velocity of 1 in/s. No programming material is used, creating a harsh metal-on-metal impact that is a reasonable simulation of a pyroshock input [4]. The explosively-loaded pyro test uses 1 lb. of C-4 using a coupled multiphase hydrocode analysis. The predicted acceleration time history in the instrumentation package for each case is shown in Figure 2; both have lightly damped response and appear qualitatively similar. All of the results are unfiltered and correspondingly will have spurious oscillations above approximately 1 khz [1]. Spectrograms of the impact and pyro simulations are shown in Figures 3 and 4, respectively.

3 Acceleration (g) Acceleration (g) Acceleration (g) 5 x 14 Bar impact Original Windowed Exponential Window 1.5 x 16 Pyro test Figure 2. Original and windowed time histories of (left) a simulated bar impact and (right) pyroshock loading of the tube Original Windowed Exponential Window 7 Bar impact (124-point Hanning window) x Figure 3. Short time Fourier transform (spectrogram) of a simulated bar impact on the structure.

4 Acceleration (g) Pyro test (124-point Hanning window) x Figure 4. Short time Fourier transform (spectrogram) of a simulated pyroshock on the bar and structure. Both spectrograms (Figure 3 and Figure 4) show very linear low frequency (< 3 Hz) behavior after the initial impulse. As the higher frequency response becomes more complex, the system begins to behave in a nonlinear fashion. The time dependence of the spectral response is hypothesized to be due to the interactions between the components in the threaded end of the system (i.e., the bulkhead and instrumentation package). A computational modal analysis of the system confirms that local modes of the bulkhead and instrumentation package begin to resonate at approximately 35 Hz. The power spectral densities of the axial output for both the pyroshock and impact tests are shown in Figure 5. The total energy in the bar impact PSD is significantly lower than the pyroshock test. Otherwise, the two PSD s are very close, both showing the first several evenly-spaced axial modes of the system. Again, the local modes of the bulkhead and instrumentation are reflected in the more complicated mode structure in Figure 5.

5 A(f) Single-Sided Amplitude Spectrum of a(t) Bar impact Pyro test Figure 5. Single-sided amplitude spectrum of the simulated impact and pyroshock tests. EXPERIMENT A pyroshock experiment was performed as an initial validation of the simulations presented in the previous section. The impulse input to the pipe system was 155 grams of explosive at the end of the transfer bar. The pipe system is suspended with compliant structures to simulate free-free boundary conditions. The instrumentation package consisted of a shock-hardened data recorder with shock accelerometers. A custom triaxial mount with Endevco model 727A-6k [11] piezoresistive shock accelerometers (6 kg n full scale) was stud-mounted to the package, providing strong coupling to the system. Triaxial data from the instrumentation package is shown in Figure 6 below. The peak accelerations are comparable in all three channels. It is also immediately evident that the structural damping is much larger than predicted in the simulations. The particular test article used in this experiment had been previously used in other impact testing, therefore some internal damage is expected with a corresponding increase in the damping coefficients. Spectrograms of the axial (Figure 7) and lateral (Figure 8) output response show a much richer dynamic response than the computational models. This was expected due to the relative simplicity of the model and perfect axisymmetric response in the system. The other notable feature in the axial response is the nonlinear response of the various modes.

6 Acceleration (g) Acceleration (g) 6 4 Acceleration Data from Pyroshock Test Axial Lateral 1 Lateral x 1-3 Figure 6. Axial and lateral sensor response to pyroshock input on the structure. Pyro test (124-point Hanning window) x x 1-3 Figure 7. Short time Fourier transform (spectrogram) of the axial response to pyroshock.

7 Acceleration (g) Pyro test (124-point Hanning window) x x 1-3 Figure 8. Short time Fourier transform (spectrogram) of the lateral response of the pipe to pyroshock. An experimental modal analysis of the structure was also performed post-test to characterize the low level (linear) response of the system and estimate the damping. An axial PSD from the modal analysis is shown in Figure 9 below. The first axial mode of the pipe is approximately 92 Hz, agreeing with the previous analysis and evident in the spectrograms. Structural damping was significantly higher than previously thought, with a damping ratio of 3.47% for the first axial mode. Local modes of the instrumentation package and bulkhead began at f = 374 Hz; this agrees with the observed spectral response from the pyroshock data. Figure 9. PSD of the axial sensors in the instrumentation package from modal analysis. FUTURE WORK The next step in this investigation is to fully characterize and isolate the nonlinear dynamic response of the system. This will include a focus on interfaces (both computationally and experimentally) and more rigorous model correlation and validation. Experimental improvements will come through more output points and development of instrumentation to measure the input levels on the system.

8 SUMMARY Computational and experimental pyroshock tests were performed to analyze the dynamic response of a hardened pipe with composite filler. Both the computational and the experimental data showed nonlinearities. Where the model predicted the axial modes would be linear, spectral data from the experiment show that the frequencies of these modes were time dependent. Additionally, the predictions by the model significantly underestimated the structural damping as well as the modal response of the instrumentation package when compared with experimental modal data. Further exploration and isolation of the particular nonlinear mechanisms and sources of increased damping is indicated. ACKNOWLEDGEMENTS J. F. acknowledges research funding from Dr. David Stargel of the Air Force Office of Scientific Research (AFOSR). The authors also thank Prof. Doug Adams (Purdue) for helpful discussions. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Air Force. REFERENCES [1] Harris, C.M., and Piersol, A.G., 22, Shock and Vibration Handbook, 5th Edition, McGraw-Hill, New York. [2] Powers, D., "Summary of Testing Techniques," Shock and Vibration Bulletin, 1986, Vol. 56, pp [3] Keon, S.P., "Pyrotechnic Shock Testing: Real Test Lab Experiences at EBA&D," 26. [4] Bai, M., and Thatcher, W., "High G Pyrotechnic Shock Simulation Using Metal-to-Metal Impact," Shock and Vibration Bulletin, 1979, Vol. 49, pp [5] Davie, N., "The Controlled Response of Resonating Fixtures Used to Simulate Pyroshock Environments," Shock and Vibration Bulletin, 1986, Vol. 56, pp [6] Parry, D.J., et al., "Hopkinson bar pulse smoothing," Measurement Science and Technology, 1995, Vol. 6, No. 5, pp [7] Inman, D.J., 28, Engineering Vibration, Pearson, Upper Saddle River, pp [8] Johnson, G.R., et al., 1987, "User Instructions for the EPIC-3 Code," available from AFATL-TR [9] 29, LS-DYNA User's Manual, LSTC. [1] Idesman, A.V., et al., "A new explicit predictor-multicorrector high-order accurate method for linear elastodynamics," Journal of Sound and Vibration, 28, Vol. 31, No. 1-2, pp [11] 25, "Model 727A Accelerometer Data Sheet," Endevco Corporation.