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 𝜔 𝑚 𝑛 , [ ( 𝑠 ) 1 ] Natural frequency ratioStiffness 𝑟 𝑚 𝑛 , [ ( 𝑚 𝑚 𝑠 ) 2 ]

M1: 𝑚 =1, 𝑛 =16.7839 𝑒 37.1888 𝑒 6
M2: 𝑚 =1, 𝑛 =32.5381 𝑒 4 𝜔 3 1 / 𝜔 1 1 = 2 . 6 8 1.2548 𝑒 8
M3: 𝑚 =3, 𝑛 =14.2430 𝑒 4 𝜔 3 1 / 𝜔 1 3 = 1 . 6 8 4.3085 𝑒 8
M4. m =3, 𝑛 =36.1008 𝑒 4 𝜔 3 3 / 𝜔 3 1 = 1 . 4 5 5.8140 𝑒 8