2. Solution de référence

2.1. Méthode de calcul

2.1.1. Statique

Déplacements en \(B\)

• Traction simple \({u}_{x}=\frac{{F}_{x}L}{ES}\)

• Flexion pure \({u}_{z}=-\frac{{M}_{y}{L}^{2}}{2E{I}_{y}}\) \({\theta}_{y}=\frac{{M}_{y}L}{E{I}_{y}}\)

• Flexion pure \({u}_{y}=\frac{{M}_{z}{L}^{2}}{2E{I}_{z}}\) \({\theta}_{z}=\frac{{M}_{z}L}{E{I}_{z}}\)

Contrainte maximum en \(A\)

• Traction simple \({\sigma}_{x}=\frac{{F}_{x}}{S}\)

• Flexion pure \({\sigma}_{x}=-\frac{{M}_{y}}{\frac{2{I}_{y}}{h}}\)

• Flexion pure \({\sigma}_{x}=-\frac{{M}_{z}}{\frac{{\mathrm{2I}}_{z}}{b}}\)

2.1.2. Fréquences propres en flexion

Mode 1 : \({f}_{1}=\frac{3.516}{2{L}^{2}\pi }\sqrt{\frac{\mathit{EI}}{\rho S}}\)

Mode 2 : \({f}_{2}=\frac{22.0345}{2{L}^{2}\pi }\sqrt{\frac{\mathit{EI}}{\rho S}}\)

2.2. Grandeurs et résultats de référence

2.2.1. Statique

• Déplacements \((m)\)

Point	\(\mathit{DX}\)	\(\mathit{DY}\)	\(\mathit{DZ}\)
\(B\)	\(8.3333\times {10}^{-5}\)	\(1.6667\times {10}^{-4}\)	\(-2.5\times {10}^{-4}\)

• Contraintes \((N/{m}^{2})\)

Point	\(\mathit{SIXX}\)	\(\mathit{SIYY}\)	\(\mathit{SIZZ}\)	\(\mathit{SIXY}\)	\(\mathit{SIXZ}\)	\(\mathit{SIYZ}\)
\(\mathit{A1}(5.0,1.5,-1.0)\)	\(-0.3333\)	\(0.\)	\(0.\)	\(0.\)	\(0.\)	\(0.\)
\(\mathit{A2}(5.0,1.5,1.0)\)	\(1.6667\)	\(0.\)	\(0.\)	\(0.\)	\(0.\)	\(0.\)

2.2.2. Fréquences propres en flexion

Mode	Fréquence \(\mathit{Hz}\)
\(1\)	\(0.014449\)
\(2\)	\(0.090549\)

2.3. Incertitudes sur la solution

Solution analytique.