Nonlinear targeted energy transfer (TET) is applied to suppress the excessive vibration of an axially moving string with transverse wind loads. The coupling dynamic equations used are modeled by a nonlinear energy sink (NES) attached to the string to absorb vibrational energy. By a two-term Galerkin procedure, the equations are discretized, and the effects of vibration suppression by numerical methods are demonstrated. Results show that the NES can effectively suppress the vibration of the axially moving string with transverse wind loadings, thereby protecting the string from excessive movement.

The structures of axial speed-dependent behaviors have been analyzed in numerous studies [

Traditional linear vibration absorbers have been used in various engineering fields. However, vibration suppression strongly responds only at the natural frequency of the vibration absorber. The nonlinear energy sink (NES) functions as an effective vibration absorber for a nonlinear system. The NES has recently been reported to engage in resonance over a very broad frequency range, has a small additional mass, and can perform targeted energy transfer (TET). Nonlinear TET has been used in numerous engineering structures for vibration suppression, such as drill-string [

The present study focuses on the vibration suppression of an axially moving string with certain and steady transverse wind loads by using NES. The coupling dynamic differential equations of an axially moving string and the NES with transverse wind loads are established. In addition, the governing equations are approximately discretized by the two-term Galerkin procedure. The effects of vibration suppression are finally demonstrated by numerical simulation.

Figure

An axially moving string with a nonlinear energy sink (NES).

The length of the axially moving string is represented by

In (

The NES equation of motion is given by

The interaction force

The attachment point displacement and velocity are expressed as follows [

The nondimensional quantities are given as follows:

Substituting (

By using a tractable finite-dimensional dynamical system, governing equations (

Substituting (

Equation (

The effectiveness of the NES coupled to an axially moving string at varying axial speeds is demonstrated. Equations (

Response of the axially moving string and NES for different axial speeds (solid line: axially moving string’s response,

To further demonstrate the effectiveness of the NES, the responses of the string with the NES and without the NES are presented in Figures

Comparison of the transient response of axially moving string with and without NES under varying speed (solid line: string coupled with NES; dotted line: string without NES).

In Figure

Comparison of the transient response of axially moving string with and without NES under varying attaching location (solid line: string coupled with NES; dotted line: string without NES).

The vibration of an axially moving string with transverse wind loads is effectively suppressed using the NES. The results of the simulation experiments indicate that at various flow speeds, the NES can irreversibly transfer and dissipate vibrational energy from the axially moving string. By considering the adding internal degrees of freedom to the NES, vibration suppression is most clearly demonstrated at

The authors acknowledge the funding support of the Natural Science Foundation of Liaoning Province (201102170).