Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H _∞ and H ₂ optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H _∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H ₂ optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H _∞ and H ₂ optimization procedures shows that for a beam under random force excitation, use of H₂ optimum parameters resulting in smaller mean square motion than the other optimization.     

A growth model for dynamic slugs in gas–liquid horizontal pipes

Long liquid slugs, with sizes reaching 500 pipe diameters or more, may form in gas–liquid horizontal pipe flow at intermediate liquid loadings. Such slugs cause serious operational upsets due to the strong fluctuations in flow supply and pressure. Therefore, predicting the transition from short (hydrodynamic) to long slug flow regimes may play a significant role in preventing or reducing the negative effects caused by the long slugs.     

Anti-wear beam effects on gas–solid hydrodynamics in a circulating fluidized bed

Anti-wear beams installed on water walls of circulating fluidized bed (CFB) boilers are one of the most effective ways to protect against water-wall erosion. Beam effects from, for example, beam size and superficial gas velocity were investigated on gas–solid hydrodynamics in a CFB test rig using CFD simulations and experimental methods. The downward flow of the wall layer solids is observed to be disrupted by the beam but is then restored some distance further downstream. When falling solids from the wall layer hit the anti-wear beam, the velocity of the falling solids decreases rapidly. A fraction of the solids accumulates on the beam. Below the beams, the falling solids have reduced velocities but upward-moving solids were observed on the wall. The effect of the beam increases with width and superficial gas velocity. Wear occurs mainly above the beam and its variation with width is different above to below the beam. There is an optimum width that, when combined with beam height, results in less erosion.     

An electron moiré method for a common SEM

In the electron moiré method, a high-frequency grating is used to measure microscopic deformation, which promises significant potential applications for the method in the microscopic analysis of materials. However, a special beam scanning control device is required to produce a grating and generate a moiré fringe pattern for the scanning electron microscope (SEM). Because only a few SEMs used in the material science studies are equipped with this device, the use of the electron moiré method is limited. In this study, an electron moiré method for a common SEM without the beam control device is presented. A grating based on a multi-scanning concept is fabricated in any observing mode. A real-time moiré pattern can also be generated in the SEM or an optical filtering system. Without the beam control device being a prerequisite, the electron moiré method can be more widely used. The experimental results from three different types of SEMs show that high quality gratings with uniform lines and less pitch error can be fabricated by this method, and moiré patterns can also be correctly generated.The project supported by the National Natural Science Foundation of China (10662005) and JSPS fellowship in Japan. The English text was polished by Keren Wang.     

Exact solutions and mathematical properties of boundary‐value problems for dynamic‐diffusion boundary layers

The paper studies boundaryvalue problems for dynamicdiffusion boundary layers occurring near a vertical wall at high Schmidt numbers and for dynamic boundary layers whose inner edge is adjacent to the dynamicdiffusion layers. Exact solutions for boundary layers at small and large times are derived. The wellposedness of the boundaryvalue problem for a steady dynamicdiffusion layer is studied.     

Nonlinear dynamic behavior of a clamped–clamped beam from BNC nanotube impacted by fullerene

Nonlinear Dynamics - We investigate the rational and semi-rational solutions of the integrable Kadomtsev–Petviashvili (KP)-based system, which appears in fluid mechanics, plasma physics, and...     

On constructing a Green’s function for a semi-infinite beam with boundary damping

The main aim of this paper is to contribute to the construction of Green’s functions for initial boundary value problems for fourth order partial differential equations. In this paper, we consider a transversely vibrating homogeneous semi-infinite beam with classical boundary conditions such as pinned, sliding, clamped or with a non-classical boundary conditions such as dampers. This problem is of important interest in the context of the foundation of exact solutions for semi-infinite beams with boundary damping. The Green’s functions are explicitly given by using the method of Laplace transforms. The analytical results are validated by references and numerical methods. It is shown how the general solution for a semi-infinite beam equation with boundary damping can be constructed by the Green’s function method, and how damping properties can be obtained.     

Rarefied gas flow in a channel with specular‐diffuse boundary conditions for arbitrary knudsen numbers. Onsager relations

The problem of a rarefied gas flow in a channel for arbitrary Knudsen numbers has been solved analytically for the first time in the case where the scattering of gas molecules on the channel walls can be described by speculardiffuse boundary conditions. The mean free path of gas molecules is assumed to be constant, i.e., the collision frequency is proportional to molecular velocity. The gas moves under the action of a streamwise temperature gradient. Exact relations for heat and mass fluxes and for meanmass velocity are obtained. It is shown that the Onsager relations are valid within the entire range of Knudsen numbers in the problem of heat and mass transfer in a channel. The dependence of heat and mass fluxes on the Knudsen number (channel thickness) is analyzed. A comparison with available results is performed.     

Equations of dynamics of a mixture composed of a gas and hollow selective‐permeable microspheres

Based on the laws of conservation of mass, momentum, and energy, equations of dynamics of multiphase systems, which are gas mixtures with hollow microspheres with selectively permeable shells, are obtained under the assumption of quasisteadiness of the process offilling the microspheres by the gas. Acoustic characteristics of the system composed of a uniform gas and hollow permeable microspheres are studied using a simplified (onevelocity and onetemperature) model. The frequency dependences of velocity and damping coefficient of sound are determined with regard for gas density (pressure) relaxation inside the microspheres.     

Delayed saturation controller for vibration suppression in a stainless-steel beam

This paper considers the effect of time delays on the saturation control of first-mode vibration of a stainless-steel beam. Time delay is commonly caused by measurements of the system states, transport delay, on-line computation, filtering and processing of data, calculating and executing of control forces as required in control processing. The method of multiple scales is employed to obtain the analytical solutions of limit cycles and their stability and to investigate the bifurcations of the system under consideration. All the predictions from analytical solutions are in agreement with the numerical simulation. The analytical results show that a delay can change the range of the saturation control, either widening or shrinking the effective frequency bandwidth. Thus, vibration control of a beam can be achieved using an appropriate choice of the delay in a self-feedback signal. From the examples illustrated, this paper provides a positive example that time delay can also be utilized to suppress vibration in systems when time delay cannot be neglected.     

Nonlinear dynamic analysis and sliding mode control for?a?gyroscope system

This paper employs differential transformation (DT) method to analyze and control the dynamic behavior of a gyroscope system. The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic, quasiperiodic, and chaotic responses of the center of gravity. Furthermore, the results reveal the changes which take place in the dynamic behavior of the gyroscope system as the external force is increased. The current analytical results by DT method are found to be in good agreement with those of Runge?CKutta (RK) method. In order to suppress the chaotic behavior in gyroscope system, the sliding mode controller (SMC) is used and guaranteed the stability of the system from chaotic motion to periodic motion. Numerical simulations are shown to verify the results. The proposed DT method and controlling scheme provide an effective means of gaining insights into the nonlinear dynamics and controlling of gyroscope systems.     

“Simple” solutions of the equations of dynamics for a polytropic gas

The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 5–12, March–April, 1999.     

Revised model coefficients for vibrational relaxation in a nitrogen–oxygen gas mixture

A numerical investigation of thermal non-equilibrium flows requires species specific relaxation rates, which are often calculated using the Landau–Teller model. This model requires the determination of collision specific relaxation times, which can be computed using Millikan and White’s empirical formula. The coefficients used in this formula for each specific collision pair form a set of coefficients, which are assessed here. The focus of the investigation lies on their performance in hypersonic low-temperature (300–2,500?K) flows that occur at shock-tunnel nozzle exits or in supersonic combustion ramjets (scramjets) before combustion. Two experimental validation cases are chosen; a shock-tunnel nozzle and a sharp cone in hypersonic cross-flow experiment. A comparison of the experimentally measured vibrational temperatures at the nozzle exit against numerical data shows large discrepancies for two commonly used coefficient sets. A revised set of coefficients is proposed that greatly improves the agreement between the numerical and experimental results. Furthermore, the numerically generated shock shape over the sharp cone using the revised set of coefficients correlates well with the experimental measurements.     

Multi-layer analytic solution for k-ω model equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics (CFD), the k-ω model has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting. Here, a multi-layer analytic expression is postulated for two lengths (stress and kinetic energy lengths), yielding an analytic solution for the k-ω model equations in pipe flow. Approximate local balance equations are analyzed to determine the key parameters in the solution, which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ω model, and hence the analytic construction is fully validated. The results provide clear evidence that the k-ω model sets in it a multilayer structure, which is similar to but different, in some insignificant details, from the Navier-Stokes (N-S) turbulence. This finding explains why the k-ω model is so popular, especially in computing the near-wall flow. Finally, the analysis is extended to a newly-refined k-ω model called the structural ensemble dynamics (SED) k-ω model, showing that the SED k-ω model has improved the multi-layer structure in the outer flow but preserved the setting of the k-ω model in the inner region.     

Local topography‐induced pressure gradient effects on the wake and power output of a model wind turbine

Wind-tunnel experiments were performed to study the effect of favorable and adverse constant pressure gradients (PG) from local changes in the topography right downwind of a model wind turbine. Particle image velocimetry was used to characterize the near and intermediate wake regions. We explored five scenarios, two favorable, two adverse PG, and a case with negligible PG. Results show that the PGs induce a wake deflection and modulate the wake. They imposed a relatively small impact on the turbulence kinetic energy and kinematic shear stress but a comparatively dominant effect on the bulk flow on the flow recovery. Based on this, a simple formulation is used to describe the impact of PG on the wake. We modeled the base flow through a linearized perturbation method; the wake is obtained by solving a simplified, integrated streamwise momentum equation. This approach reasonably estimated the flow profile and PG-induced power output variations.     

Exact solution of the capillary diffusion equation for a three‐component mixture

The paper gives an exact solution of the steady system of equations for stable threecomponent diffusion in the entire range of concentrations for a long capillary under a controlled capillary pressure differential. The solution allows one to calculate the distributions of component concentrations and mixture density along the capillary. It is shown that if the diffusion coefficients are markedly different, an extremum of mixture density can arise inside the capillary. In particular, if the density of the mixture in the upper flask is higher than that in the lower flask and the stratification of the system is generally stable, a region with a reverse density gradient that is unstable against gravity convection can appear inside the capillary. A comparison with experimental results shows that the resistance to gravity convection is disturbed when an extremum of mixture density arises in the channel during steady diffusion.     

A high-order theory for static–dynamic analysis of laminated plates using a special warping model

In this paper, special warping functions (dynamic modes) are used to develop a high-order theory for static–dynamic analysis of laminated plates. The dynamic modes take into account the difference of stiffness of each layer. Through comparison with elasticity solution of Pagano (1969), with the classical models (Bolle, 1947; Reissner, 1945, 1975, 1985; Mindlin, 1951), with the high-order theory of Lo et al. (1977) and the homogeneous warping theory of Hassis (2000), it is shown that the present theory correctly and simply models effects attainable only by high-order theories and sometimes not attainable by the homogeneous high-order theories.