The Transient Dynamics of a Beam Mounted on Spring Supports and Equipped with the Nonlinear Energy Sink

Abstract

The transient dynamics of a beam mounted on springer-damper support and equipped with a nonlinear energy sink (NES) is investigated under the effects of shock loads. The equations of motion are derived using the Hamilton's principle leading to four hybrid ordinary and partial differential equations and descritized using the Galerkin method. An adaptive Newmark method is employed for accurate and efficient numerical simulation and the results are used to assess the efficiency of the NES by conducting various parametric studies. The mechanisms of targeted energy transfer from the beam to the NES are indicated using the wavelet transform and Hilbert–Huang transform of the responses. Numerous modes are recognized to contribute to the response and the modes with smaller particiaption of the rigid-body motions are found to be strongly engaged in the transient resonance capture (TRC) at the initial stage of the motion. The modes with dominant rigid-body motions are, however found to be less engaed in an effective TRC. The enhanced empirical mode decomposition, with different masking signals are used to extract narrow-band intrinsic mode functions (IMFs) and simultaneous 1:1 transient resonances are observed between different IMFs of the responses especially at the initial stage of the motion.