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A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar

机译：纳米纤维混凝土柱非线性横向振动的分形Boussinesq方程

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摘要

An approximate Hamilton principle is established for the transverse vibration of a reinforced concrete pillar by considering the dissipation energy, and a generalized Boussinesq equation is obtained. The exp-function method is adopted to solve the equation, and its solution properties are discussed and elucidated, including solitary solution, blowup solution, and discontinuous solution. In order to study the effect of a porous structure on the vibration property, fractal calculus is used to derive the fractal Boussinesq equation, and a fractal variational principle is also established. The fractal model confers many attractive properties, which can not be revealed by the traditional protocol. The effect of the nanofiber-reinforced concrete structure on its wave morphology is discussed and illustrated. A blowup solution can be converted into a flat solution by adjusting the value of the fractal derivative order. The paper sheds new light on the design of reinforced concrete pillars to avoid vibration damage.
机译：考虑耗散能量，建立了钢筋混凝土柱横向振动的近似汉密尔顿原理，得到了一个广义的Boussinesq方程。采用exp函数法求解方程，讨论并阐明其解性质，包括孤立解，爆破解和不连续解。为了研究多孔结构对振动特性的影响，使用分形演算来推导分形的Boussinesq方程，并建立了分形变分原理。分形模型具有许多吸引人的特性，而传统协议无法揭示这些特性。讨论并举例说明了纳米纤维增强混凝土结构对其波形态的影响。可以通过调整分形导数阶数的值将爆破溶液转换为扁平溶液。本文为钢筋混凝土柱的设计提供了新的思路，以避免振动损坏。

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  • 来源
    《Applied Mathematical Modelling》 |2020年第6期|437-448|共12页
  • 作者

    Fei-Yu Ji; Chun-Hui He; Jing-Jing Zhang; Ji-Huan He;

  • 作者单位

    School of Science Xi'an University of Architecture and Technology Xi'an China;

    School of Science Xi'an University of Architecture and Technology Xi'an China National Engineering Laboratory for Modem Silk College of Textile and Clothing Engineering Soochow University 199 Ren-Ai Road Suzhou China;

    School of Science East China Jiaotong University Nanchang 330013 China;

    School of Science Xi'an University of Architecture and Technology Xi'an China National Engineering Laboratory for Modem Silk College of Textile and Clothing Engineering Soochow University 199 Ren-Ai Road Suzhou China School of Science East China Jiaotong University Nanchang 330013 China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Fractal concrete; Solitary wave; two-scale transform; Blasting demolition; Railway bridge monotoring;

    机译：分形混凝土孤波二阶变换爆破拆除;铁路桥梁监控;

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