Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Abstract

This study investigated the damping effects of a dynamic vibration absorber (DVA) attached to a hinged-hinged nonlinear Euler-Bernoulli beam. The model constructed in this study was used to simulate suspended nonlinear elastic beam systems or vibrating elastic beam systems on a nonlinear Winkler-type foundation. This makes the modeling in this study applicable to suspension bridges, railway tracks, and even carbon nanotubes. The hinged-hinged beam in this study includes nonlinear stretching effects, which is why we adopted the method of multiple scales (MOMS) to analyze the frequency responses of fixed points in various modes. The use of amplitudes and vibration modes made it possible to examine the internal resonance. Our results indicate that particular elastic foundations or suspension systems can cause 1:3 internal resonance in a beam. The use of 3D maximum amplitude contour plots (3DMACPs) enabled us to obtain a comprehensive understanding of various DVA parameters, including mass, spring coefficient, and the location of DVA on the beam, and thereby combine them for optimal effect. Our results were verified using numerical calculations.

Vibration reduction of continuous moving loads on a nonlinear simple beam resting on an elastic foundation

“…This study improves the author's earlier work (Wang and Lu [5]) for a wider range of prediction on internal resonance conditions. The continuous concentrated moving load is applied on this nonlinear beam system.…”

“…This study thus provides a wider range of possibilities for I.R. conditions than the methodology proposed by Wang and Lu [5].…”

“…Using Newton's 2nd Law, Euler's angle transformation, and Taylor series expansion, this study is able to obtain the basic equations of motion for the nonlinear beam. It is noted that any rotations in the beam are excluded; i. nonlinear simple beam resting on an elastic foundation [5,10], the equation of motion for the 2D beam (see Fig. 1) is shown as:…”

“…Wang and Kuo [4] discussed a hinged-free nonlinear Euler-Bernoulli beam resting on a nonlinear elastic foundation, and found that placing a dynamic vibration absorber (DVA) with appropriate mass could prevent internal resonance and suppress vibrations in the beam. Wang and Lu [5] reported that, in a system with a hinged-hinged nonlinear beam resting on a nonlinear elastic foundation, 1:3 (internal resonance (I.R.)) occurs within the 1st and 3rd modes when the ratio of the elastic modulus of the foundation to that of the beam is .…”

“…The results showed that the instead of TMD's mass and spring & damping coefficients, the location of the TMD also played an important role in system damping effect. In the present work, the authors' nonlinear beam model [5] is considered. Their analytical result for internal resonance conditions is verified and improved by a simple numerical method.…”