• Steel and Composite Structures
• /
• v.50 no.2
• /
• pp.201-216
• /
• 2024

This paper is motivated by the lack of studies relating to vibration and nonlinear resonance of fluid-conveying cantilever porous GPLR pipes with fractional viscoelastic model resting on nonlinear foundations. A dynamical model of cantilever porous Graphene Platelet Reinforced (GPLR) pipes conveying fluid and resting on nonlinear foundation is proposed, and the vibration, natural frequencies and primary resonant of such system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with fractional viscoelastic model is used to govern the construction relation of the nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied on pipe and excitation frequency is close to the first natural frequency. The governing equation for transverse motion of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.13 no.12
• /
• pp.938-946
• /
• 2003

Length of an unconstrained viscoelastic damping layer on beams is determined to maximizeloss factor using a numerical search method. The fractional derivative model can describe damping characteristics of viscoelastic damping materials accurately, and is used to represent nonlinearity of complex modulus with frequencies and temperatures. Equivalent flexural rigidity of the unconstrained beam is obtained using Ross, Ungar, Kelvin[RUK] equation. The loss factors of partially covered unconstrained beam are calculated by a modal strain energy method. Optimal lengths of the unconstrained viscoelastic damping layer of beams are identified with ambient temperatures and thickness ratios of beam and damping layer by using a finite-difference-based steepest descent method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.665-671
• /
• 2003

Length of an unconstrained viscoelastic damping layer on beams is determined to maximize loss factor using a numerical search method. The fractional derivative model can describe damping characteristics of the viscoelastic damping material, and is used to represent nonlinearity of complex modulus with frequencies and temperatures. Equivalent flexural rigidity of the unconstrained beam is obtained using Ross, Ungar, Kerwin(RUK) equation. The loss factors of partially covered unconstrained beam are calculated by a modal strain energy method. Optimal lengths of the unconstrained viscoelastic damping layer of beams are obtained with respect to ambient temperatures and thickness ratios of beam and damping layer.

• Journal of Pharmaceutical Investigation
• /
• v.41 no.3
• /
• pp.161-171
• /
• 2011

The objective of the present study is to systematically characterize a linear viscoelastic behavior of petroleum jelly in small amplitude oscillatory shear flow fields correspondent to the rheological ground state. With this aim, using a strain-controlled rheometer, the dynamic viscoelastic properties of commercially available petroleum jelly have been measured at $37^{\circ}C$ (body temperature) over a wide range of angular frequencies at an extremely small strain amplitude of 0.1 %. In this article, the linear viscoelastic behavior was reported in detail and then explained from a structural view-point of petroleum jelly and discussed in depth with respect to the consumer's requirements. Main findings obtained from this study can be summarized as follows : (1) The storage modulus is always greater than the loss modulus over an entire range of angular frequencies studied, meaning that the linear viscoelastic behavior of petroleum jelly is dominated by an elastic nature rather than a viscous nature. (2) Petroleum jelly shows a desirable linear viscoelastic behavior with respect to the consumer's requirements because it is undesirable for the product to flow down from the skin at an initial stage upon contact with the human skin. (3) A fractional derivative model shows an excellent applicability to describe a linear viscoelastic behavior of petroleum jelly. However, this model should be used with a special caution because there exists no physical meaning for the model parameters. (4) A modified form of the Cox-Merz rule gives a good ability to predict the relationship between steady shear flow properties (nonlinear behavior) and dynamic viscoelastic properties (linear behavior) for petroleum jelly.

• Korea-Australia Rheology Journal
• /
• v.18 no.2
• /
• pp.67-81
• /
• 2006

Using a strain-controlled rheometer, the dynamic viscoelastic properties of aqueous xanthan gum solutions with different concentrations were measured over a wide range of strain amplitudes and then the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a broad range of angular frequencies. In this article, both the strain amplitude and concentration dependencies of dynamic viscoelastic behavior were reported at full length from the experimental data obtained from strain-sweep tests. In addition, the linear viscoelastic behavior was explained in detail and the effects of angular frequency and concentration on this behavior were discussed using the well-known power-law type equations. Finally, a fractional derivative model originally developed by Ma and Barbosa-Canovas (1996) was employed to make a quantitative description of a linear viscoelastic behavior and then the applicability of this model was examined with a brief comment on its limitations. Main findings obtained from this study can be summarized as follows: (1) At strain amplitude range larger than 10%, the storage modulus shows a nonlinear strain-thinning behavior, indicating a decrease in storage modulus as an increase in strain amplitude. (2) At strain amplitude range larger than 80%, the loss modulus exhibits an exceptional nonlinear strain-overshoot behavior, indicating that the loss modulus is first increased up to a certain strain amplitude(${\gamma}_0{\approx}150%$) beyond which followed by a decrease in loss modulus with an increase in strain amplitude. (3) At sufficiently large strain amplitude range (${\gamma}_0>200%$), a viscous behavior becomes superior to an elastic behavior. (4) An ability to flow without fracture at large strain amplitudes is one of the most important differences between typical strong gel systems and concentrated xanthan gum solutions. (5) The linear viscoelastic behavior of concentrated xanthan gum solutions is dominated by an elastic nature rather than a viscous nature and a gel-like structure is present in these systems. (6) As the polymer concentration is increased, xanthan gum solutions become more elastic and can be characterized by a slower relaxation mechanism. (7) Concentrated xanthan gum solutions do not form a chemically cross-linked stable (strong) gel but exhibit a weak gel-like behavior. (8) A fractional derivative model may be an attractive means for predicting a linear viscoelastic behavior of concentrated xanthan gum solutions but classified as a semi-empirical relationship because there exists no real physical meaning for the model parameters.

• Structural Engineering and Mechanics
• /
• v.63 no.1
• /
• pp.89-102
• /
• 2017

In this work, we present a theoretical framework to study the thermovisco-elastic responses of homogeneous, isotropic and perfectly conducting medium subjected to inclined load. Based on recently developed generalized thermoelasticity theory with fractional order strain, the two-dimensional governing equations are obtained in the context of generalized magnetothermo-viscoelasticity theory without energy dissipation. The Kelvin-Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of the material. The resulting formulation of the field equations is solved analytically in the Laplace and Fourier transform domain. On the application of inclined load at the surface of half-space, the analytical expressions for the normal displacement, strain, temperature, normal stress and tangential stress are derived in the joint-transformed domain. To restore the fields in physical domain, an appropriate numerical algorithm is used for the inversion of the Laplace and Fourier transforms. Finally, we have demonstrated the effect of magnetic field, viscosity, mechanical relaxation time, fractional order parameter and time on the physical fields in graphical form for copper material. Some special cases have also been deduced from the present investigation.

• Structural Engineering and Mechanics
• /
• v.41 no.1
• /
• pp.113-137
• /
• 2012

Frame structures with viscoelastic (VE) dampers mounted on them are considered in this paper. It is the aim of this paper to compare the dynamic characteristics of frame structures with VE dampers when the dampers are modelled by means of different models. The classical rheological models, the model with the fractional order derivative, and the complex modulus model are used. A relatively large structure with VE dampers is considered in order to make the results of comparison more representative. The formulae for dissipation energy are derived. The finite element method is used to derive the equations of motion of the structure with dampers and such equations are written in terms of both physical and state-space variables. The solution to motion equations in the frequency domain is given and the dynamic properties of the structure with VE dampers are determined as a solution to the appropriately defined eigenvalue problem. Several conclusions concerning the applicability of a family of models of VE dampers are formulated on the basis of results of an extensive numerical analysis.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2011.04a
• /
• pp.744-749
• /
• 2011

Silicon oil in viscous fluid damper has a viscoelastic feature that show stiffness besides damping. These properties depend on frequency and are non-linear. A lot of research has been conducted in order to identify viscoelastic damper with mathematical model. Fractional Derivative Maxwell Model has been widely used, but this model did not explain the effect of damper size change on the damper performance. In this paper, the experimental study was conducted to validate damper's dynamic behaviors when total damper's size is changed while maintaining same aspect ratio and orifice size.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.12 s.255
• /
• pp.1581-1587
• /
• 2006

An optimization formulation is proposed to minimize sound pressures in a two-dimensional cavity by controlling the attachment area of viscoelastic unconstrained damping materials. For the analysis of structural- acoustic systems, a hybrid approach that uses finite elements for structures and boundary elements for cavity is adopted. Four-parameter fractional derivative model is used to accurately represent dynamic characteristics of the viscoelastic materials with respect to frequency and temperature. Optimal layouts of the unconstrained damping layer on structural wall of cavity are identified according to temperatures and the amount of damping material by using a numerical search algorithm.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.05a
• /
• pp.1023-1026
• /
• 2007

Optimal damping layout of the constrained viscoelastic damping layer on beam is identified with temperatures by using a gradient-based numerical search algorithm. An optimal design problem is defined in order to determine the constrained damping layer configuration. A finite element formulation is introduced to model the constrained damping layer beam. The four-parameter fractional derivative model and the Arrhenius shift factor are used to describe dynamic characteristics of viscoelastic material with respect to frequency and temperature. Frequency-dependent complex-valued eigenvalue problems are solved by using a simple resubstitution algorithm in order to obtain the loss factor of each mode and responses of the structure. The results of the numerical example show that the proposed method can reduce frequency responses of beam at peaks only by reconfiguring the layout of constrained damping layer within a limited weight constraint.