Vibrational Modal Frequencies and Shapes of Two-Span Continuous Timber Flooring Systems

Binsheng Zhang*, Tony Kilpatrick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Based on classic vibrational bending theory on beams, this paper provides comprehensive analytical formulae for dynamic characteristics of two equal span continuous timber flooring systems, including frequency equations, modal frequencies and modal shapes. Four practical boundary conditions are considered for end supports, including free, sliding, pinned and fixed boundaries, and a total of sixteen combinations of flooring systems are created. The deductions of analytical formulae are also expanded to two unequal span continuous flooring systems with pinned end supports and empirical equations for obtaining the fundamental frequency are proposed. The acquired analytical equations for vibrational characteristics can be applied for practical design of two-span continuous flooring systems. Two practical design examples are provided as well.
Original languageEnglish
Article number2981935
Number of pages12
JournalShock and Vibration
Publication statusPublished - 28 Apr 2019


  • two-span continuous timber floors
  • frequency equations
  • modal frequencies
  • mode shapes


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