Existence of quasi-periodic responses in quasi-periodically forced nonlinear mechanical systems

Abstract Forced responses of mechanical systems are crucial design and performance criteria. Hence, their robust reliable calculation is vital importance. While numerical computation periodic benefits from an extensive mathematical basis, the literature for quasi-periodically forced limited. More specifically, absence applicable general existence criterion quasi-periodic orbits nonlinear impedes definitive conclusions methods such as harmonic balance. In this work, we establish a vibratory with stiffness terms. Our does not rely on any small parameters hence large response forcing amplitudes. On explicit examples, demonstrate how our can be utilized to justify subsequent computations responses.