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

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Abstract

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
Volume2019
DOIs
Publication statusPublished - 28 Apr 2019

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Timber
timber
bending theory
deduction
free boundaries
Boundary conditions
dynamic characteristics
sliding
boundary condition
boundary conditions

Keywords

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

Cite this

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title = "Vibrational Modal Frequencies and Shapes of Two-Span Continuous Timber Flooring Systems",
abstract = "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.",
keywords = "two-span continuous timber floors, frequency equations, modal frequencies , mode shapes",
author = "Binsheng Zhang and Tony Kilpatrick",
note = "Acceptance from webpage",
year = "2019",
month = "4",
day = "28",
doi = "10.1155/2019/2981935",
language = "English",
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}

Vibrational Modal Frequencies and Shapes of Two-Span Continuous Timber Flooring Systems. / Zhang, Binsheng; Kilpatrick, Tony.

In: Shock and Vibration, Vol. 2019, 2981935, 28.04.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Vibrational Modal Frequencies and Shapes of Two-Span Continuous Timber Flooring Systems

AU - Zhang, Binsheng

AU - Kilpatrick, Tony

N1 - Acceptance from webpage

PY - 2019/4/28

Y1 - 2019/4/28

N2 - 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.

AB - 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.

KW - two-span continuous timber floors

KW - frequency equations

KW - modal frequencies

KW - mode shapes

U2 - 10.1155/2019/2981935

DO - 10.1155/2019/2981935

M3 - Article

VL - 2019

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