Preliminary report on the energy balance for nonlinear oscillations

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Variational approach for nonlinear oscillators (2007, unknown): “The approximate energy approach [9,10] can be applied not only to weakly nonlinear equations, but also strongly nonlinear ones.”
Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position (2018, methodology): “(10) By using Hamilton’s principle and the variational principle (He, 2002, 2010; Younesian et al., 2010), the equations of motion can be derived as ∂Nx ∂x = I0Ü − I1 ∂Ẅ ∂x ; ∂2Mx ∂x2 + ∂ ∂x ( Nx ∂W ∂x ) = I0Ẅ + I1 ∂Ü ∂x − I2 ∂2Ẅ ∂x2 , (11) where dot-superscript convention indicates the di…”
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, methodology): “This method was proposed by He [90] in 387 2002.”