Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation

2002 ◽  
Vol 23 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Zhu Zheng-you ◽  
Li Gen-guo ◽  
Cheng Chang-jun
Keyword(s):  
Fractional Derivative ◽  
Constitutive Relation ◽  
Timoshenko Beam ◽  
Dynamical Analysis ◽  
Fractional Derivative Constitutive Relation ◽  
Viscoelastic Timoshenko Beam

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

scholarly journals The transversal creeping vibrations of a fractional derivative order constitutive relation of nonhomogeneous beam

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Katica (Stevanovic) Hedrih
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Constitutive Relation ◽  
Continuous Functions ◽  
Beam Dynamic ◽  
Fractional Differential ◽  
Elastic Form ◽  
Partial Fractional Differential Equation ◽  
Derivative Order

We considered the problem on transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces. It is assumed that the layers of the bar were made of nonhomogenous continuously creeping material and the corresponding modulus of elasticity and creeping fractional order derivative of constitutive relation of each layer are continuous functions of the length coordinate and thickness coordinates. Partial fractional differential equation and particular solutions for the case of natural vibrations of the beam of creeping material of a fractional derivative order constitutive relation in the case of the influence of rotation inertia are derived. For the case of natural creeping vibrations, eigenfunction and time function, for different examples of boundary conditions, are determined. By using the derived partial fractional differential equation of the beam vibrations, the almost sure stochastic stability of the beam dynamic shapes, corresponding to thenth shape of the beam elastic form, forced by a bounded axially noise excitation, is investigated. By the use of S. T. Ariaratnam's idea, as well as of the averaging method, the top Lyapunov exponent is evaluated asymptotically when the intensity of excitation process is small.

Stabilization of a viscoelastic Timoshenko beam fixed into a moving base

2019 ◽  
Vol 14 (5) ◽  
pp. 501 ◽  
Author(s):  
Amirouche Berkani ◽  
Nasser-eddine Tatar
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Equilibrium State ◽  
Timoshenko Beam ◽  
Relaxation Function ◽  
Control Force ◽  
Timoshenko System ◽  
Translational Displacement ◽  
Moving Base ◽  
Viscoelastic Timoshenko Beam

In this paper, we are concerned with a cantilevered Timoshenko beam. The beam is viscoelastic and subject to a translational displacement. Consequently, the Timoshenko system is complemented by an ordinary differential equation describing the dynamic of the base to which the beam is attached to. We establish a control force capable of driving the system to the equilibrium state with a certain speed depending on the decay rate of the relaxation function.

Free Vibration of Elastic Timoshenko Beam on Fractional Derivative Winkler Viscoelastic Foundation

2011 ◽  
Vol 368-373 ◽  
pp. 1034-1037 ◽  
Author(s):  
Qi Fang Yan ◽  
Zi Ping Su
Keyword(s):  
Free Vibration ◽  
Fractional Derivative ◽  
Shear Deformation ◽  
Timoshenko Beam ◽  
Shape Factor ◽  
Viscoelastic Foundation ◽  
Deformation Function ◽  
Numerical Example ◽  
Foundation Model ◽  
Derivative Order

The fractional derivative Winkler viscoelastic foundation model is established by introducing the concept of fractional derivative. The control equations of free vibration of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are also built by considering the shear deformation and rotary inertia, and the control equations of elastic Timoshenko beam are decoupled by using the deformation function and considering the properties of fractional derivative, and the expressions of deflection and section corner of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are obtained. The influences of fractional derivative order and shear shape factor on the free vibration of elastic Timoshenko beam are discussed by numerical example.

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