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Shock and Vibration
Volume 2014 (2014), Article ID 294271, 21 pages
http://dx.doi.org/10.1155/2014/294271
Review Article

Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration

1Vehicle Technology Directorate, US Army Research Laboratory, APG, MD 21005, USA
2US Army Aberdeen Test and Center (ATC), APG, MD 21005, USA
3US Army Materiel System Activity Analysis (AMSAA), APG, MD 21005, USA
4US Army Research Office, Durham, NC 27709, USA
5Naval Undersea Warfare Center Division, Keyport, WA 98345, USA
6Center for Advanced Life Cycle Engineering (CALCE), University of Maryland, College Park, MD 20742, USA

Received 17 July 2013; Accepted 5 February 2014; Published 10 April 2014

Academic Editor: Nuno Maia

Copyright © 2014 Ed Habtour et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. E. Shigley and C. R. Mischke, Mechanical Engineering Design, McGraw-Hill, Boston, Mass, USA, 6th edition, 2001.
  2. N. E. Dowling, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Prentice Hall, Upper Saddle River, NJ, USA, 2nd edition, 1999.
  3. I. Elishakoff, “Generalized eringen problem: influence of axial force on random vibration response of simply supported beam,” Structural Safety, vol. 4, no. 4, pp. 255–265, 1987. View at Google Scholar · View at Scopus
  4. C. Leser, L. Juneja, S. Thangjitham, and N. E. Dowling, “On multi-axial random fatigue load modeling,” SAE Technical Paper 980696, Society of Automotive Engineering, 1996. View at Google Scholar
  5. Y. Liu and S. Mahadevan, “Multiaxial high-cycle fatigue criterion and life prediction for metals,” International Journal of Fatigue, vol. 27, no. 7, pp. 790–800, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. X. Pitoiset, A. Preumont, and A. Kernilis, “Tools for a multiaxial fatigue analysis of structures submitted to random vibrations,” in Proceedings of the European Conference on Spacecraft Structures Materials and Mechanical Testing, Braunschweig, Germany, November 1998.
  7. D. J. Segalman, C. W. G. Fulcher, G. M. Reese, and R. V. Field Jr., “Efficient method for calculating r.m.s. von Mises stress in a random vibration environment,” Journal of Sound and Vibration, vol. 230, no. 2, pp. 393–410, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Socie and G. Marquis, Multiaxial Fatigue, Society of Automotive Engineers, Warrendale, Pa, USA, 2000.
  9. K. A. Sweitzer, Random Vibration Response Statistics for Fatigue Analysis of Nonlinear Structures [Ph.D. thesis], University of Southampton, Southampton, UK, 2006.
  10. W. E. Whiteman and M. S. Berman, “Fatigue failure results for multi-axial versus uniaxial stress screen vibration testing,” Shock and Vibration, vol. 9, no. 6, pp. 319–328, 2002. View at Google Scholar · View at Scopus
  11. M. Paulus, A. Dasgupta, and E. Habtour, “Life estimation model of a cantilevered beam subjected to complex random vibration,” Fatigue and Fracture of Engineering Materials and Structures, vol. 35, no. 11, pp. 1058–1070, 2012. View at Google Scholar
  12. R. M. French, R. Handy, and H. L. Cooper, “A comparison of simultaneous and sequential single-axis durability testing,” Experimental Techniques, vol. 30, no. 5, pp. 32–37, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. W. E. Whiteman and M. Berman, “Inadequacies in uniaxial stress screen vibration testing,” Journal of the Institute of Environmental Sciences and Technology, vol. 44, no. 4, pp. 20–23, 2001. View at Google Scholar · View at Scopus
  14. E. Habtour, C. Choi, G. Drake, A. Dasgupta, and M. Al-Bassyiouni, “Improved reliability testing with multiaxial electrodynamics vibration,” in Proceedings of the 56th Annual Reliability and Maintainability Symposium, San Jose, Calif, USA, 2010.
  15. E. Habtour, C. Choi, M. Osterman, and A. Dasgupta, “Novel approach to improve electronics reliability in the next generation of US army small unmanned ground vehicles under complex vibration conditions,” Journal of Failure Analysis and Prevention, vol. 12, no. 1, pp. 86–95, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. C. J. Dodds and C. H. Ward, “The ubiquitous four-poster,” Engineering Integrity Society, vol. 16, no. 1, pp. 17–23, 2005. View at Google Scholar
  17. C. M. Awate, S. M. Panse, and C. J. Dodds, “Validation of an accelerated test on a four-post road simulator,” Paper 2007-26-070, Society of Automotive Engineering, pp. 761–767, 2007.
  18. C. J. Dodds and A. R. Plummer, “Laboratory road simulation for full vehicle testing a review,” in Proceedings of the Symposium on International Automotive Technology, 2001.
  19. J. C. Delamotte, R. F. Nascimento, and J. R. F. Arruda, “Simple models for the dynamic modeling of rotating tires,” Shock and Vibration, vol. 15, no. 3-4, pp. 383–393, 2008. View at Google Scholar · View at Scopus
  20. C. Q. Liu, “Combination of an improved FRF-based substructure synthesis and power flow method with application to vehicle axle noise analysis,” Shock and Vibration, vol. 15, no. 1, pp. 51–60, 2008. View at Google Scholar · View at Scopus
  21. N. W. M. Bishop, “Vibration fatigue analysis in the finite element environment,” in Proceedings of the 16th Encuentro del Grupo Español de Fractura, Torremolinos, Spain, 1999.
  22. M. H. A. Bonte, A. De Boer, and R. Liebregts, “Prediction of mechanical fatigue caused by multiple random excitations,” in Proceedings of the ISMA Conference, pp. 697–708, September 2004. View at Scopus
  23. M. H. A. Bonte, A. de Boer, and R. Liebregts, “Determining the von Mises stress power spectral density for frequency domain fatigue analysis including out-of-phase stress components,” Journal of Sound and Vibration, vol. 302, no. 1-2, pp. 379–386, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. P. H. Wirsching, T. L. Paez, and K. Ortiz, Random Vibrations: Theory and Practice, John Wiley and Sons, New York, NY, USA, 1995.
  25. T. Dirlik, Application of Computers in Fatigue Analysis [Ph.D. thesis], University of Warwick, Warwick, UK, 1985.
  26. D. A. Thomas, K. Avers, and M. Pecht, “The “trouble not identified” phenomenon in automotive electronics,” Microelectronics Reliability, vol. 42, no. 4-5, pp. 641–651, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. D. H. Hodges and G. A. Pierce, Introduction to Structural Dynamics and Aeroelasticity, 2nd edition, 2011.
  28. J. M. Sater, C. R. Crowe, R. Antcliff, and A. Das, “An assessment of smart Air and space structures: demonstrations and technology,” IDA Report P-3552, Log: H 00-002035, Institute for Defense Analysis, Alexandria, Va, USA, 2000. View at Google Scholar
  29. M. R. M. C. Da Silva, “Non-linear flexural-flexural-torsional-extensional dynamics of beams-I. Formulation,” International Journal of Solids and Structures, vol. 24, no. 12, pp. 1225–1234, 1988. View at Google Scholar · View at Scopus
  30. M. R. M. Crespo Da Silva and C. L. Zaretzky, “Nonlinear flexural-flexural-torsional interactions in beams including the effect of torsional dynamics. I: primary resonance,” Nonlinear Dynamics, vol. 5, no. 1, pp. 3–23, 1994. View at Publisher · View at Google Scholar · View at Scopus
  31. E. H. Dowell, “Damping in beams and plates due to slipping at the support boundaries,” Journal of Sound and Vibration, vol. 105, no. 2, pp. 243–253, 1986. View at Google Scholar · View at Scopus
  32. D. H. Hodges and E. H. Dowell, “Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades,” NASA Technical Notes NASA TN D-7818, 1974. View at Google Scholar
  33. D. S. Whithead, “The analysis of blade vibration due to random excitation,” Tech. Rep. 3253, United Kingdom Ministry of Aviation: Aeronautical Research Council Reports and Memoranda, London, UK, 1960. View at Google Scholar
  34. M. Aykan and M. Çelik, “Vibration fatigue analysis and multi-axial effect in testing of aerospace structures,” Mechanical Systems and Signal Processing, vol. 23, no. 3, pp. 897–907, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. G. V. Chary, E. Habtour, and G. S. Drake, “Improving the reliability in the next generation of US army platforms through physics of failure analysis,” Journal of Failure Analysis and Prevention, vol. 12, no. 1, pp. 75–58, 2012. View at Publisher · View at Google Scholar · View at Scopus
  36. Y. Zhou, M. Al-Bassyiouni, and A. Dasgupta, “Vibration durability assessment of sn3.0ag0.5cu and sn37pb solders under harmonic excitation,” Journal of Electronic Packaging, vol. 131, no. 1, 2009. View at Publisher · View at Google Scholar · View at Scopus
  37. J. H. Lau, Solder Joint Reliability, Theory and Applications, Van Nostrand Reinhold, New York, NY, USA, 1990.
  38. J. Lau, K. Gratalo, E. Schneider, T. Marcotte, and T. Baker, “Solder joint reliability of large plastic ball grid array assemblies under bending, twisting, and vibration conditions,” Circuit World, vol. 22, no. 1, pp. 27–32, 1995. View at Google Scholar · View at Scopus
  39. J. H. Lau and P. Yi, Solder Joint Reliability, of BGA, CSP, Flip Chip and Fine Pitch SMT Assemblies, McGraw-Hill, New York, NY, USA, 1997.
  40. X. Liu, V. K. Sooklal, M. A. Verges, and M. C. Larson, “Experimental study and life prediction on high cycle vibration fatigue in BGA packages,” Microelectronics Reliability, vol. 46, no. 7, pp. 1128–1138, 2006. View at Publisher · View at Google Scholar · View at Scopus
  41. X. Yang, Y. Luo, and Q. Gao, “Constitutive modeling on time-dependent deformation behavior of 96.5Sn-3.5Ag solder alloy under cyclic multiaxial straining,” Journal of Electronic Packaging, vol. 129, no. 1, pp. 41–47, 2007. View at Publisher · View at Google Scholar · View at Scopus
  42. Y. Zhou, M. Al-Bassyiouni, and A. Dasgupta, “Harmonic and random vibration durability of SAC305 and Sn37Pb solder alloys,” IEEE Transactions on Components and Packaging Technologies, vol. 33, no. 2, pp. 319–328, 2010. View at Publisher · View at Google Scholar · View at Scopus
  43. J. Gu, D. Barker, and M. Pecht, “Prognostics implementation of electronics under vibration loading,” Microelectronics Reliability, vol. 47, no. 12, pp. 1849–1856, 2007. View at Publisher · View at Google Scholar · View at Scopus
  44. D. B. Barker, Y. S. Chen, and A. Dasgupta, “Estimating the vibration fatigue life of quad leaded surface mount components,” Journal of Electronic Packaging, vol. 115, no. 2, pp. 195–200, 1993. View at Google Scholar · View at Scopus
  45. R. S. Li, “A methodology for fatigue prediction of electronic components under random vibration load,” Journal of Electronic Packaging, vol. 123, no. 4, pp. 394–400, 2001. View at Publisher · View at Google Scholar · View at Scopus
  46. E. Martynenko, W. Zhou, A. Chudnovsky, R. S. Li, and L. Poglitsch, “High cycle fatigue resistance and reliability assessment of flexible printed circuitry,” Journal of Electronic Packaging, vol. 124, no. 3, pp. 254–259, 2002. View at Publisher · View at Google Scholar · View at Scopus
  47. S. Mathew, D. Das, M. Osterman, M. Pecht, R. Ferebee, and J. Clayton, “Virtual remaining life assessment of electronic hardware subjected to shock and random vibration life cycle loads,” Journal of the Institute of Environmental Sciences and Technology, vol. 50, no. 1, pp. 86–97, 2007. View at Google Scholar · View at Scopus
  48. S. Shetty, V. Lehtinen, A. Dasgupta, V. Halkola, and T. Reinikainen, “Fatigue of chip scale package interconnects due to cyclic bending,” Journal of Electronic Packaging, vol. 123, no. 3, pp. 302–308, 2001. View at Publisher · View at Google Scholar · View at Scopus
  49. M. Ernst, C. Choi, A. Dasgupta, and E. Habtour, “Physics of failure models for multiaxial vibration fatigue in electronics assemblies,” in Proceedings of the Accelerated Stress Testing and Reliability Workshop, Ontario, Canada, 2012.
  50. A. C. Eringen, “Response of beams and to random loads,” Journal of Applied Mechanics, vol. 24, pp. 46–52, 1957. View at Google Scholar
  51. R. E. Herbert, “Random vibrations of a nonlinear elastic beam,” Journal of the Acoustical Society of America, vol. 36, no. 11, pp. 2090–2094, 1964. View at Google Scholar
  52. I. Elishakoff and D. Livshits, “Some closed-form solutions in random vibration of Bernoulli-Euler beams,” International Journal of Engineering Science, vol. 22, no. 11-12, pp. 1291–1301, 1984. View at Google Scholar · View at Scopus
  53. I. Elishakoff, J. Fang, and R. Caimi, “Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique,” International Journal of Solids and Structures, vol. 32, no. 11, pp. 1571–1584, 1995. View at Google Scholar · View at Scopus
  54. R. A. Ibrahim and R. J. Somnay, “Nonlinear dynamic analysis of an elastic beam isolator sliding on frictional supports,” Journal of Sound and Vibration, vol. 308, no. 3–5, pp. 735–757, 2007. View at Publisher · View at Google Scholar · View at Scopus
  55. C.-H. Ho, R. A. Scott, and J. G. Eisley, “Non-planar, non-linear oscillations of a beam-I. Forced motions,” International Journal of Non-Linear Mechanics, vol. 10, no. 2, pp. 113–127, 1975. View at Google Scholar · View at Scopus
  56. C.-H. Ho, R. A. Scott, and J. G. Eisley, “Non-planar, non-linear oscillations of a beam II. Free motions,” Journal of Sound and Vibration, vol. 47, no. 3, pp. 333–339, 1976. View at Google Scholar · View at Scopus
  57. M. R. M. Crespo da Silva and C. C. Glynn, “Nonlinear flexural-flexural-torsional dynamics of inextensional beams. I: equations of motion,” Journal of Structural Mechanics, vol. 6, no. 4, pp. 437–448, 1978. View at Google Scholar · View at Scopus
  58. M. R. M. Crespo de Silva and C. C. Glynn, “Nonlinear flexural-flexural-torsional dynamics of inextensional beams. II: forced motions,” Journal of Structural Mechanics, vol. 6, no. 4, pp. 449–461, 1978. View at Google Scholar · View at Scopus
  59. M. R. M. C. Da Silva, “Non-linear flexural-flexural-torsional-extensional dynamics of beams-II. Response analysis,” International Journal of Solids and Structures, vol. 24, no. 12, pp. 1235–1242, 1988. View at Google Scholar · View at Scopus
  60. A. H. Nayfeh and P. F. Pai, “Non-linear non-planar parametric responses of an inextensional beam,” International Journal of Non-Linear Mechanics, vol. 24, no. 2, pp. 139–158, 1989. View at Google Scholar · View at Scopus
  61. P. F. Pai and A. H. Nayfeh, “Non-linear non-planar oscillations of a cantilever beam under lateral base excitations,” International Journal of Non-Linear Mechanics, vol. 25, no. 5, pp. 455–474, 1990. View at Google Scholar · View at Scopus
  62. C. L. Zaretzky and M. R. M. Crespo da Silva, “Nonlinear flexural-flexural-torsional interactions in beams including the effect of torsional dynamics. II: combination resonance,” Nonlinear Dynamics, vol. 5, no. 2, pp. 161–180, 1994. View at Publisher · View at Google Scholar · View at Scopus
  63. H. N. Arafat, A. H. Nayfeh, and C.-M. Chin, “Nonlinear nonplanar dynamics of parametrically excited cantilever beams,” Nonlinear Dynamics, vol. 15, no. 1, pp. 31–61, 1998. View at Google Scholar · View at Scopus
  64. A. H. Nayfeh and H. N. Arafat, “Investigation of subcombination internal resonances in cantilever beams,” Shock and Vibration, vol. 5, pp. 289–296, 1998. View at Google Scholar
  65. A. H. Nayfeh and H. N. Arafat, “Nonlinear response of cantilever beams to combination and subcombination resonances,” Shock and Vibration, vol. 5, no. 5-6, pp. 277–288, 1998. View at Google Scholar · View at Scopus
  66. H. N. Arafat, Nonlinear Dynamic Analysis of Cantilever Beam [Ph.D. thesis], Virginia Polytechnic Institute and State University, Blacksburg, Va, USA, 1999.
  67. J. R. Banerjee, “Explicit analytical expressions for frequency equation and mode shapes of composite beams,” International Journal of Solids and Structures, vol. 38, no. 14, pp. 2415–2426, 2001. View at Publisher · View at Google Scholar · View at Scopus
  68. P. Malatkar and A. H. Nayfeh, “On the transfer of energy between widely spaced modes in structures,” Nonlinear Dynamics, vol. 31, no. 2, pp. 225–242, 2003. View at Publisher · View at Google Scholar · View at Scopus
  69. P. Malatkar and A. H. Nayfeh, “A parametric identification technique for single-degree-of-freedom weakly nonlinear systems with cubic nonlinearities,” Journal of Vibration and Control, vol. 9, no. 3-4, pp. 317–336, 2003. View at Google Scholar · View at Scopus
  70. P. Malatkar, Nonlinear Vibrations of Cantilever Beams and Plates [Ph.D. thesis], Virginia Polytechnic Institute and State University, Blacksburg, Va, USA, 2003.
  71. T. J. Anderson, B. Balachandran, and A. H. Nayfeh, “Nonlinear resonances in a flexible cantilever beam,” Journal of Vibration and Acoustics, vol. 116, no. 4, pp. 480–484, 1994. View at Google Scholar · View at Scopus
  72. J. Dugundji and V. Mukhopadhyay, “Lateral bending-torsion vibrations of a thin beam under parametric excitation,” Journal of Applied Mechanics, vol. 40, no. 3, pp. 693–698, 1973. View at Google Scholar · View at Scopus
  73. D. M. Tang and E. H. Dowell, “Damping in beams and plates due to slipping at the support boundaries. Part 2: numerical and experimental study,” Journal of Sound and Vibration, vol. 108, no. 3, pp. 509–522, 1986. View at Google Scholar · View at Scopus
  74. C. W. S. To, “Vibration of a cantilever beam with a base excitation and tip mass,” Journal of Sound and Vibration, vol. 83, no. 4, pp. 445–460, 1982. View at Google Scholar · View at Scopus
  75. M. P. Cartmell and J. W. Roberts, “Simultaneous combination resonances in a parametrically excited cantilever beam,” Strain, vol. 23, no. 3, pp. 117–126, 1987. View at Google Scholar · View at Scopus
  76. B. Balachandran and A. H. Nayfeh, “Nonlinear motions of beam-mass structure,” Nonlinear Dynamics, vol. 1, no. 1, pp. 39–61, 1990. View at Publisher · View at Google Scholar · View at Scopus
  77. B. Balachandran and A. H. Nayfeh, “Observations of modal interactions in resonantly forced beam-mass structures,” Nonlinear Dynamics, vol. 2, no. 2, pp. 77–117, 1991. View at Publisher · View at Google Scholar · View at Scopus
  78. J. W. Jaworski and E. H. Dowell, “Free vibration of a cantilevered beam with multiple steps: comparison of several theoretical methods with experiment,” Journal of Sound and Vibration, vol. 312, no. 4-5, pp. 713–725, 2008. View at Publisher · View at Google Scholar · View at Scopus
  79. M. Ansari, E. Esmailzadeh, and N. Jalili, “Coupled vibration and parameter sensitivity analysis of rocking-mass vibrating gyroscopes,” Journal of Sound and Vibration, vol. 327, no. 3–5, pp. 564–583, 2009. View at Publisher · View at Google Scholar · View at Scopus
  80. A. M. Wickenheiser, “Design optimization of linear and non-linear cantilevered energy harvesters for broadband vibrations,” Journal of Intelligent Material Systems and Structures, vol. 22, no. 11, pp. 1213–1225, 2011. View at Publisher · View at Google Scholar · View at Scopus
  81. M. Ansari, E. Esmailzadeh, and N. Jalili, “Exact frequency analysis of a rotating cantilever beam with tip mass subjected to torsional-bending vibrations,” Journal of Vibration and Acoustics, vol. 133, no. 4, Article ID 041003, 2011. View at Publisher · View at Google Scholar · View at Scopus
  82. A. Erturk and D. J. Inman, “Parameter identification and optimization in piezoelectric energy harvesting: analytical relations, asymptotic analyses, and experimental validations,” Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, vol. 225, no. 4, pp. 485–496, 2011. View at Publisher · View at Google Scholar · View at Scopus
  83. A. Erturk, “Assumed-modes modeling of piezoelectric energy harvesters: euler-bernoulli, rayleigh, and timoshenko models with axial deformations,” Computers and Structures, vol. 106-107, pp. 214–227, 2012. View at Google Scholar
  84. M. Esmaeili, N. Jalili, and M. Durali, “Dynamic modeling and performance evaluation of a vibrating beam microgyroscope under general support motion,” Journal of Sound and Vibration, vol. 301, no. 1-2, pp. 146–164, 2007. View at Publisher · View at Google Scholar · View at Scopus
  85. S. C. Stanton, C. C. McGehee, and B. P. Mann, “Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator,” Physica D: Nonlinear Phenomena, vol. 239, no. 10, pp. 640–653, 2010. View at Publisher · View at Google Scholar · View at Scopus
  86. C. P. Green and J. E. Sader, “Torsional frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope,” Journal of Applied Physics, vol. 92, no. 10, pp. 6262–6274, 2002. View at Publisher · View at Google Scholar · View at Scopus
  87. S. C. Stanton, A. Erturk, B. P. Mann, E. H. Dowell, and D. J. Inman, “Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects,” Journal of Intelligent Material Systems and Structures, vol. 23, no. 2, pp. 183–199, 2012. View at Publisher · View at Google Scholar · View at Scopus
  88. S. C. Stanton, B. A. M. Owens, and B. P. Mann, “Harmonic balance analysis of the bistable piezoelectric inertial generator,” Journal of Sound and Vibration, vol. 331, no. 15, pp. 3617–3627, 2012. View at Publisher · View at Google Scholar · View at Scopus
  89. H. J. R. Westra, D. M. Karabacak, S. H. Brongersma, M. Crego-Calama, H. S. J. Van Der Zant, and W. J. Venstra, “Interactions between directly- and parametrically-driven vibration modes in a micromechanical resonator,” Physical Review B: Condensed Matter and Materials Physics, vol. 84, no. 13, Article ID 134305, 2011. View at Publisher · View at Google Scholar · View at Scopus
  90. K. Wolf and O. Gottlieb, “Nonlinear dynamics of a cantilever beam actuated by piezoelectric layers in symmetric and asymmetric configuration,” Tech. Rep. ETR-2001-02, Institute of Technology, Haifa, Israel, 2001. View at Google Scholar
  91. L. G. Villanueva, R. B. Karabalin, M. H. Matheny, D. Chi, J. E. Sader, and M. L. Roukes, “Nonlinearity in nanomechanical cantilevers,” Physical Review B, vol. 87, Article ID 024304, 2013. View at Google Scholar
  92. V. Kumar, J. K. Miller, and J. F. Rhoads, “Nonlinear parametric amplification and attenuation in a base-excited cantilever beam,” Journal of Sound and Vibration, vol. 330, no. 22, pp. 5401–5409, 2011. View at Publisher · View at Google Scholar · View at Scopus
  93. J. F. Rhoads, N. J. Miller, S. W. Shaw, and B. F. Feeny, “Mechanical domain parametric amplification,” Journal of Vibration and Acoustics, vol. 130, no. 6, Article ID 061006, 2008. View at Publisher · View at Google Scholar · View at Scopus
  94. S. F. Ali, S. Adhikari, M. I. Friswell, and S. Narayanan, “The analysis of piezomagnetoelastic energy harvesters under broadband random excitations,” Journal of Applied Physics, vol. 109, no. 7, Article ID 074904, 2011. View at Publisher · View at Google Scholar · View at Scopus
  95. G. Wu, H. Ji, K. Hansen et al., “Origin of nanomechanical cantilever motion generated from biomolecular interactions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 98, no. 4, pp. 1560–1564, 2001. View at Publisher · View at Google Scholar · View at Scopus
  96. K. S. Hwang, J. H. Lee, J. Park, D. S. Yoon, J. H. Park, and T. S. Kim, “In-situ quantitative analysis of a prostate-specific antigen (PSA) using a nanomechanical PZT cantilever,” Lab on a Chip: Miniaturisation for Chemistry and Biology, vol. 4, no. 6, pp. 547–552, 2004. View at Publisher · View at Google Scholar · View at Scopus
  97. J. Dorignac, A. Kalinowski, S. Erramilli, and P. Mohanty, “Dynamical response of nanomechanical oscillators in immiscible viscous fluid for in Vitro biomolecular Recognition,” Physical Review Letters, vol. 96, no. 18, Article ID 186105, 2006. View at Publisher · View at Google Scholar · View at Scopus
  98. A. Salehi-Khojin, S. Bashash, and N. Jalili, “Modeling and experimental vibration analysis of nanomechanical cantilever active probes,” Journal of Micromechanics and Microengineering, vol. 18, no. 8, Article ID 085008, 2008. View at Publisher · View at Google Scholar · View at Scopus
  99. V. Seena, A. Fernandes, P. Pant, S. Mukherji, and V. Ramgopal Rao, “Polymer nanocomposite nanomechanical cantilever sensors: material characterization, device development and application in explosive vapour detection,” Nanotechnology, vol. 22, no. 29, Article ID 295501, 2011. View at Publisher · View at Google Scholar · View at Scopus
  100. S. Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, UK, 2nd edition, 1998.
  101. D. Segalman, G. Reese, R. Field Jr., and C. Fulcher, “Estimating the probability distribution of von Mises stress for structures undergoing random excitation,” Journal of Vibration and Acoustics, vol. 122, no. 1, pp. 42–48, 2000. View at Google Scholar · View at Scopus
  102. S. Sarkani, D. P. Kihl, and J. E. Beach, “Fatigue of welded joints under narrowband non-Gaussian loadings,” Probabilistic Engineering Mechanics, vol. 9, no. 3, pp. 179–190, 1994. View at Google Scholar · View at Scopus
  103. D. Radaj, C. M. Sonsino, and W. Fricke, Fatigue Assessment of Welded Joints By Local Approaches, Woodhead Publishing Limited, Cambridge, UK, 2006.
  104. A. Z. Palmgren, “Die Lebensdauer Von Kugellagern,” Zeitschriyt Des Vereines Der Deutschen Ingenioeren, vol. 68, pp. 339–341, 1924. View at Google Scholar
  105. M. A. Miner, “Cumulative damage in fatigue,” Journal of Applied Mechanics, vol. 12, no. 3, pp. 159–164, 1945. View at Google Scholar
  106. J. W. Miles, “On structural fatigue under random loading,” Journal of the Aeronautical Sciences, vol. 21, no. 11, pp. 753–762, 1957. View at Google Scholar
  107. S. H. Crandall, “Zero crossings, peaks, and other statistical measures of random responses,” Journal of the Acoustical Society of America, vol. 35, no. 11, pp. 1693–1699, 1963. View at Google Scholar
  108. Y. K. Lin, “Probability distributions of stress peaks in linear and nonlinear structures,” AIAA Journal, vol. 1, no. 5, pp. 1133–1138, 1963. View at Google Scholar
  109. J. S. Bendat, “Probability functions for random responses-prediction of peaks, fatigue damage, and catastrophic failures,” NASA CR-33, N64-17990, 1964. View at Google Scholar
  110. S. O. Rice, “Mathematical analysis of random noise,” Selected Papers on Noise and Stochastic Processes, Dover, New York, NY, USA, 1954. View at Google Scholar
  111. N. W. M. Bishop, The Use of Frequency Domain Parameters to Predict Structural Fatigue [Ph.D. thesis], University of Warwick, 1988.
  112. N. W. M. Bishop and F. Sherratt, “Theoretical solution for the estimation of “rainflow” ranges from power spectral density data,” Fatigue and Fracture of Engineering Materials and Structures, vol. 13, no. 4, pp. 311–326, 1990. View at Google Scholar · View at Scopus
  113. K. Upadhyayula and A. Dasgupta, “Physics-of-failure guidelines for accelerated qualification of electronic systems,” Quality and Reliability Engineering International, vol. 14, no. 6, pp. 433–447, 1998. View at Google Scholar · View at Scopus
  114. E. Habtour, M. Paulus, and A. Dasgupta, “Modeling approach for predicting the rate of frequency change of notched beam exposed to Gaussian random excitation,” Shock and Vibration, 2013. View at Publisher · View at Google Scholar
  115. Y. Lu, Random Vibration Analysis of Higher-Order Nonlinear Beams and Composite Plates with Applications of ARMA Models [Ph.D. thesis], Virginia Polytechnic Institute and State University, Blacksburg, Va, USA, 2008.
  116. T. Łagoda, E. Macha, and A. Niesłony, “Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading,” Fatigue and Fracture of Engineering Materials and Structures, vol. 28, no. 4, pp. 409–420, 2005. View at Publisher · View at Google Scholar · View at Scopus
  117. X. Pitoiset and A. Preumont, “Spectral methods for multiaxial random fatigue analysis of metallic structures,” International Journal of Fatigue, vol. 22, no. 7, pp. 541–550, 2000. View at Publisher · View at Google Scholar · View at Scopus
  118. X. Pitoiset, I. Rychlik, and A. Preumont, “Spectral methods to estimate local multiaxial fatigue failure for structures undergoing random vibrations,” Fatigue and Fracture of Engineering Materials and Structures, vol. 24, no. 11, pp. 715–727, 2001. View at Publisher · View at Google Scholar · View at Scopus
  119. A. Carpinteri, E. Macha, R. Brighenti, and A. Spagnoli, “Expected principal stress directions under multiaxial random loading. Part I: theoretical aspects of the weight function method,” International Journal of Fatigue, vol. 21, no. 1, pp. 83–88, 1999. View at Google Scholar · View at Scopus
  120. A. Carpinteri, R. Brighenti, E. Macha, and A. Spagnoli, “Expected principal stress directions under multiaxial random loading. Part II: numerical simulation and experimental assessment through the weight function method,” International Journal of Fatigue, vol. 21, no. 1, pp. 89–96, 1999. View at Google Scholar · View at Scopus
  121. Y. Liu and S. Mahadevan, “A unified multiaxial fatigue damage model for isotropic and anisotropic materials,” International Journal of Fatigue, vol. 29, no. 2, pp. 347–359, 2007. View at Publisher · View at Google Scholar · View at Scopus
  122. Y. Liu, Stochastic Modeling of Multiaxial Fatigue and Fracture [Ph.D. thesis], Vanderbilt University, Nashville, Tenn, USA, 2006.
  123. S. Lambert, E. Pagnacco, and L. Khalij, “A probabilistic model for the fatigue reliability of structures under random loadings with phase shift effects,” International Journal of Fatigue, vol. 32, no. 2, pp. 463–474, 2010. View at Publisher · View at Google Scholar · View at Scopus
  124. C. Braccesi, F. Cianetti, G. Lori, and D. Pioli, “An equivalent uniaxial stress process for fatigue life estimation of mechanical components under multiaxial stress conditions,” International Journal of Fatigue, vol. 30, no. 8, pp. 1479–1497, 2008. View at Publisher · View at Google Scholar · View at Scopus
  125. C. Braccesi, F. Cianetti, G. Lori, and D. Pioli, “The frequency domain approach in virtual fatigue estimation of non-linear systems: the problem of non-Gaussian states of stress,” International Journal of Fatigue, vol. 31, no. 4, pp. 766–775, 2008. View at Google Scholar
  126. G. Allegri and X. Zhang, “On the inverse power laws for accelerated random fatigue testing,” International Journal of Fatigue, vol. 30, no. 6, pp. 967–977, 2008. View at Publisher · View at Google Scholar · View at Scopus
  127. Z. Lei and C. Qiu, “A dynamic stochastic finite element method based on dynamic constraint mode,” Computer Methods in Applied Mechanics and Engineering, vol. 161, no. 3-4, pp. 245–255, 1998. View at Google Scholar · View at Scopus
  128. S. I. McNeill, “A method for determining the fatigue critical plane for biaxial random vibration in the frequency domain: technical Note,” Fatigue and Fracture of Engineering Materials and Structures, vol. 33, no. 6, pp. 390–394, 2010. View at Publisher · View at Google Scholar · View at Scopus
  129. T. Lagoda, E. Macha, and W. Bȩdkowski, “Critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime,” International Journal of Fatigue, vol. 21, no. 5, pp. 431–443, 1999. View at Publisher · View at Google Scholar · View at Scopus
  130. P. A. Tibbits, “Application of algorithms for percentiles of von mises stress from combined random vibration and static loadings,” Journal of Vibration and Acoustics, vol. 133, no. 4, Article ID 044502, 2011. View at Publisher · View at Google Scholar · View at Scopus
  131. H. Guechichi, S. Benkabouche, A. Amrouche, and M. Benkhettab, “A high fatigue life prediction methodology under constant amplitude multiaxial proportional loadings,” Materials Science and Engineering A, vol. 528, no. 13-14, pp. 4789–4798, 2011. View at Publisher · View at Google Scholar · View at Scopus
  132. D. Gregory, F. Bitsy, and D. O. Smallwood, “Comparison of the response of a simple structure to single axis and multiple axis random vibration inputs,” in Proceedings of the 79th Shock and Vibration Symposium, Orlando, Fla, USA, 2008.
  133. U. Füllekrug, “Utilization of multi-axial shaking tables for the modal identification of structures,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 359, no. 1786, pp. 1753–1770, 2001. View at Publisher · View at Google Scholar · View at Scopus
  134. D. E. Newland, An Introduction to Random Vibrations, Spectral and Wavelet Analysis, Dover, Mineola, NY, USA, 2005.
  135. T. Dahlberg, “The effect of modal coupling in random vibration analysis,” Journal of Sound and Vibration, vol. 228, no. 1, pp. 157–176, 1999. View at Google Scholar · View at Scopus
  136. E. Habtour, M. Pohland, and A. Dasgupta, “Dynamic characterization of circuit card assemblies using multi-degree-of-freedom random vibration,” in Proceedings of the Accelerated Stress Testing and Reliability Workshop, San Francisco, Calif, USA, 2011.
  137. L. Meirovitch, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddel River, NJ, USA, 1997.
  138. M. Cesnik, J. Slavic, and M. Boltezar, “Uninterrupted and accelerated vibrational fatigue testing with simultaneous monitoring of the natural frequency and damping,” Journal of Sound and Vibration, vol. 331, pp. 5370–5382, 2012. View at Google Scholar
  139. A. Perkins and S. K. Sitaraman, “Analysis and prediction of vibration-induced solder joint failure for a ceramic column grid array package,” Journal of Electronic Packaging, vol. 130, no. 1, 2008. View at Publisher · View at Google Scholar · View at Scopus
  140. C. Rainieri, G. Fabbrocino, and E. Cosenza, “Near real-time tracking of dynamic properties for standalone structural health monitoring systems,” Mechanical Systems and Signal Processing, vol. 25, no. 8, pp. 3010–3026, 2011. View at Publisher · View at Google Scholar · View at Scopus
  141. R.-J. Wang and D.-G. Shang, “Fatigue life prediction based on natural frequency changes for spot welds under random loading,” International Journal of Fatigue, vol. 31, no. 2, pp. 361–366, 2009. View at Publisher · View at Google Scholar · View at Scopus
  142. Y. J. Yan, L. Cheng, Z. Y. Wu, and L. H. Yam, “Development in vibration-based structural damage detection technique,” Mechanical Systems and Signal Processing, vol. 21, no. 5, pp. 2198–2211, 2007. View at Publisher · View at Google Scholar · View at Scopus