In the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

The purpose of this study is to examine the acoustic performance of parallel simple expansion mufflers by a new approach for an acceleration of computational time required. The fast multipole method separated the field points and source points into two terms by means of addition theorem. When the boundary is divided into uniform meshes, the integration of source element can be calculated fast. Therefore, the fast multipole method, when compared with the boundary element method, reduces CPU time from an order of N2 to NlogγN, where N is the number of unknowns and γ is a constant. The numerical results have been compared with experiments and analytical approaches based on pressure and velocity continuity, as well as the modal meshing approach; the results clearly show that the agreements are good.

The objective of this study was to derive e an anisotropic viscoplastic rate dependent constitutive model. The model was derived on the basis of the viscoplastic theory proposed by Kutter and Sathialingam and the yield surface function suggested by Wheeler et al. The adopted yield surface function was more consistent with the yield surface of the Taipei silty clay, compared with the existing constitutive models. The model was confirmed able to simulate the undrained stress strain response for the K0-consolidated undrained compression and extension tests. The model was also used to simulate the isotropic consolidated and K0-consolidated undrained creep test. Results show that the predicted strain from the proposed model was close to the test data. Especially the model is able to predict the tertiary creep failure when the soil is subject to high stress level.

Conventionally, only three components of stress, i.e., the membrane stresses (1σxx, 1σyy, 1σxy) in x-y plane along span directions, are considered in deriving the buckling equations of thin plates using energy approaches. Of particular interest in this study is to take all the six components of stress into account in formulating the potential energy for an orthotropic plate. By invoking the conditions of stress equilibrium for the plate and Green's theorem to relate the potential energy to external virtual works, all the instability potential terms associated with the non-conventional stresses (1σxz, 1σyz, 1σzz) can either cancel those terms conventionally referred to as higher-order terms or combine with them to yield some new but meaningful terms. For this reason, the present approach contains more physical and compact meaning than conventional ones in the process of derivation. With the present governing differential equations, bending buckling problems of orthotropic rectangular plates will be investigated in this study.

The Kastner formula for cavity contraction is one of the commonly used formulae for the cavity contraction problem in tunnel excavation, and it is based on the assumption of small displacement around the cavity with no volume change in the plastic zone. In this paper, the errors arising from these assumptions are discussed, and the volume change of the plastic zone is considered. It can be seen that this assumption is reasonable for normal situations, but for rock with weak shear strength, the Kastner formula should be used with care, especially in situations where there will be relatively large volume changes in the plastic zone.

Vibration induced by gears includes important data about gearbox condition. We can use dynamic modeling of gear vibration for increasing our information about vibration generating mechanisms in gearboxes and dynamic behavior of gearbox in the presence of some kind of gear defects. In this paper a six degree-of-freedom nonlinear dynamic model including different gear errors and defects is developed for investigation of effects of tooth localized defect and profile modifications on overall gear dynamics. Interactions between tooth modifications and profile error are studied and the role of profile modification in dynamic response when a localized defect is incurred by a tooth is shown. It is indicated that although profile modifications and profile errors are micro-geometrical, they have considerable effects on vibrations of gear pair. Especially for the case of root relieved teeth that is shown to be more effective in reduction of vibration in the presence of tooth localized defect. Finally, the simulation results are compared with results from literature and the model is verified.

When fluid passes a cavitator in the supercavitating flow, a supercavity forms behind the cavitator. Variation of the cavitator attack angle can influence theshape of the formed supercavity behind the cavitator. Consequently, it will affect the stability of supercavity behind the supercavitating cavitator with after body. In this study, a direct boundary element method (DBEM) is being formulated and numerically solved for3D unbounded potential flowspassing supercavitating bodies of revolution at different attack angles. In the analysis of potential flows passing supercavitating bodies at non-zero attack angles, a cavity closure model must be employed in order to close the mathematical formulationand guarantee the solution uniqueness. In the present study, we employ modified Riabouchinsky closure model. Since the location of the cavity surface is unknown at prior, an iterative scheme is used and for the first stage, an arbitrary cavity surface is assumed. The flow field is then solved and by an iterative process, the location of the cavity surface is corrected. Upon convergence, the exact boundary conditions are satisfied on the body-cavity boundary. A powerful CFD codeis developed to solve the 3D supercavitating flows behind all types of axisymmetric cavitators (such as disk, cone, etc) at zero and non-zero attack angles. The predictions of the CFD code are compared with those generated by verified existing data. The predictions of the code for supercavitating cones and disks seem to be excellent. Using the obtained data from CFD code, we investigate the supercavity shapesand corresponding stability at different attack angles with a fixed cavitation number.

Convective flow and heat transfer in an inclined channel bounded by two rigid plates is studied, where the lower plate is fixed and upper plate is moving with a constant velocity. One of the regions filled with clear viscous fluid and the other region filled with the porous matrix saturated with a viscous fluid different from the fluid in the first region are considered. The coupled nonlinear equations are mainly solved numerically using finite difference method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Both the velocity and temperature profiles enhance as the values of buoyancy parameter GP, height ratio h, Brinkman number Br, density ratio n and thermal expansion ratio b increase but reduce as the values of porous parameter σ, viscosity ratio λand thermal conductivity ratio λT increase. The Nusselt numbers at upper plate diminish as GP, h and Br increase, whereas they increase as σ, λ and λT increase. The lower plate Nusselt numbers are reversely affected by the relevant parameters. The effect of σ and GP on shear stress profiles are drawn and discussed.

Heterogeneous asphalt mixture is treated as a two-phase composite consisting of asphalt mastic, namely a mixture of asphalt and fine aggregates, and coarse aggregates in this paper. A novel three-dimensional (3D) random modeling frame for asphalt mixture is developed, and as its applications, some numerical samples involving various polyhedric coarse aggregates with given gradations are generated. Viscoelastic asphalt mastic is simply characterized by the generalized Maxwell model whose parameters are determined by fitting the uniaxial compressive creep experimental data of asphalt mastic. After validation, the 3D random numerical samples are used to perform a series of numerical experiments in order to evaluate the influences of coarse aggregate distribution, content, average size, size deviation, shape and loading rate on the mechanical behaviors of asphalt mixture quantitatively. Finally, some important conclusions are given.

In this paper, based on the viscoelastic theory, the creep buckling and post-buckling behaviors of a viscoelastic functionally graded material (FGM) cylindrical shell with initial deflection subjected to a uniform in-plane load are investigated. The material properties of the viscoelastic FGM cylindrical shell are assumed to vary through the structural thickness according to a power law distribution of the volume fraction of constituent materials and Poisson's ratio is assumed as a constant. Considering the transverse shear deformation and geometric nonlinearity, the constitutive relation of the viscoelastic FGM cylindrical shell is established. By means of the Newton-Newmark method and the Boltzmann superposition principle, the problem for the creep buckling and post-buckling of the FGM cylindrical shell is solved. The numerical results reveal that the transverse shear deformation, volume fraction and geometric parameters have significant effects on the creep buckling and post-buckling of the viscoelastic FGM cylindrical shell.

A numerical study is carried out to study the effects of variable fluid properties on the boundary layer flow and heat transfer of a nanofluid at a flat sheet. The effects of Brownian motion, thermophoresis and viscous dissipation due to frictional heating are also considered. The temperature-dependent variable fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function and a linear function of temperature. Using a similarity transformation, the governing non-linear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and these equations are solved numerically by Keller-Box method. Velocity, temperature, and nanoparticles volume fraction profiles are presented and analyzed for several sets of values of the governing parameters; namely, variable fluid viscosity, variable thermal conductivity, Brownaian motion, thermophoresis and plate-velocity parameters with changes in the Prandtl and Schmidt numbers. It is observed that there is an increase in the skin friction in the upstream movement of the plate: But quite the opposite is true in the downstream movement of the plate. Also, the effect of the Schmidt number and the Brownian motion parameter is to reduce the Sherwood number, where as the effect of thermophoresis parameter is to enhance it.

In this paper, the deflection, natural frequency and damping quality factor of a viscoelastic microplate under an electrostatic actuation are investigated. The microplate is assumed as a CNT-reinforced nanocomposite microplate, and an electrostatic actuation is applied on it. The nonlinear equations of motion are derived using the Von-Karman plate theory, and the Kelvin-Voigt viscoelastic model. In order to obtain the material properties of the nanocomposite microplate, the Eshelby–Mori–Tanaka method is implemented. The static pull-in instability of the microplate is obtained. It is shown that the nanocomposite microplate can both increase the deflection and natural frequency of the micro devices. So, one may have a nanocomposite microplate with the same deflection of the SiO2 microplate, while its frequency would be 1.45 times of the SiO2 microplate. This characteristic is highly desirable in microswitches. Also, it is shown that the damping quality factor of the nanocomposite microplate is much greater than SiO2 microplate. This fact limits the implementation of a nanocomposite microplate as a vibrating element of the micro devises. So, there are great beneficial static and frequency response characteristics for nanocomposite microplates. But, it is not recommended for microresonators due to high damping characteristics.

This paper presents the flow structure under a partially inundated bridge deck measured by using particle image velocimetry (PIV) and flow visualization techniques. The approaching flow was subcritical having Froude number F in the range 0.12 ∼ 0.55. The proximity ratio Pr (= ratio of clearance below the bridge deck h to the total depth of deck D) was varied from 0.57 to 2. Depending upon the Froude number F and proximity ratio Pr, four types of flow structures under the bridge deck were recognized. In flow Type I, the water surface elevation on the downstream side of bridge deck is slightly lower than the counterpart on the upstream side, and the shear layer formed at the bottom of upstream girder continuously fluctuates and touches soffit of all girders. In the case of flow Type II, the water surface on downstream side of bridge deck is lower than that on the upstream side and the shear layer originating from the upstream girder impinges near the third cavity between girders. However, in both the cases, the cavities between the girders are completely occupied by vortices. On the contrary, in the cases of flow Type III and flow Type IV, the flow is separated from the upstream girder edge. However, in flow Type III, the separated flow impinges on successive girders and cavities are partially filled by water; while in flow Type IV, the flow is totally separated from the deck bottom like orifice flow. The phenomena of vortex formation within the cavities are discussed for the cases of flow Type I and flow Type II. Also, for the vertical distribution of mean streamwise velocity in the shear layer below bridge deck, the nonlinear regression equations are developed. Using the distributions of measured mean streamwise velocity within the shear layer below the bridge deck at different streamwise distances, the similarity profile is obtained. The mean velocity deficit (usl – usu) and representative thickness bs are considered as the appropriate characteristic velocity and length scales for developing similarity profile. The proposed characteristic scales provided unique similarity profiles having promising regression coefficient. The similarity profile proposed is suitable for more general case of bridge deck having different bridge girders and even for rectangular block without girder. Further, the turbulence characteristics for the flow below the bridge deck are also presented.

In this paper, single-phase laminar forced convection of nanofluids flow over a 2D horizontal backward facing step (BFS) subjected to bleeding condition (suction/blowing) is investigated numerically. The continuity, momentum and energy equations are solved by computational fluid dynamic (CFD) technique, while the SIMPLE algorithm is employed for pressure-velocity coupling. Various volume fractions of nano-particles are dispersed in a base fluid (water) to produce different types of nanoflouids. In each test case, the velocity and temperature fields are computed to verify the hydrodynamic and thermal behaviors of convective system. Besides, the distributions of Nusselt number and friction coefficient at the stepped wall are obtained. Comparison between the present numerical results with experiment shows a good consistency.

In this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.

This article describes the boundary layer flow and heat transfer in a second grade fluid over a stretching sheet. Heat transfer analysis is carried out in the presence of a Newtonian heating. The partial differential systems have been transformed into the ordinary differential systems by appropriate relations. Homotopy analysis method (HAM) is used for the solutions. Graphical and tabulated results are presented to see the significance of influential parameters on the velocity and temperature fields. It is seen that temperature profiles and heat transfer rate significantly increase by increasing the conjugate parameter (γ) for Newtonian heating.