Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach

This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.

DYNAMIC STABILITY OF AXIALLY MOVING VISCOELASTIC BEAMS WITH PULSATING SPEED

Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonsWated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.

Experimental studies on active control of a dynamic system via a time-delayed absorber

The traditional passive absorber is fully effective within a narrow and certain frequency band.To solve this problem,a time-delayed acceleration feedback is introduced to convert a passive absorber into an active one.Both the inherent and the intentional time delays are included.The former mainly comes from signal acquiring and processing,computing,and applying the actuation force,and its value is fixed.The latter is introduced in the controller,and its value is actively adjustable.Firstly,the mechanical model is established and the frequency response equations are obtained.The regions of stability are delineated in the plane of control parameters.Secondly,the design scheme of control parameters is performed to help select the values of the feedback gain and time delay.Thirdly,the experimental studies are conducted.Effects of both negative and positive feedback control are investigated.Experimental results show that the proper choices of control parameters may broaden the effective frequency band of vibration absorption.Moreover,the time-delayed absorber greatly suppresses the resonant response of the primary system when the passive absorber totally fails.The experimental results are in good agreement with the theoretical predictions and numerical simulations.

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.

Resonance frequencies and stability of a current-carrying suspended nanobeam in a longitudinal magnetic field

The resonance frequencies and stability of a nanobeam in a longitudinal magnetic field are investigated.To this aim,a three dimensional beam model is used in which the small-scale effect is taken into account based on the nonlocal elasticity theory.The Lorentz forces are obtained in terms of the local elastic rotations of the beam and the thermal stress due to current is modeled as an axial compressive force.Using the Galerkin method,the governing equations of motion are solved and the stability boundary of the nanobeam is determined.

Flow-pipe-soil coupling mechanisms and predictions for submarine pipeline instability

The stability of a submarine pipeline on the seabed concerns the flow-pipe-soil coupling, with influential factors related to the ocean waves and/or currents, the pipeline and the surrounding soils. A flow-pipe-soil coupling system generally has various instability modes, including the vertical and lateral on-bottom instabilities, the tunnel-erosion of the underlying soil and the subsequent vortex-induced vibrations（VIVs） of free-spanning pipelines. This paper reviews the recent advances of the slip-line field solutions to the bearing capacity, the flow-pipe-soil coupling mechanism and the prediction for the lateral instability, the multi-physical coupling analysis of the tunnel-erosion, and the coupling mechanics between the VIVs and the local scour. It is revealed that the mechanism competition always exists among various instability modes, e.g., the competition between the lateral-instability and the tunnel-erosion. Finally, the prospects and scientific challenges for predicting the instability of a long-distance submarine pipeline are discussed in the context of the deep-water oil and gas exploitations.