Examining Steinberg's Octave Rule Applicability for Electronic Systems Exposed to Multiaxial Vibration

Matthew Ernst, Ed Habtour*, Abhijit Dasgupta

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


This paper explores the role of nonlinear dynamical phenomena in calculating the stress amplitude in large electronic components exposed to biaxial vibration loading. Nonlinear analytical studies are presented where a component exposed to combined axial and transverse vibratory base excitation is idealized using a nonlinear structural beam element with a tip mass. Harmonic and random base vibration excitation studies are conducted. The results provided in this paper confirm that Steinberg's Octave rule may not be applicable for electronic components exposed to high amplitude multiaxial vibrations. In fact, components exposed to biaxial vibration are highly dependent on the phase angle between the orthogonal axes and the frequency ratio between the axial and transverse excitation frequencies. At critical frequency ratios, undesirable constructive and destructive stress amplification phenomena may appear if the system is exposed to a harsh multidirectional vibration environment.
Original languageEnglish
Pages (from-to)561-568
JournalIEEE Transactions on Components, Packaging and Manufacturing Technology
Issue number4
Publication statusPublished - 2016
Externally publishedYes


  • electronics packaging
  • Reliability
  • Fatigue
  • Multiaxial
  • Vibration
  • Nonlinear dynamics


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