Purpose <p>Multiple span beams with internal hinge are commonly seen in mechanical and civil engineering. Its engineering application scope is very broad, including medium and small-span bridges on highways or railways, as well as connection components for floating platforms in marine engineering, etc. Furthermore, under the influence of external aerodynamic and hydrodynamic forces, harmonic excitation will occur, causing the structure to undergo buckling. Its stability and nonlinear vibration properties are critical for mechanical design. This paper investigates the stability and nonlinear forced vibration characteristic of a two span beam with a free internal hinge under axial compressive force.</p> Methods <p>Von Karman geometric nonlinearity is introduced to establish the governing equation of the beam. The motion equations of the beam under pre- and post-buckling states are discretized based on Hamilton’s principle and the assumed mode method. An experimental validation was performed to test the fundamental natural frequency and the mode shape of the beam. The nature frequency in post-buckling states is calculated through generalized eigenvalue method. The Pseudo-arclength continuation method is applied to analyze the nonlinear vibration performance of the beam in pre- and post-buckling states. Critical load’s change trend via the internal hinge position is obtained through numeric calculation.</p> Results <p>Influence of axial load and damping coefficient on forced vibration are analyzed. In pre- and post-buckling states, the forced vibration manifests hardening and softening nonlinearity respectively. Besides, the suppression influence of damping on nonlinear vibration is also presented.</p> Conclusions <p>This paper can be helpful for mechanical design with hinge linked structures.</p>

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Nonlinear Vibration Analyses of Two-Span Hinge Connected Beams in Transition Between Pre- and Post-Buckling States

  • Yuqi Ma,
  • Guo Yao

摘要

Purpose

Multiple span beams with internal hinge are commonly seen in mechanical and civil engineering. Its engineering application scope is very broad, including medium and small-span bridges on highways or railways, as well as connection components for floating platforms in marine engineering, etc. Furthermore, under the influence of external aerodynamic and hydrodynamic forces, harmonic excitation will occur, causing the structure to undergo buckling. Its stability and nonlinear vibration properties are critical for mechanical design. This paper investigates the stability and nonlinear forced vibration characteristic of a two span beam with a free internal hinge under axial compressive force.

Methods

Von Karman geometric nonlinearity is introduced to establish the governing equation of the beam. The motion equations of the beam under pre- and post-buckling states are discretized based on Hamilton’s principle and the assumed mode method. An experimental validation was performed to test the fundamental natural frequency and the mode shape of the beam. The nature frequency in post-buckling states is calculated through generalized eigenvalue method. The Pseudo-arclength continuation method is applied to analyze the nonlinear vibration performance of the beam in pre- and post-buckling states. Critical load’s change trend via the internal hinge position is obtained through numeric calculation.

Results

Influence of axial load and damping coefficient on forced vibration are analyzed. In pre- and post-buckling states, the forced vibration manifests hardening and softening nonlinearity respectively. Besides, the suppression influence of damping on nonlinear vibration is also presented.

Conclusions

This paper can be helpful for mechanical design with hinge linked structures.