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

Binsheng Zhang; Tony Kilpatrick

doi:10.1155/2019/2981935

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 journal › Article

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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 language	English
Article number	2981935
Number of pages	12
Journal	Shock and Vibration
Volume	2019
DOIs	https://doi.org/10.1155/2019/2981935
Publication status	Published - 28 Apr 2019

Keywords

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

Documents and Links

10.1155/2019/2981935

Zhang, B. and Kilpatrick, T. (2019) Vibrational Modal Frequencies and Shapes of Two-Span Continuous Timber Flooring Systems
Copyright © 2019 Binsheng Zhang and Tony Kilpatrick. 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.
Final published version, 3.53 MBLicence: CC BY

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Ben Zhang

bzh1@gcu.ac.uk

Civil Engineering and Environmental Management - Professor

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Cite this

Zhang, B., & Kilpatrick, T. (2019). Vibrational Modal Frequencies and Shapes of Two-Span Continuous Timber Flooring Systems. Shock and Vibration, 2019, [2981935]. https://doi.org/10.1155/2019/2981935

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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.

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KW - modal frequencies

KW - mode shapes

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