Fuzzy Fractional Vibration Equation of Large Membrane

2016 ◽  
pp. 155-189
Keyword(s):  
Vibration Equation

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

Dynamic Stability of an Axially Moving Yarn with Time-Dependent Tension

2014 ◽  
Vol 900 ◽  
pp. 753-756 ◽  
Author(s):  
You Guo Li
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Second Law ◽  
Order Ordinary Differential Equation ◽  
Vibration Equation ◽  
Transversal Vibration ◽  
First Order ◽  
Homotopy Perturbation ◽  
Axially Moving

In this paper the nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin element. A partial differential equation governing the transversal vibration is derived from Newtons second law. Galerkin method is used to truncate the governing nonlinear differential equation, and thus first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result, the condition which should be avoided in the weaving process for resonance is obtained.

scholarly journals Uncertain spring vibration equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Lifen Jia ◽  
Wei Dai
Keyword(s):  
Vibration Equation

An algorithm for solving the fractional vibration equation

2012 ◽  
Vol 23 (2) ◽  
pp. 228-237 ◽  
Author(s):  
S. T. Mohyud-Din ◽  
A. Yıldırım
Keyword(s):  
Vibration Equation

Research on Horizontal Displacement and Torsion Coupling Effect of Structure-Soil System

2013 ◽  
Vol 275-277 ◽  
pp. 1107-1110
Author(s):  
Nan Jiang ◽  
Hui Fang Zhao
Keyword(s):  
Energy Transfer ◽  
Nonlinear Interaction ◽  
Coupling Effect ◽  
Kinematic Hardening ◽  
Horizontal Displacement ◽  
Torsional Stiffness ◽  
Soil System ◽  
Vibration Equation ◽  
Interaction System ◽  
Effect Of Structure

In this paper, the vibration equation of the structure-soil nonlinear interaction system was qualitatively analyzed by using the modern dynamic theory. Based on the multilinear kinematic hardening mode, the nonlinear finite element method was applied for the solution of the horizontal and torsional stiffness between the foundation and soil interaction system. And a mechanical model of the structure-soil nonlinear interaction system was established. The Lagrange energy method is used to build the coupling vibration equation of the structural horizontal displacement and torsion. The Primary resonance of the structure-soil nonlinear interaction system was studied by using the multiple scales method. By analyzing the nonlinear coupling interaction between different structures and soil, the coupling effect of structure system was revealed by appearing energy transfer from high order horizontal vibration to low order torsional vibration, and also the vibration characteristics and the behavior of energy transfer were obtained.

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