Transient Vibrations of a Simply Supported Viscoelastic Beam of a Fractional Derivative Type Under the Transient Motion of the Supports

2016 ◽  
pp. 113-124
Author(s):  
Jan Freundlich
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Beam ◽  
Transient Motion ◽  
Simply Supported ◽  
Derivative Type

Stability of an elastic rod on a fractional derivative type of foundation

2004 ◽  
Vol 277 (1-2) ◽  
pp. 149-161 ◽  
Author(s):  
T.M. Atanackovic ◽  
B. Stankovic
Keyword(s):  
Fractional Derivative ◽  
Elastic Rod ◽  
Derivative Type

Dynamic Interaction of Viscoelastic Soil and Fractional Derivative Type Lining with a Circular Tunnel

2012 ◽  
Vol 170-173 ◽  
pp. 1542-1545
Author(s):  
Min Jie Wen ◽  
Zi Ping Su ◽  
Hui Tuan He
Keyword(s):  
Steady State ◽  
Fractional Derivative ◽  
Dynamic Interaction ◽  
Constitutive Behavior ◽  
Steady State Response ◽  
Circular Tunnel ◽  
Resonance Effects ◽  
Material Parameters ◽  
State Response ◽  
Derivative Type

Coupled harmonic vibration of viscoelastic soil and fractional derivative type lining system with a deeply buried circular tunnel is investigated in the frequency domain. Based on theory of elastic and fractional derivative, steady state response of the viscoelastic soil and lining system is studied. Regarding the lining as a medium with fractional derivative constitutive behavior, and the analytical expressins of the displacement and stress of the soil and lining are respectively obtained by the continuity conditions on the inner boundary of lining and the interface between the soil and the lining. The order of fractional derivative model has a greater influence on system dynamic response, and it dependent on the material parameters of lining. With the frequency increasing, the resonance effects of system decrease.

Vertical Vibration Amplification of a Saturated Fractional Derivative Type Viscoelastic Soil Layer

2012 ◽  
Vol 170-173 ◽  
pp. 1142-1146
Author(s):  
Min Jie Wen ◽  
Hui Tuan He
Keyword(s):  
Fractional Derivative ◽  
Layer Thickness ◽  
Water Pressure ◽  
Soil Layer ◽  
Vertical Vibration ◽  
Saturated Soil ◽  
Amplification Coefficient ◽  
Geometrical Parameters ◽  
Derivative Type ◽  
Soil Skeleton

Regarding the soil skeleton as viscoelastic medium with fractional derivative constitutive behavior, the influences of the soil skeleton viscosity and the soil layer thickness of saturated fractional derivative viscoelastic soil layer on the vertical vibration amplification coefficient is studied in the frequency domain by using the theory of Biot and one dimensional wave. The analytical expressions of the displacement, stress and pore water pressure of saturated soil layer are obtained by decoupling dynamic control equations and bounding the soil layer boundary conditions. The influences of physical and geometrical parameters of the saturated soil on vertical vibration amplification are investigated, and it is revealed that the vertical vibration amplification of the saturated classic elastic, fractional derivative type viscoelastic saturated soil and saturated classic viscoelastic soil are different when the soil layer thickness are changed; the material parameters of the fractional derivative model have great influences on the vertical vibration amplification coefficient.

Dynamics of a Fractional Derivative Type of a Viscoelastic Rod With Random Excitation

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Teodor Atanacković ◽  
Marko Nedeljkov ◽  
Stevan Pilipović ◽  
Danijela Rajter-Ćiri
Keyword(s):  
Fractional Derivative ◽  
Weak Solutions ◽  
Constitutive Equations ◽  
Fractional Derivatives ◽  
Random Excitation ◽  
Bounded Noise ◽  
White Noise Process ◽  
Derivative Type ◽  
Axial Vibrations ◽  
Viscoelastic Rod

AbstractThe axial vibrations of a viscoelastic rod with a body attached to its end are investigated. The problem is modelled by the constitutive equations with fractional derivatives as well as with the perturbations involving a bounded noise and a white noise process. The weak solutions for the equations given below in two cases of constitutive equations as well as their stochastic moments are determined.

scholarly journals Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation

2013 ◽  
Vol 20 (6) ◽  
pp. 1103-1112 ◽  
Author(s):  
Jan Freundlich
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Material ◽  
Material Model ◽  
Model Parameters ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Liouville Fractional Derivative ◽  
Damping Model

The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.

On the Contact Problem of a Rigid Punch Pressed on a Viscoelastic Beam

1972 ◽  
Vol 39 (2) ◽  
pp. 461-468 ◽  
Author(s):  
C. H. Wu ◽  
T. C. T. Ting
Keyword(s):  
Contact Problem ◽  
Smooth Surface ◽  
Contact Region ◽  
Contact Problems ◽  
Contact Boundary ◽  
Viscoelastic Beam ◽  
Rigid Punch ◽  
Loading History ◽  
Simply Supported ◽  
Rigid Smooth

The contact problem of a symmetric rigid punch pressed at the midspan of a simply supported viscoelastic beam is studied. This is equivalent to a cantilever beam loaded at the free end against a rigid smooth surface. Explicit solutions are obtained for the length of the contact region, the contact pressure, the contact force at the contact boundary, and the curvature of the beam outside of the contact regions. As in other contact problems, the solution does not depend on the entire loading history.

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