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<p>This study focuses on the nonlinear dynamic behavior of flexible slender structures (FSS) such as cables, ropes, threads, and biological tissues. The “geometrically exact beam formulation” (GE beam formulation) developed by Reissner and Simo is employed to accurately describe the inertial and stiffness properties of these structures. Given that the vibration damping in FSS materials exceeds that of metals, incorporating damping effects into the beam model is essential. The strain in GE beams differs from that defined in conventional continuum mechanics, necessitating a distinct constitutive law. Previous work by Simo et al. provided a quadratic energy function under hyper-elasticity theory. This paper introduces the fractional-order Kelvin-Voigt model for material damping, investigating 1) the incorporation of fractional differential damping terms into GE beam theory, 2) the numerical calculation of finite element discretized systems, and 3) the response characteristics of beam systems with fractional differential damping.</p>

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Introduction of fractional damping to nonlinear GE beam model

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Nobuyuki Shimizu,
  • Takeshi Fujikawa,
  • Masataka Fukunaga

摘要

This study focuses on the nonlinear dynamic behavior of flexible slender structures (FSS) such as cables, ropes, threads, and biological tissues. The “geometrically exact beam formulation” (GE beam formulation) developed by Reissner and Simo is employed to accurately describe the inertial and stiffness properties of these structures. Given that the vibration damping in FSS materials exceeds that of metals, incorporating damping effects into the beam model is essential. The strain in GE beams differs from that defined in conventional continuum mechanics, necessitating a distinct constitutive law. Previous work by Simo et al. provided a quadratic energy function under hyper-elasticity theory. This paper introduces the fractional-order Kelvin-Voigt model for material damping, investigating 1) the incorporation of fractional differential damping terms into GE beam theory, 2) the numerical calculation of finite element discretized systems, and 3) the response characteristics of beam systems with fractional differential damping.