Nonlinear Dynamics of Variable Mass Oscillators

This chapter starts by bringing a summary of the analytical dynamics of mechanical systems with mass varying explicitly with time and position. The extended Lagrange’s equations for such systems are re-analysed and simpler forms are derived. Hamiltonian’s formulations for non-material volumes are discussed. Examples are worked out: (i) a two-degrees of freedom variable mass system and (ii) a one-degree of freedom model of an oscillating water column excited by incoming free surface waves or by parametric excitations caused by motions imposed to the pipe. Then, the nonlinear response of the water column oscillator driven by random free surface waves is assessed by statistical methods.