Perturbation Methods for a Continuum Metamodel

Perturbation methods, already used in the first part of the book to analyze the sample system, are here applied to general structures. The metamodel introduced in Sect. 5.2 is considered, for which several nonlinear problems, of different nature, are investigated. The static perturbation method is used: (i) in elastostatics (in which the stiffness operator is non-singular), and (ii) in buckling (in which the stiffness operator is instead singular). The Multiple Scale Method is employed to tackle dynamic problems, i.e.: (i) the external resonance phenomena (primary, sub-harmonic and super-harmonic); (ii) the parametric excitation of conservative systems with periodically time-variant properties; (iii) the dynamic bifurcation of nonconservative systems. Here, only the bifurcation equations are derived, since their study requires performing the same steps illustrated in Chaps. 2 – 4 .