• Advances in aircraft and spacecraft science
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• 제10권3호
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• pp.257-279
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• 2023

This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium.

• Korea-Australia Rheology Journal
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• 제18권2호
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• pp.67-81
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• 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.

• Advances in aircraft and spacecraft science
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• 제4권3호
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• pp.269-280
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• 2017

The natural vibration analysis of microbeams resting on visco-Pasternak's foundation is presented. The thermoelasticity theory of Green and Naghdi without energy dissipation as well as the classical Euler-Bernoulli's beam theory is used for description of natural frequencies of the microbeam. The generalized thermoelasticity model is used to obtain the free vibration frequencies due to the coupling equations of a simply-supported microbeam resting on the three-parameter viscoelastic foundation. The fundamental frequencies are evaluated in terms of length-to-thickness ratio, width-to-thickness ratio and three foundation parameters. Sample natural frequencies are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

• Wind and Structures
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• 제29권2호
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• pp.99-110
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• 2019

This paper provides a simple numerical method to determine the optimal parameters of tuned mass damper (TMD) and viscoelastic dampers (VEDs) in frame structure for wind vibration control considering the soil-structure interation (SSI) effect in frequency domain. Firstly, the numerical model of frame structure equipped with TMD and VEDs considering SSI effect is established in frequency domain. Then, the genetic algorithm (GA) is applied to obtain the optimal parameters of VEDs and TMD. The optimization process is demonstrated by a 20-storey frame structure supported by pile group for different soil conditions. Two wind resistant systems are considered in the analysis, the Structure-TMD system and the Structure-TMD-VEDs system. The example proves that this method can quickly determine the optimal parameters of energy dissipation devices compared with the traditional finite element method, thus is practically valuable.

• Geomechanics and Engineering
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• 제4권1호
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• pp.67-78
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• 2012

Soil foundations exhibit significant creeping deformation, which may result in excessive settlement and failure of superstructures. Based on the theory of viscoelasticity and fractional calculus, a fractional Kelvin-Voigt model is proposed to account for the time-dependent behavior of soil foundation under vertical line load. Analytical solution of settlements in the foundation was derived using Laplace transforms. The influence of the model parameters on the time-dependent settlement is studied through a parametric study. Results indicate that the settlement-time relationship can be accurately captured by varying values of the fractional order of differential operator and the coefficient of viscosity. In comparison with the classical Kelvin-Voigt model, the fractional model can provide a more accurate prediction of long-term settlements of soil foundation. The determination of influential distance also affects the calculation of settlements.

• Steel and Composite Structures
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• 제45권3호
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• pp.409-423
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• 2022

Nowadays, there is a high demand for great structural implementation and multifunctionality with excellent mechanical properties. The porous structures reinforced by graphene platelets (GPLs) having valuable properties, such as heat resistance, lightweight, and excellent energy absorption, have been considerably used in different engineering implementations. However, stiffness of porous structures reduces significantly, due to the internal cavities, by adding GPLs into porous medium, effective mechanical properties of the porous structure considerably enhance. This paper is relating to vibration analysis of fluidconveying cantilever porous graphene platelet reinforced (GPLR) pipe with fractional viscoelastic model resting on foundations. A dynamical model of cantilever porous GPLR pipes conveying fluid and resting on a foundation is proposed, and the vibration, natural frequencies and primary resonant of such a 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 the fractional viscoelastic model is used to govern the construction relation of nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied to the pipe and the excitation frequency is close to the first natural frequency. The governing equation for transverse motions 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.

• Steel and Composite Structures
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• 제50권2호
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• pp.201-216
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• 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.

• Structural Monitoring and Maintenance
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• 제6권4호
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• pp.317-346
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• 2019

Performance assessment of pavements proves useful, in terms of handling the ride quality, controlling the travel time of vehicles and adequate maintenance of pavements. Roughness profiles provide a good measure of the deteriorating condition of the pavement. For the accurate estimates of pavement roughness from dynamic vehicle responses, vehicle parameters should be known accurately. Information on vehicle parameters is uncertain, due to the wear and tear over time. Hence, condition monitoring of pavement requires the identification of pavement roughness along with vehicle parameters. The present study proposes a scheme which estimates the roughness profile of the pavement with the use of accurate estimates of vehicle parameters computed in parallel. Pavement model used in this study is a two-layer Euler-Bernoulli beam resting on a nonlinear Pasternak foundation. The asphalt topping of the pavement in the top layer is modeled as viscoelastic, and the base course bottom layer is modeled as elastic. The viscoelastic response of the top layer is modeled with the help of the Burgers model. The vehicle model considered in this study is a half car model, fitted with accelerometers at specified points. The identification of the coupled system of vehicle-pavement interaction employs a coupled scheme of an unbiased minimum variance estimator and an optimization scheme. The partitioning of observed noisy quantities to be used in the two schemes is investigated in detail before the analysis. The unbiased minimum variance estimator (MVE) make use of a linear state-space formulation including roughness, to overcome the linearization difficulties as in conventional nonlinear filters. MVE gives estimates for the unknown input and fed into the optimization scheme to yield estimates of vehicle parameters. The issue of ill-posedness of the problem is dealt with by introducing a regularization equivalent term in the objective function, specifically where a large number of parameters are to be estimated. Effect of different objective functions is also studied. The outcome of this research is an overall measure of pavement condition.

• Structural Engineering and Mechanics
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• 제80권6호
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• pp.727-736
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• 2021

In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.

• Steel and Composite Structures
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• 제52권1호
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• pp.45-56
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• 2024

This paper proposes an analytical solution for the free vibration, bending and buckling a functionally graded (FG) beam resting on viscoelastic foundation. The materials characteristics of the FG beam are considered to be varying across the thickness according several power law functions. The governing equations are found analytically using a quasi-3D model that contains undetermined integral forms and involves few unknowns to derive. Navier's method for simply supported beam is employed to solve the problem. Numerical examples are presented and studied to demonstrate the accuracy and effectiveness of the proposed model. Then, a detailed parametric study is presented in the form of tables and graphs to study and analyze the effects of the different parameters on the response of FG beams with different material compositions resting on a viscoelastic foundation.