An analytical approach for shock response of fractional viscoelastic beams with tip mass

被引:0
作者
Heidarpour, Behzad [1 ]
Rahi, Abbas [1 ,2 ]
Shahravi, Morteza [1 ]
机构
[1] Shahid Beheshti Univ, Fac Mech & Energy Engn, Tehran, Iran
[2] Shahid Beheshti Univ, Fac Mech & Energy Engn, Tehran 5475548, Iran
关键词
shock; fractional viscoelastic; variable order; Kelvin-Voigt model; DYNAMIC-RESPONSE; VIBRATIONS; RESONANCE; CALCULUS; MODEL;
D O I
10.1177/10775463241242600
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
This paper specifically analyzes the behavior of a beam with fractional viscoelastic properties and a tip mass under shock. The shock is applied longitudinally to the beam, and a fractional Kelvin-Voigt model is employed to describe the viscoelastic properties. Additionally, the paper examines the fractional viscoelastic power as a function of time during the shock. The equation of motion for the fractional viscoelastic beam with a tip mass is derived using Hamilton's principle. In order to ensure accurate analysis of the results, the graphs are carefully analyzed in both the time and frequency domains. To solve the equations, the special technique provided for differential equations of variable order (VO) is used. Two distinct methods, namely, absolute method and square root of the sum of squares method, are thoroughly examined to calculate the absolute acceleration. Subsequently, the most suitable method is selected based on the evaluation results. The study's results demonstrate that the damping parameters of the viscoelastic beam have a significant impact on shock transmissibility. Additionally, the findings demonstrate that the ability to transfer shocks can be manipulated by modifying the system's geometry and mass.
引用
收藏
页数:11
相关论文
共 35 条
  • [1] Analytical solution for stochastic response of a fractionally damped beam
    Agrawal, OP
    [J]. JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2004, 126 (04): : 561 - 566
  • [2] Alexander JE, 2009, SOUND VIB, V43, P6
  • [3] Atanackovic TM, 2002, Z ANGEW MATH MECH, V82, P377, DOI 10.1002/1521-4001(200206)82:6<377::AID-ZAMM377>3.0.CO
  • [4] 2-M
  • [5] Bagley R. L., 1979, APPL GEN DERIVATIVES
  • [6] FRACTIONAL CALCULUS - A DIFFERENT APPROACH TO THE ANALYSIS OF VISCOELASTICALLY DAMPED STRUCTURES
    BAGLEY, RL
    TORVIK, PJ
    [J]. AIAA JOURNAL, 1983, 21 (05) : 741 - 748
  • [7] A THEORETICAL BASIS FOR THE APPLICATION OF FRACTIONAL CALCULUS TO VISCOELASTICITY
    BAGLEY, RL
    TORVIK, PJ
    [J]. JOURNAL OF RHEOLOGY, 1983, 27 (03) : 201 - 210
  • [8] Numerical analysis of nonlinear variable fractional viscoelastic arch based on shifted Legendre polynomials
    Cao, Jiawei
    Chen, Yiming
    Wang, Yuanhui
    Zhang, Hua
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (11) : 8798 - 8813
  • [9] A causal fractional derivative model for acoustic wave propagation in lossy media
    Chen, Wen
    Hu, Shuai
    Cai, Wei
    [J]. ARCHIVE OF APPLIED MECHANICS, 2016, 86 (03) : 529 - 539
  • [10] Nonlinear vibration isolation of a viscoelastic beam
    Ding, Hu
    Zhu, Min-Hui
    Chen, Li-Qun
    [J]. NONLINEAR DYNAMICS, 2018, 92 (02) : 325 - 349