Geometric Simplification of a Wooden Building Connector in Dynamic Finite Element Model
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1 1/16 Geometric Simplification of a Wooden Building Connector in Dynamic Finite Element Model ACOUSTICS Nantes A. Tribaleau,, N. Tahani, B. Brouard, J.M. Génevaux, O. Dazel, LAUM, UMR CNRS 6613, Avenue Olivier Messiaen, LE MANS CRITT Bois, 27 rue Philippe Séguin, EPINAL 27 April 2012
2 2/16 Context and aim Quick description Context in building acoustic : Aim : PhD thesis on prediction of sound insulation of wooden joist floors Unknown dynamic behavior of wooden building connector ( static behavior ) Determinant in flanking transmission of vibration and boundary conditions of floor Simplified model of the wooden connector (stiffness and damping) To be used in a FE method (large structure : floor)
3 3/16 Outlines 1 Introduction Context and aim Method decription 2 Modal analysis of joist Mechanical properties of wooden joists Resonance frequency Damping factor estimation Comparaison with a numerical model 3 Modal analysis of the assembly (joist + connector + beam) Case study Simplified model Method for determining connector s stiffness Comparaions between numerical and experimental results 4 Conclusion and perspectives
4 4/16 Method description
![[mm] ρ 440±30 [kg.](/docs-images/82/86249758/images/5-1.jpg "m 3 ] No machining after drying and sawing Unknown : Axial Young s")
5 5/16 Modal analysis of joist Mechanical properties of wooden joists Known : Wood species : spruce Anisotropic material Size : [mm] ρ 440±30 [kg.m 3 ] No machining after drying and sawing Unknown : Axial Young s modulus (E L ) and others Damping factor Joist section
6 6/16 Modal analysis of joist Resonance frequency - Elastic modulus estimation Modulus 10 1 of frequency responce A/F - Experimental results 10 0 Acc/F beam #1 -rho= 424 beam #2 -rho= beam #3 -rho= Frequency [Hz] Free-free boundary condition 6 first resonance frequency [Hz] Mode Determine the longitudinal Young s modulus
7 Modal analysis of joist Damping factor estimation First mode : 16Hz Modulus of frequency responce A/F - 1 st mode - normalized 1 beam #1 -rho= 424 beam #2 -rho= 443 beam #3 -rho= Fifth mode : 210Hz Modulus of frequency responce A/F - 5 th mode - normalized 1 beam #1 -rho= 424 beam #2 -rho= 443 beam #3 -rho= Acc/F normalized Acc/F normalized Reduced frequency Reduced frequency 7/16 Damping factor (η) Mode % % % 0.9 % 0.6 % % 0.7 % 0.8 %
8 8/16 Modal analysis of joist Comparaison with numerical model 10 1 Modulus of frequency responce A/F - p on #1 Modulus Ei or Gij Legend Numerical model with Freefem++ Test with constant or variable orthotropic Hook s law material Structural damping (η = 0.01) Frequency Experimental results FEM results (E i,g ij = cst) FEM results (E i (ω),g ij (ω)) Acc/F Acc/F Exp. (ref.) FEM E=cst 10-3 FEM E(w) Frequency [Hz] 10 1 Modulus of frequency responce A/F - position # Exp. (ref.) FEM E=cst 10-4 FEM E(w) Frequency [Hz]
9 9/16 Modal analysis of joist Synthesis
10 10/16 Modal analysis of the assembly First case study Force along honrizontal direction (y-axis) Free boundary conditions
11 11/16 Modal analysis of the assembly Simplified model FEM matrix construction with coupling : FEM applied on joist and beam Choose vertices on the border of section
12 12/16 Modal analysis of the assembly Simplified model FEM matrix construction with coupling : Additionnal strain and dissipative energy (coupling matrix stiffeness) Mass of connector is neglected
13 13/16 Modal analysis of the assembly Method for determining connector s stiffness 10 1 Modulus of frequency responce A/F 10 0 Acc/F Frequency [Hz] Joist Beam Joist Beam Joist Beam
14 14/16 Modal analysis of the assembly Response frequency - comparaison between num. and exp. results 10 2 Modulus of frequency responce A/F - point # Acc/F Exp Num. ky= 8.2e Frequency [Hz] Force exc. Acc. meas.
15 15/16 Conclusion and perspectives Simplified model to reduce geometric complexity Stiffness value K y has been determined Good agreement on resonnant frequency ( on anti-resonant freq.) Further work Estimate damping along tested axis (y-axis) Behavior along other axis : K x,k z value? Refine the Hook law model of material Perspectives Assembly wall and floor : flanking transmission quantification Understand the influence of stiffness value along each direction on flanking transmission Design better connectors for reducing vibration transfer
16 16/16 Thanks for your attention
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