Stress Wave Attenuation in Noncollinear Structures Subjected to Impulsive Transient Loadings
Publication: Journal of Engineering Mechanics
Volume 142, Issue 5
Abstract
This paper presents an exploration of noncollinear Timoshenko beam structures for attenuating the stress waves generated from impulsive transient loadings. Due to the existence of the noncollinear segments, flexural waves are generated in addition to the longitudinal waves. Furthermore, the resulting waves are dispersive and thus provide higher potential for the attenuation of the stress waves. Symmetric patterns are found to be more appropriate for increasing the stress-wave attenuation capacity, as these patterns can eliminate bending stress effects at the boundary of the structures. More generally, an adaptive optimization methodology is developed to find the most efficient layout of the noncollinear stress-wave attenuators (NSWAs). This methodology uses genetic algorithms (GA), coupled with an explicit finite-element (FE) method for analyzing the wave-propagation behavior of the structures. The developed methodology is capable of updating the FE model of each trial solution, as the geometric characteristics of the solutions are evolving during the optimization procedure. Through this evolutionary design process, the attenuation capacity of the noncollinear structures is observed to be a complex function of the number of noncollinear segments and the relative wavelength associated with the transient loading. In addition, the results show that the single-material noncollinear structures are not effective for attenuating the amplitudes of transient pulse loadings with longer durations, such as blast waves. Most interestingly, however, by incorporating geometric and material discontinuities, bimaterial NSWAs are found to provide impressive levels of attenuation within compact geometries. Although much analytical and experimental validation remains, designs along these lines could help to initiate a paradigm shift from hardening of structures for blast protection towards a protective systems design approach featuring creative management of stress wave propagation.
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Acknowledgments
The research described in this paper was funded primarily by the US National Science Foundation under Grant No. CMMI-0900338 with additional support to the first author by MCEER. The authors gratefully acknowledge this support.
References
ABAQUS 6.12 [Computer software]. Dassault Systems Simulia, Providence, RI.
Ajdari, A., Nayeb-Hashemi, H., and Vaziri, A. (2011). “Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures.” Int. J. Solids Struct., 48(3), 506–516.
Alleyne, D., and Cawley, P. (1991). “A two-dimensional Fourier transform method for the measurement of propagating multimode signals.” J. Acoust. Soc. Am., 89(3), 1159–1168.
Anfinsen, L. (1967). “Optimum design of layered elastic stress wave attenuators.” J. Appl. Mech., 34(3), 751–755.
Carlsson, L., Sindelar, P., and Nilsson, S. (1986). “Decay of end effects in graphite/epoxy bolted joints.” Compos. Sci. Technol., 26(4), 307–321.
Chakraborty, A., and Gopalakrishnan, S. (2003). “A spectrally formulated finite element for wave propagation analysis in functionally graded beams.” Int. J. Solids Struct., 40(10), 2421–2448.
Desmond, T. (1981). “Theoretical and experimental investigation stress waves at a junction of three bars.” ASME J. Appl. Mech., 48(1), 148–154.
Dharmasena, K. P., Wadley, H. N., Xue, Z., and Hutchinson, J. W. (2008). “Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading.” Int. J. Impact Eng., 35(9), 1063–1074.
Doyle, J., and Kamle, S. (1987). “An experimental study of the reflection and transmission of flexural waves at an arbitrary T-joint.” J. Appl. Mech., 54(1), 136.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning, Addison-Wesly, Boston.
Guz’, A., and Kokhanenko, Y. V. (1995). “Edge effects in composites.” Int. Appl. Mech., 31(3), 165–181.
Holland, J. H. (1975). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence, University of Michigan Press, Ann Arbor, MI.
Horgan, C., and Simmonds, J. (1994). “Saint-Venant end effects in composite structures.” Compos. Eng., 4(3), 279–286.
Horgan, C. O. (1982). “Saint-Venant end effects in composites.” J. Compos. Mater., 16(5), 411–422.
Lee, J., and Kolsky, H. (1972). “The generation of stress pulses at the junction of two noncollinear rods.” J. Appl. Mech., 39(3), 809.
Lindholm, U., and Doshi, K. (1965). “Wave propagation in an elastic nonhomogeneous bar of finite length.” J. Appl. Mech., 32(1), 135–142.
Luo, X., Aref, A. J., and Dargush, G. F. (2009). “Analysis and optimal design of layered structures subjected to impulsive loading.” Comput. Struct., 87(9), 543–551.
Luo, X., Aref, A. J., and Dargush, G. F. (2011). “Optimal design of bundled layered elastic stress wave attenuators.” J. Comput. Civ. Eng., 387–395.
MATLAB R2012a [Computer software]. MathWorks, Natick, MA.
Mei, C. (2012). “Free vibration analysis of classical single-story multi-bay planar frames.” J. Vibr. Control, 19(13), 2022–2035.
Mei, C., and Mace, B. (2005). “Wave reflection and transmission in Timoshenko beams and wave analysis of Timoshenko beam structures.” J. Vibr. Acoust., 127(4), 382–394.
Mitchell, M. (1998). An introduction to genetic algorithms (complex adaptive systems), MIT Press, Cambridge, MA.
Moser, F., Jacobs, L. J., and Qu, J. (1999). “Modeling elastic wave propagation in waveguides with the finite element method.” Ndt & E Int., 32(4), 225–234.
Naik, N., Goel, R., and Kulkarni, M. D. (2008). “Stress wave attenuation in ceramic plates.” J. Appl. Phys., 103(10), 103504.
Pandya, K. S., Dharmane, L., Pothnis, J. R., Ravikumar, G., and Naik, N. (2012). “Stress wave attenuation in composites during ballistic impact.” Polym. Test., 31(2), 261–266.
Rafiee-Dehkharghani, R. (2015). “Stress wave scattering in solids for mitigating impulsive loadings.” Ph.D. thesis, State Univ. of New York, Buffalo, NY.
Rafiee-Dehkharghani, R., Aref, A., and Dargush, G. (2014). “Characterization of multilayered stress wave attenuators subjected to impulsive transient loadings.” J. Eng. Mech., 04014137.
Rafiee-Dehkharghani, R., Aref, A., and Dargush, G. (2015a). “Planar stress wave attenuation in plates with circular voids and inclusions.” Compos. Part B: Eng., 75, 307–318.
Rafiee-Dehkharghani, R., Bansal, D., Aref, A., and Dargush, G. (2015b). “Interface profile optimization for planar stress wave attenuation in bi-layered plates.” Compos. Part B: Eng., 82, 129–142.
Ruzzene, M., and Baz, A. M. (2000). “Attenuation and localization of wave propagation in periodic rods using shape memory inserts.” SPIE’s 7th Annual Int. Symp. on Smart Structures and Materials, International Society for Optics and Photonics, Bellingham, WA.
Tsypkin, Y. Z., and Nikolic, Z. J. (1971). Adaptation and learning in automatic systems, Academic Press, New York.
Velo, A. P., and Gazonas, G. A. (2003). “Optimal design of a two-layered elastic strip subjected to transient loading.” Int. J. Solids Struct., 40(23), 6417–6428.
Zhao, H., Elnasri, I., and Abdennadher, S. (2005). “An experimental study on the behaviour under impact loading of metallic cellular materials.” Int. J. Mech. Sci., 47(4), 757–774.
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Published In
Journal of Engineering Mechanics
Volume 142 • Issue 5 • May 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 6, 2015
Accepted: Dec 1, 2015
Published online: Jan 19, 2016
Published in print: May 1, 2016
Discussion open until: Jun 19, 2016
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