Mathematical Problems in Engineering / 2009 / Article / Tab 2

Research Article

Modal Decoupling Using the Method of Weighted Residuals for the Nonlinear Elastic Dynamics of a Clamped Laminated Composite

Table 2

Modal parameters of the Duffing equation.

ModeNatural frequency πœ” π‘š 𝑛 , [ ( 𝑠 ) βˆ’ 1 ] Natural frequency ratioStiffness π‘Ÿ π‘š 𝑛 , [ ( π‘š π‘š β‹… 𝑠 ) βˆ’ 2 ]

M1: π‘š =1, 𝑛 =16.7839 𝑒 37.1888 𝑒 6
M2: π‘š =1, 𝑛 =32.5381 𝑒 4 πœ” 3 1 / πœ” 1 1 = 2 . 6 8 1.2548 𝑒 8
M3: π‘š =3, 𝑛 =14.2430 𝑒 4 πœ” 3 1 / πœ” 1 3 = 1 . 6 8 4.3085 𝑒 8
M4. m =3, 𝑛 =36.1008 𝑒 4 πœ” 3 3 / πœ” 3 1 = 1 . 4 5 5.8140 𝑒 8

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