The Instability Mechanism of a Confined Rod Under Axial Vibrations

Abstract

We studied the stability of a confined rod under axial vibrations through a combination of analytical and numerical analysis. We find that the stability of the system is significantly different than in the static case and that both the frequency and magnitude of the applied vibrational force play an important role. In particular, while larger vibrational forces always tend to destabilize the system, our analysis indicates that the effect of the frequency is not obvious and monotonic. For certain frequencies, a very small force is sufficient to trigger an instability, while for others the rod is stable even for large forces. Furthermore, we find that the stability of the confined rod is significantly enhanced by the presence of frictional contact and that in this case also the magnitude of the perturbation affects its response.

Coupled longitudinal and transverse vibrations of tensioned Euler-Bernoulli beams with general linear boundary conditions

“…Using instead Timoshenko beam theory can lead to minor quantitative changes of the results [18][19][20], which however will not affect the governing mechanism of the considered phenomena. We note that the considered tension of the beam is moderate, Solving the modal equations ( 18), (19) implies truncation of the series (11), (12). To get accurate results for the considered beam and accounting for the restrictions on the maximum frequency that can be measured experimentally by the available equipment, we take into account all modal coordinates with natural frequencies below 30 KHz; this corresponds to the lowest 7 transverse modes, and the lowest 2 longitudinal modes.…”

“…More recent papers [6][7][8][9] can also be mentioned; for example, in [9] planar transverse-longitudinal vibrations of Timoshenko beams were studied for hinged-hinged transverse boundary conditions. In [10,11] the dynamic response of axially loaded Euler-Bernoulli beams and their buckling due to dynamic loading applied has been studied. For perfectly straight beams with symmetric boundary conditions and excitation aligned with the longitudinal axis, the coupling between transverselongitudinal vibrations is essentially nonlinear, and strongly depends on the boundary conditions.…”

Molecular Dynamics Simulation of Tensile Behavior on Ceramic Particles Reinforced Aluminum Matrix Nanocomposites

“…These include potential for utilization as mirror housings on various vehicle types, door handles, engine covers and intake manifolds and timing belt covers. More general applications currently being considered include usage as impellers and blades for vacuum cleaners, aircraft parts, power tool housings, mower hoods and covers for portable electronics such as mobile phones and pagers [14,15,16]. Although substantial technical challenges remain in fabrication, several methods have been developed, e.g.…”