Abstract: This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system ...

Abstract: This paper presents a method for analyzing the stability of the linearly related modes of nonlinear two-degree-of-freedom oscillatory systems. For systems described by the coupled equations ẍ1 ...

Abstract: The coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of m1ẍ1 + k = 1n akx1k + k = 1n Ak(x1 − x2)k = 0m2ẍ2 + k = 1n bkx2k ...

Abstract: This paper, “Symmetric Arc Solutions of ζ̈ = ζn ,” presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ...

Abstract: This paper presents methods for determining the exact solutions of certain two-degree-of-freedom nonlinear systems with high-degree polynomial restoring forces. The exact solutions are the normal ...