Some aspects of control systems as dynamical systems

Linear control semigroupsL=Gl(d,R) are associated with semilinear control systems of the form whereA:R ^m gl(d,R) is continuous in some open set containingU. The semigroupL then corresponds to the solutions with piecewise constant controls, i.e., L acts in a natural way onR ^d {0}, on the sphereS ^d–1, and on the projective spaceP ^d–1. Under the assumption that the group generated byL in Gl(d,R) acts transitively onP ^d–1, we analyze the control structure of the action ofL onP ^d–1: We characterize the sets inP ^d–1, where the system is controllable (the control sets) using perturbation theory of eigenvalues and (generalized) eigenspaces of the matrices g L For nonlinear control systems on finitedimensional manifoldsM, we study the linearization on the tangent bundleTM and the projective bundleP M via the theory of Morse decompositions, to obtain a characterization of the chain-recurrent components of the control flow onU×PM. These components correspond uniquely to the chain control sets onP M, and they induce a subbundle decomposition ofU×TM. These results are used to characterize the chain control sets ofL acting onP ^d–1 and to compare the control sets and chain control sets.Research supported in part by NSF Grant DMS 8813976 and DFG Grant Co 124/6-1.     

The gross hydrostatic-pressure effect as related to foil and wire strain gages

An analysis of gross pressure effect for strain gages is presented. This is defined as the difference between the predicted hydrostatic strain and the experimental strain. Values of the theoretical strain per unit pressure are based on the Voigt-Reuss-Hill approximation using published values of elastic moduli and compliances. These theoretical values are adjusted by the pressure effect calculated from an equation based on the assumption that the pressure effect is independent of the elastic properties of the substrate. The modified values of theoretical strain per unit pressure are then compared with the experimentally observed values. The differences are small except for the substrate materials of zinc, cadmium and lead. Experimental pressure-strain data are presented for constantan foil gages mounted on tungsten, copper, tin, molybdenum, titanium, cadmium, brass, zinc and lead as well as constantan wire gages mounted on steel, aluminum and magnesium for hydrostatic pressures up to 140 ksi. Data for foil and wire gages mounted with various adhesives are presented and show that the adhesive or backing materials appear to have a relatively minor effect on the over-all gage performance.     

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh's quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.     

Sensitivity matrices as keys to local structural system properties of large-scale nonlinear systems

Nonlinear Dynamics - Sensitivities are shown to play a key role in a highly efficient algorithm, presented in this paper, to establish three fundamental structural system properties: local...     

Doubly nonlinear parabolic-type equations as dynamical systems

In this paper, we study a class of doubly nonlinear parabolic PDEs, where, in addition to some weak nonlinearities, also some mild nonlinearities of porous media type are allowed inside the time derivative. In order to formulate the equations as dynamical systems, some existence and uniqueness results are proved. Then the existence of a compact attractor is shown for a class of nonlinear PDEs that include doubly nonlinear porous medium-type equations. Under stronger smoothness assumptions on the nonlinearities, the finiteness of the fractal dimension of the attractor is also obtained.     

Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems

The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are Used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.     

Relative permeability and capillary pressure functions of porous media as related to the displacement growth pattern

Visualization experiments of the unsteady immiscible displacement of a fluid by another are performed on glass-etched pore networks of well-controlled morphology by varying the fluid system and flow conditions. The measured transient responses of the fluid saturation and pressure drop across the porous medium are introduced into numerical solvers of the macroscopic two-phase flow equations to estimate the non-wetting phase, k_rnw, and wetting phase, k_rw, relative permeability curves and capillary pressure, P_c, curve. The correlation of k_rnw, k_rw, and P_c with the displacement growth pattern is investigated. Except for the capillary number, wettability, and viscosity ratio, the immiscible displacement growth pattern in a porous medium may be governed by the shear-thinning rheology of the injected or displaced fluid, and the porous sample length as compared to the thickness of the frontal region. The imbibition k_rnw increases as the flow pattern changes from compact displacement to viscous fingering or from viscous to capillary fingering. The imbibition k_rw increases as the flow pattern changes from compact displacement or capillary fingering to viscous fingering. As the shear-thinning behaviour of the NWP strengthens and/or the contact angle decreases, then the flow pattern is gradually dominated by irregular interfacial configurations, and the imbibition k_rnw increases. The imbibition P_c is a decreasing function of the capillary number or increasing function of the injected phase viscosity in agreement with the linear thermodynamic theory.     

Global stability of equilibrium manifolds,and “peaking” behavior in quadratic differential systems related to viscoelastic models

We study a model inspired by the Oldroyd-B equations for viscoelastic fluids. The objective is to better understand the nonlinear coupling between the stress and velocity fields in viscoelastic flows, and thus gain insight into the reasons that cause the loss of accuracy of numerical computations at high Weissenberg number. We derive a model system by discarding the stress-advection and stress-relaxation terms in the Oldroyd-B model. The reduced (unphysical) model, which bears some resemblance to a viscoelastic solid, only retains the stretching of the stress due to velocity gradients and the induction of velocity by the stress field. Our conjecture is that such a system always evolves toward an equilibrium in which the stress builds up such to cancel the external forces. This conjecture is supported by numerous simulations. We then turn our attention to a finite dimensional model (i.e., a set of ordinary differential equations) that has the same algebraic structure as our model system. Numerical simulations indicate that the finite-dimensional analog has a globally attracting equilibrium manifold. In particular, it is found that subsets of the equilibrium manifold may be unstable, leading to a “peaking” behavior, where trajectories are repelled from the equilibrium manifold at one point, and are eventually attracted to a stable equilibrium point on the same manifold. Generalizations and implications to solutions of the Oldroyd-B model are discussed.     

The role of porous media in biomedical engineering as related to magnetic resonance imaging and drug delivery

Pertinent works associated with magnetic resonance imaging (MRI) and drug delivery are reviewed in this work to demonstrate the role of transport theory in porous media in advancing the progress in biomedical applications. Diffusion process is considered significant in many therapies such as delivering drugs to the brain. Progress in development of the diffusion equation using local volume-averaging technique and evaluation of the applications associated with the diffusion equation are analyzed. Tortuosity and porosity have a significant effect on the diffusion transport. Different relevant models of tortuosity are presented and mathematical modeling of drug release from biodegradable delivery systems are analyzed in this investigation. New models for the kinetics of drug release from porous biodegradable polymeric microspheres under bulk erosion and surface erosion of the polymer matrix are presented in this study. Diffusion of the dissolved drug, dissolution of the drug from the solid phase, and erosion of the polymer matrix are found to play a central role in controlling the overall drug release process. This study paves the road for the researchers in the area of MRI and drug delivery to develop comprehensive models based on porous media theory utilizing fewer assumptions as compared to other approaches.     

A novel rigid wheel for agricultural machinery applicable to paddy field with muddy soil

The working performance of agricultural machinery is largely determined by the walking performance of the wheel when driving in complex unstructured soil. However, the driving performance of existing wheels is not satisfactory for paddy field with muddy soil. The purpose of the current study is therefore to propose a novel rigid wheel for agricultural machinery which is applicable to paddy field with muddy soil. Firstly, a novel arc edge shaped wheel was designed based on the principles of mechanics on the ground. Then the driving performance of this arc edge shaped wheel was evaluated using FE modeling of interaction between rigid wheel and soil. Finally, the structure originally designed arc edge shaped wheel was improved according to FE modeling results, and this improved design was further evaluated by both FE simulation and prototype experiments. Both FE modeling and experimental results indicate that the improved arc edge shaped wheel proposed in this study has a good driving performance with regarding to wheel sinkage and soil reaction force. The proposed arc edge shaped wheel could be used as an effective component of rice harvester for paddy field with muddy soil.     

舰载旋转机械基础冲击响应建模和数值计算

针对舰载旋转机械的水下非接触爆炸冲击动力学响应问题,提出了一种基础冲击转子-轴承系统建模理论.结合牛顿运动定理、动量矩定理和Timoshenko梁理论,推导出了系统动力学微分方程,方程综合考虑了转子的旋转惯性力、剪切力、陀螺效应、轴向力、轴向扭矩以及轴承的油膜力.通过在时间域和空间域分别采用直接积分法和Galerkin...