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Impact loading occurs when a moving object collides with a stationary structure, such as a rod with a uniform cross-sectional area fixed at one end. Under these conditions, the rod absorbs the kinetic energy from the striking object, leading to deformation and subsequent stress development. As the rod returns to its original position and reaches maximum stress, the absorbed energy, initially manifested as kinetic energy, transforms entirely into strain energy.
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Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
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Nonlinear dynamics induced in a structure by seismic and environmental loading.

Philippe Guéguen1, Paul Johnson2, Philippe Roux1

  • 1ISTerre, Université de Grenoble Alpes, CNRS/IFSTTAR, BP 53, 38041 Grenoble cedex 9, France.

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Summary

Civil engineering structures show nonlinear elastic behavior even under minimal deformation. This study reveals significant changes in resonance frequency and damping, bridging lab and seismic scales for universal nonlinear dynamics.

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Area of Science:

  • Structural Engineering
  • Solid Mechanics
  • Geophysics

Background:

  • Elastic parameters like resonance frequency and damping are crucial for structural integrity.
  • Nonlinear elastic behavior has been observed in various materials and at seismic scales.
  • A gap exists in understanding nonlinear elastic behavior at small deformation scales in civil structures.

Purpose of the Study:

  • To investigate nonlinear elastic behavior in civil engineering structures under very weak deformations.
  • To quantify changes in resonance frequency and damping at strain levels below yield deformation.
  • To connect laboratory-scale observations with seismic-scale phenomena.

Main Methods:

  • Applying very weak dynamic and quasi-static deformations to civil engineering structures.
  • Measuring changes in resonance frequency and damping coefficients.
  • Analyzing data for strain levels orders of magnitude below the yield deformation (approx. 10(-3)).

Main Results:

  • Observed nonlinear softening and recovery in elastic parameters (resonance frequency and damping).
  • Modal frequencies shifted by approximately 1% under weak seismic or atmospheric loading.
  • Damping increased by over 100% for strain levels between 10(-7) and 10(-4).

Conclusions:

  • Civil engineering structures exhibit significant nonlinear elastic behavior at very low strain levels.
  • These findings bridge the gap between laboratory and seismic scales for nonlinear elasticity.
  • The results support the concept of universal nonlinear elastic behavior across diverse systems and scales.