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.

https://www.ije.ir/article_73037_00ede28e98757e8c40ccdc7510c482c5.pdf

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

In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are changed to non-dimensional form and discretized via Galerkin’ method. The bifurcation diagrams and Poincare' portraits are represented in the case that the mean axial speed, the speed fluctuation and the mass eccentricity are respectively varied. The dynamical behaviors are numerically identified based on the Poincare' portraits. Numerical simulations indicate that quasi-periodic motion occurs in the transverse vibrations of the string by variation of axial speed and mass eccentricity.

https://www.ije.ir/article_72741_4a5844eff54c960b76bcdd264b64f86f.pdf

H. Heydari

Papers

Nonlinear Dynamics of the Rotational Slender Axially Moving String with Simply Supported Conditions