DENSITY FUNCTIONAL FOR STRUCTURES OF COLLOIDS CONFINED IN A SLIT-LIKE PORE

A density functional theory is applied to calculating the local density profiles of colloids confined in a slit-like pore as well as the radial distribution functions of bulk colloids. The interaction between the colloidal particles is described using a hard-core Yukawa model. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu （2002） for the hard-core contribution and a corrected mean-field theory for the attractive contribution. Comparison with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of colloids in the vicinity of contact over the original mean-field theory. Both the present corrected theory and simulations suggest that there are depletion and desorption for the colloid with strong attraction between particles at low temperature.     

Understanding of the flow behaviour on a Helmholtz resonator excited by grazing flow

In this study, a large eddy simulation of the three-dimensional shear flow over a flow-excited Helmholtz resonator has been implemented. The simulations have been performed over a wide range of flow speeds to analyse the effect of the inlet flow properties on the excitation condition. For validation proposes, the results obtained from the numerical simulations have been compared with published experimental data and show that numerical modelling provides an accurate representation of the pressure fluctuations inside the cavity. The main objective of this paper is to gain an understanding of the flow features over a flow-excited Helmholtz resonator. To this end, using the numerical model, the interaction of a turbulent boundary layer with a Helmholtz resonator has been considered, and the characteristics of the flow inside the resonator and over the orifice for various flow conditions are also analysed.     

Dynamic analysis of a novel wide-tunable microbeam resonator with a sliding free-of-charge electrode

In this paper, a MEMS-based resonator with a novel effective stiffness tunability is presented. The performance of the proposed resonator is based on the transversal vibration of the two porous cantilever microbeams with a rectangular microplate at the end of the structure. The microplate as a free-of-charge slider electrode is in contact with two other fixed substrate electrodes via the thin layer of dielectric material. Applying a constant DC voltage to the two fixed electrodes leads to the movement of free electrons in the slider and eventually to the formation of two series capacitors. As a result, the slider meets a nonlinear electrostatic force proportional to the square of the applied DC voltage. It will act as a nonlinear spring with a tunable stiffness during the oscillation of the resonator. The coupled nonlinear equations governing the longitudinal and transversal vibration of the resonator are extracted in the presence of the nonlinear voltage-sliding spring. Its steady-state solution is obtained based on a physically based learning method that makes it possible to obtain frequency response for the first harmony as well as for the higher harmonies and to predict primary and secondary resonances in different harmonies of the response. The effect of the applied tuning DC voltage, the geometrical parameters of the resonator, and the cantilever's porosity on the dynamic response of the resonator are investigated. It is shown that the tuning stiffness of this voltage-sliding spring provides a highly effective solution to realize an extreme tunable range. In the end, a modified tunable structure is introduced in which the folded beams are replaced with common ones. The modified resonator by making the nonlinear behavior of the resonator least can improve its performance significantly.

     

A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.     

A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation

In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational approach. Two additional kinds of parameters, the higher-order nonlocal parameters and the nonlocal gradient length coefficients are introduced to account for the size-dependent characteristics of nonlocal gradient materials at nanoscale. To illustrate its application values, the theory is applied for wave propagation in a nonlocal strain gradient system and the new dispersion relations derived are presented through examples for wave propagating in Euler–Bernoulli and Timoshenko nanobeams. The numerical results based on the new nonlocal strain gradient theory reveal some new findings with respect to lattice dynamics and wave propagation experiment that could not be matched by both the classical nonlocal stress model and the contemporary strain gradient theory. Thus, this higher-order nonlocal strain gradient model provides an explanation to some observations in the classical and nonlocal stress theories as well as the strain gradient theory in these aspects.     

Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations

With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator(QCR) system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.     

Drive level dependency in quartz resonators

Common piezoelectric resonators such as quartz resonators have a very high Q and ultra stable resonant frequency. However, due to small material nonlinearities in the quartz crystal, the resonator is drive level dependent, that is, the resonator level of activity and its frequency are dependent on the driving, or excitation, voltage. The size of these resonators will be reduced to one fourth of their current sizes in the next few years, but the electrical power which is applied will not be reduced as much. Hence, the applied power to resonator size ratio will be larger, and the drive level dependency may play a role in the resonator designs.We study this phenomenon using the Lagrangian nonlinear stress equations of motion and Piola–Kirchhoff stress tensor of the second kind. Solutions are obtained using COMSOL for the AT-cut, BT-cut, SC-cut and other doubly rotated cut quartz resonators and the results compared well with experimental data. The phenomenon of the drive level dependence is discussed in terms of the voltage drive, electric field, power density and current density. It is found that the drive level dependency is best described in terms of the power density. Experimental results for the AT-, BT- and SC-cut resonators in comparison with our model results are presented. Results for new doubly rotated cuts are presented. The effects of spurious modes, quality factor and air damping on DLD are presented.     

Pressure drop prediction with a modified frictional-kinetic model for alumina in bypass pneumatic conveying system

A new frictional-kinetic model is proposed and modified for pressure drop prediction of alumina in a bypass pneumatic conveying system. This new model is based on the conventional Johnson–Jackson frictional-kinetic model. The critical value of solids volume fraction and maximum packing limit are modified based on the fluidized bulk density and tapped bulk density, respectively. In addition, an offset solid volume fraction is introduced into the frictional pressure model as well as into the radial distribution functions which represents the correction factors to modify the probability of collisions between particles when solid phase becomes excessively dense. For the application of the model, computational fluid dynamics (CFD) simulations were conducted by using kinetic theory, conventional frictional-kinetic model and modified frictional-kinetic model. The simulation results were then compared with the experimental results. It was found that the modified frictional-kinetic model showed the largest improvement on pressure drop prediction results compared with results obtained from applying the kinetic theory and the conventional frictional-kinetic model, especially for denser flows with low air mass flow rates and high solid loading ratios (SLR). In addition, the solids volume investigation of CFD simulations shows a strong comparison to the actual flow conditions in the pipe, as transient slug type flow of alumina is observed.     

Studying thin film damping in a micro-beam resonator based on non-classical theories

In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The micro-gap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of pre-dicting the size dependence behaviors of the micro-beam, and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theo-ries. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the res-onator have also been investigated.     

Analytical Study of Quasilinear Self-Oscillations in the Helmholtz Resonator

A quasilinear model of the self-oscillations in the Helmholtz resonator is developed. The conditions of existence, uniqueness, and stability of periodic solutions are determined using the Lyapunov-Poincaré, local integral manifold, and averaging methods. In the first approximation, the basic parameters of the self-oscillations are calculated and their qualitative features are studied. A thermodynamic interpretation of the gas self-oscillations in the resonator is given.     

A large strain plasticity model for anisotropic materials — composite material application

In this work a generalized anisotropic model in large strains based on the classical isotropic plasticity theory is presented. The anisotropic theory is based on the concept of mapped tensors from the anisotropic real space to the isotropic fictitious one. In classical orthotropy theories it is necessary to use a special constitutive law for each material. The proposed theory is a generalization of classical theories and allows the use of models and algorithms developed for isotropic materials. It is based on establishing a one-to-one relationship between the behavior of an anisotropic real material and that of an isotropic fictitious one. Therefore, the problem is solved in the isotropic fictious space and the results are transported to the real field. This theory is applied to simulate the behavior of each material in the composite. The whole behavior of the composite is modeled by incorporating the anisotropic model within a model based on a modified mixing theory.     

A transmutation approach to underwater sound propagation

A hybrid approach is used to combine analytical computations that model the major features of the ocean with symbolic and numerical computations that model the secondary features. Integral operators are used to transmute solutions of the Helmholtz equation with constant coefficients into solutions of the Helmholtz equation with variable coefficients. The kernels of these operators satisfy certain hyperbolic partial differential equations and characteristics conditions. The transmutations preserve some, but not all, of the boundary conditions given for the Helmholtz equation.     

带冷却气流的亥姆霍兹共振器的声类比模型

亥姆霍兹共振器(HR)作为典型的被动消声装置,常被安装于航空发动机和燃气轮机的燃烧室上用以吸收噪声进而抑制燃烧热声振荡.在实际应用中,为防止燃烧室内高温气体损坏HR,常引入冷却气流从HR的背部空腔通过其颈部流入燃烧室,以保护HR.该冷却气流的温度一般显著低于燃烧室内的燃气温度.将这样的HR安装到燃烧室上时,该温差可能影...     

Design for a high energy density Kelvin–Helmholtz experiment

While many high energy density physics (HEDP) Rayleigh–Taylor and Richtmyer–Meshkov instability experiments have been fielded as part of basic HEDP and astrophysics studies, not one HEDP Kelvin–Helmholtz (KH) experiment has been successfully performed. Herein, a design for a novel HEDP X-ray driven KH experiment is presented along with supporting radiation-hydrodynamic simulation and theory.     

核燃料裂变气体辐照肿胀的相场模拟与分析

采用修正的Cahn-Hilliard方程研究辐照下核材料中气泡微结构演化过程,采用基于经典形核理论的形核算法模拟空洞形核过程,分析微结构对核材料力学性质的影响,着重考察了气体辐照肿胀应变的演化规律．分析了不同辐照强度下气泡密度和气体辐肿胀应变的演化规律,并与实验结果进行对比．     

Temperature-rate dependent constitutive theory in thermo-viscoplastic media

In this paper, a temperature-rate dependent constitutive theory in thermo-viscoplastic media is proposed. On the basis of Clausius-Duhem (C-D) entropy inequality and the generalized Helmholtz free energy defined by Green and Lindsay, it is shown under some reasonable assumptions that the constitutive models in classical thermo-plasticity theory can be extended to the temperature-rate dependent (TRD) media provided that the temperature-rate effect is taken into account and the absolute temperatureT taken as an independent constitutive variable is replaced by coldness function T^* introduced by Müller, and discussed in detail by Ru and Duan.     

SELF-EXCITED VIBRATION OF A CONTROL VALVE DUE TO FLUID–STRUCTURE INTERACTION

In this paper, the mechanism causing self-excited vibration of a piping system is determined using a dynamic model which couples the hydraulics of a piping system with the structural motion of an air-operated, plug-type automatic control valve. In the dynamic model developed, the structural system consists of a valve spring–mass system, while the fluid system consists of a pump, upstream piping, control valve and downstream piping. The coupling between the structural and the fluid systems at the control valve is obtained by making the fluid flow coefficient at the control valve to be a function of valve plug displacement, and by making the valve plug displacement to be a function of fluid pressure and velocity. The dynamic model presented in this paper, for the first time, considers compressibility of the fluid in both the upstream and downstream piping. The dynamic model presented was benchmarked against in situ measurements. The data used for the benchmarking are provided in the paper. A review of the numerical results obtained indicates that the self-excited vibration occurs due to the coincidence of water hammer, acoustic feedback in the downstream piping, high acoustic resistance at the control valve, and negative hydraulic stiffness at the control valve.     

A general solution to some plane problems of micropolar elasticity

We obtain a general solution to the field equations of plane micropolar elasticity for materials characterized by a hexagonal or equilateral triangular structure. These materials exhibit 3-fold symmetry in the plane and the elastic response is isotropic. Utilizing two displacement potential functions, the solution is obtained in terms of two analytic functions and a third function satisfying the modified homogeneous Helmholtz equation. Expressions for the two-dimensional components of displacement, stress, and couple stress, along with the resultant force on a contour, are presented. We observe that micropolar effects are most significant in material regions subjected to large deformation gradients. Specific results are presented for the classical crack problem, the half plane loaded uniformly on the surface, Flamant's problem, and the circular cylinder compressed by equal and opposite concentrated forces.     

Persoz’s gephyroidal model described by a maximal monotone differential inclusion

Persoz’s gephyroidal model, which consists of elementary rheological models (dry friction element and linear spring), can be covered by the existence and uniqueness theory for maximal monotone operators. Moreover, classical results of numerical analysis allow one to use a numerical implicit Euler scheme, with convergence order of the scheme equal to one. Some numerical simulations are presented.