Summary
The upper bound response of Nonlinear Parametrically Excited (NPE) systems is investigated. Different systems including a NPE system under pure parametric excitation, a NPE system under interacting external excitation and a NPE cantilever beam with a tip mass are considered. In order to obtain the response of the system for the whole frequency range considered, the method of varying amplitudes (MVA) is used. Employing the MVA, analytical expressions for the displacement response of the system are derived. The MVA results are compared with analytical results of the Method of Multiple Scales (MMS) and the numerical results obtained from Direct Integration (DI) of the equation of motion, showing good agreement. In order to verify the MVA results in a practical application, experimental measurements of a Nonlinear Parametrically Excited Cantilever Beam (NPECB) with a tip mass are taken, demonstrating good agreement between experiments, theory and numerical findings.
