Hashem S. Alkhaldi

Fractal Geometry-Based Hypergeometric Time Series Solution to the Hereditary Thermal Creep Model for the Contact of Rough Surfaces Using the Kelvin-Voigt Medium

This paper aims at constructing a continuous hereditary creep model for the thermoviscoelastic contact of a rough punch and a smooth surface of a rigid half-space. The used model considers the rough surface as a function of the applied load and temperatures. The material of the rough punch surface is assumed to behave as Kelvin-Voigt viscoelastic material. Such a model uses elastic springs and viscous dashpots in parallel. The fractal-based punch surface is modelled using a deterministic Cantor structure. An asymptotic power law, deduced using approximate iterative relations, is used to express the punch surface creep which is a time-dependent inelastic deformation. The suggested law utilized the hypergeometric time series to relate the variables of creep as a function of remote forces, body temperatures, and time. The model is valid when the approach of punch surface and half space is in the order of the size of the surface roughness. The closed-form results are obtained for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results show good agreement with published experimental results, and the methodology can be further extended to other structures such as the Kelvin-Voigt medium within electronic circuits and systems.

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam. The beam is attached to multi single-degree-of-freedom (SDOF) fractionally-damped systems, and it is subjected to a vehicle moving with a constant velocity. The damping characteristics of the beam and SDOF systems are described in terms of fractional derivatives. Three coupled second-order fractional differential equations are produced and then they are solved by combining the Laplace transform with the decomposition method. The obtained numerical results show that the dynamic response decreases as (a) the number of absorbers attached to the beam increases and (b) the damping-ratios of used absorbers and beam increase. However, there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. Furthermore, the obtained results show very good agreements with special case studies that were published in the literature.

Dynamic Response of a Beam With Absorber Exposed to a Running Force: Fractional Calculus Approach

This paper analyzes the transverse vibration of Bernoulli-Euler homogeneous isotropic simply-supported beam. The beam is assumed to be fractionally-damped and attached to a single-degree-of-freedom (SDOF) absorber with fractionally-damping behavior at the mid-span of the beam. The beam is also exposed to a running force with constant velocity. The fractional calculus is introduced to model the damping characteristics of both the beam and absorber. The Laplace transform accompanied by the used decomposition method is applied to solve the handled problem with homogenous initial conditions. Subsequently, curves are depicted to measure the dynamic response of the utilized beam under different set of vibration parameters and different values of fractional derivative orders for both of the beam and absorber. The results obtained show that the dynamic response decreases as both the damping-ratio of the absorber and beam increase. The results reveal that there are critical values of fractional derivative orders which are different from unity. At these optimal values, the beam behaves with less dynamic response than that obtained for the full-order derivatives model of unity order. Therefore, the fractional derivative approach provides better damping models for fractionally-damped structures and materials which may allow researchers to choose suitable mathematical models that precisely fit the corresponding experimental models for many engineering applications.© 2012 ASME

Vibration of a Beam-Oscillator System Subjected to a Moving Vehicle: Fractional Derivative Approach

The dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam is investigated. The beam is appended at its mid-span by a single-degree-of-freedom (SDOF) fractionally-damped oscillator. The beam is further subjected to a vehicle modeled as a spring-dashpot system moves with a constant velocity over the beam. Hence, the damping characteristics of the beam and SDOF attached-oscillator are formally described in terms of fractional derivatives of arbitrary orders. In the analysis, the beam, SDOF oscillator, and the vehicle are assumed to be initially at rest. A system of three coupled differential equations is produced. These equations are handled by combining the Laplace transform with the Born series. Thereafter, curves are plotted to show the effect of the moving vehicle and the fractional derivatives behavior on the dynamic response of the beam. The numerical results show that the dynamic response decreases as the damping-ratios of the used absorber and beam increase. However, there are some optimal values of fractional derivative orders which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivative model. A comparison between the moving load and moving vehicle shows a significant reduction in the beam dynamic response in the case when vehicle is compared with the running load.Copyright