Experimental and Applied Mechanics, Volume 6

Teflon impactor were (β, γ) ¼(4.0 0.5, 0.70 0.05). Force histories obtained from original CZ theory, experiment, and modified CZ theory are displayed side by side in Fig. 11.6. It can be seen that the exaggerated transient force histories obtain from original CZ theory (see Fig. 11.6a) for soft material impactors are modified (see Fig. 11.6c) based on the understanding obtained from experiments (see Fig. 11.6b). In addition, the force peaks of the profiles where modified using a universal ς and ε value found to be (ς, ε) ¼(1.50 0.10, 1.460 0.005) for best matched results. Notice that the dissipation parameter γ and solution time discrepancy parameter β depend on the impactor material. Delrin Acetal has a higher γ - parameter than Teflon because, as physically witness in our lab experiments although not measured, its restitution coefficient is significantly and visibly greater than Teflon’s. Delrin Acetal impactor behaves like a tennis ball, restoring a significant amount of energy during impact which other impactor materials transmit to the plate. On the other hand, Teflon has greater β-parameter due to its soft polymeric nature that is quantized by its low elastic modulus. Inspecting Eqs. 11.10 and 11.13, it can be observed that a low elastic modulus will lead to divergence of the solution in the time domain, resulting in the need for the β-parameter to mitigate the mathematical bias. 11.7 Conclusion In this work, we have successfully shown that CZ theory can be modified to obtain more accurate solutions by implementing a novel spiral sensor array called Theodorus spiral sensor cluster (TSSC) and two ad-hoc AUS processing techniques called the lag index (LI) and dominant frequency band (DFB) for impactor type, low velocity impact classification and the consequent application of empirically determined modification parameters. TSSC provided mutually exclusive data sets that enabled Lag coefficient and DFB to have robust sensitivity to impactor elastic modulus. This in turn was used to identify, most importantly, the soft impactors in order for the paramount and automated application of modification parameters for accurate solutions. Future studies on this topic will look into solution accuracy as a function of other impact parameters such as impact energy, impactor effective diameter, plate material properties and thickness, and the eventual correlation with experimentally determined damage indices. References 1. Zhongqing S, Chao Z, Ming H, Li C, Qiang W (2013) Acousto-ultrasonics-based fatigue damage characterization: linear versus nonlinear signal features. J Mech Sys Signal Process 45:225–239 2. Davarciog˘lu B (2010) The acousto-ultrasonic characterization of physical properties of human bones. J Appl Biol Sci 4(1):41–44 3. Xinlin QingeLiu Z (2003) Structural intensity study of plates under low-velocity impact. Int J Impact Eng 957–975 4. Yang JCS, Chun DS (1969) Application of the Hertz contact law to problems of impact in plates. United States Naval Ordnance Laboratory, White Oak, MD, NOLTR 69-152 5. Sun CT, Yang SH (1980) Contact law and impact response of laminated composite. NASA. CR-159884 6. Suemasu H, Kerth S, Maier M (1994) Indentation of spherical head indentors on transversely isotropic composit plates. J Compos Mater 28:1723–1739 7. Liu Z, Swaddiwudhipong S (1997) Response of plate and shell structures due to low velocity impact. J Eng Mech 123(12):1230–1237 8. Olsson R (2002) Engineering method for prediction of impact response and damage in sandwich panels. J Sandwich Struct Mater 4(1):83–95 9. Zheng D, Binienda WK (2009) Semianalytical solution of wave-controlled impact on composite laminates. J Aerosp Eng 22(3):318–323 10. Zener C (1941) The intrinsic inelasticity of large plates. Phys Rev 59:669–673 11. Olsson R (2002) Mass criterion for wave controlled impact response of composite plates. Composites 31(8):879–887 12. Lee HP, Lu C, Liu ZS, Xu XD (2003) The structural intensity analysis of plates under dynamic loading. Proceedings of the 16th nordic seminar on computational mechanics, Trondheim, Norway, pp 145–148 13. Victorov A (1967) Rayleigh and lamb waves. Plenum, New York, NY 14. Giurgiutiu V (2008) Structural health monitoring with piezo wafer active sensors. Elsevier, New York, NY 15. Carretero-Gonza´lez R, Khatri D, Porter MA, Kevrekidis PG, Daraio C (2009) Dissipative solitary waves in granular crystals. Phys Rev Lett 102:024102 16. Davis PJ (1993) Spirals: from theodorus to chaos. AK Peters, Wellesley, MA 17. Ljung L, Glad T (1994) Modeling of dynamic systems. Prentice Hall, Upper Saddle River, NJ 18. Orfanidis SJ (1996) Optimum signal processing: an introduction, 2nd edn. Prentice Hall, Englewood Cliffs, NJ 19. Morchen F (2003) Time series feature extraction for data mining using DWT and DFT. Data Bionics, Philipps-University Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany 20. Anstey JS, Peters DK, Dawson C (2007) An improved feature extraction technique for high volume time series data. Proceedings of the 4th conference on IASTED International Conference: Signal Processing, Pattern Recognition, and Applications. pp 74–81 21. Daraio C, Nesterenko V, Herbold E, Jin S (2004) Strongly nonlinear waves in a chain of teflon beads. American Institute of Physics, AIP Conference Proceedings, 845. pp 1507–1510 11 Classification of Low Velocity Impact Using Spiral Sensing Technique 87

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