Longitudinally Vibrating Elastic Rods with Locally and Non-Locally Reacting Viscous Dampers

Abstract

Abstract. Eigencharacteristics of a longitudinally vibrating elastic rod with locally and non-locally reacting damping are analyzed. The rod is considered as a continuous system and complex eigenfrequencies are determined as solution of a characteristic equation. The variation of the damping ratios with respect to damper locations and damping coefficients for the first four eigenfrequencies are obtained. It is shown that at any mode of locally or non-locally damped elastic rod, the variation of damping ratio with damper location is linearly proportional to absolute value of the mode shape of undamped system. It is seen that the increasing damping coefficient does not always increase the damping ratio and there are optimal values for the damping ratio. Optimal values for external damping coefficients of viscous dampers and locations of the dampers are presented.

Longitudinal Vibration of CNTs Viscously Damped in Span

“…[11] Khademolhosseini, F., Phani, A.S., Nojeh, A., Rajapakse, N., Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes, IEEE Transactions on Nanotechnology, 11, [34][35][36][37][38][39][40][41][42][43]2012 …”

“…Damping effect on rods for various boundary conditions is investigated at macro scale by [33][34][35]. Viscoelastic properties of SWCNTs are investigated with a semi-analytical approach and associated damping mechanism at nano scale by Zhou et al [36].…”

Convergence Study of Variational Space-Time Coupled Least-Squares Frameworks in Simulation of Wave Propagation in Viscoelastic Medium

“…ere have been studies on one-dimensional viscoelastic analysis of axial wave propagation through rod with various damping models. e authors of [8][9][10] demonstrated realistic behavior of viscous damping for analyzing actual dynamic systems.…”

Exact frequency response of bars with multiple dampers

“…The frequency analysis of bars with dampers has been addressed in some studies [25][26][27][28][29][30][31][32]. For a bar with an end viscous damper, Hull [25] built the exact DGFs in a closed form.…”

“…[28,29], a tip mass and a single in-span mass damper in Ref. [30], two in-span grounded dampers [31]. An approximate formulation of the eigenvalue problem has been pursued in Ref.…”