Eigenvibrations of a bar with elastically attached load

We study the problem on the eigenvibrations of a bar with an elastically attached load. The problem is reduced to finding the eigenvalues and eigenfunctions of an ordinary secondorder differential problem with a spectral parameter nonlinearly occurring in the boundary condition at the load attachment point. We prove the existence of countably many simple positive eigenvalues of the differential problem. The problem is approximated by a grid scheme of the finite element method. We study the convergence and accuracy of the approximate solutions.     

Elastic-plastic states of a rotating inhomogeneously heated strain hardening hollow shaft

Based on Tresca's yield criterion and the flow rule associated with it, the behaviour of a linearly strain-hardening elastic-plastic hollow shaft subject to a positive radial temperature gradient and monotonously increasing angular speed is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Frequency analysis of rotating truncated conical shells using the Haar wavelet method

In this study, we present an analysis of the frequency characteristics of rotating truncated conical shells using the Haar wavelet method. Based on the Love first-approximation theory, the governing equations are formulated by considering the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotation. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. By considering the boundary conditions, the eigenvalue equation is obtained to determine the vibration behaviors of rotating conical shells. To validate the current analysis, the results obtained by the proposed method are compared with those reported previously, where the agreement is very good. Finally, we investigate the effects of the geometrical parameters, rotation speed, and boundary conditions on the vibration characteristics of rotating conical shells and the results are presented.     

Occurrence of Taylor vortices in the flow between two rotating conical cylinders

The behavior of the flow between two coaxial conical cylinders with the inner one rotating and the outer one stationary is studied numerically. Special attention is paid to the occurrence of Taylor vortices in basic flow and unsteady helical vortices. It is found that, in basic flow, the vortices occur in the direction toward smaller radius, while toward bigger radius in unsteady helical vortices; moreover, the unsteady helical vortices can coexist with unstable steady Taylor vortices. The results suggest that the behavior of conical flow is dominated by a competition between the meridional flow and radial flow. The effect of meridional flow is most significant at small apex angle or in basic flow and helical vortices, while the radial flow dominates the structure at larger apex angle or in steady vortical flow. In order to get better understanding the competition and the transition of Taylor–Couette flow to conical flow, a velocity angle related to velocity components is defined, and the pattern evolution of velocity, streamlines and the velocity angle are examined with respect to apex angle, as well as Reynolds number. Finally, the statistical properties of turbulent conical flow are investigated.     

A cohomology attached to a function

In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and we prove that it satisfies both the excision and the Mayer-Vietoris axioms. For a regular function we show that the cohomology is related to the de Rham cohomology. Finally, we use it to give a new proof of a well-known result of A. Dimca [Compositio Math. 76 (1990) 19-47] in complex analytic geometry.     

Numerical computation of end plate effect on Taylor vortices between rotating conical cylinders

End plate effect on Taylor vortices between rotating conical cylinders is studied by numerical method in this paper. We suppose that the inner cone rotates together with the end plate at the top and the outer one as well as the end plate at the bottom remains at rest. It is found that the instability sets in at a critical Reynolds number about Re = 80. Increase Re to about Re = 200 the first single clockwise vortex is formed near the top of the flow system. Further increase Re to about Re = 440 another clockwise vortex is formed under the first one. At about Re = 448 the third vortex is formed which rotates in counterclockwise direction between the first two vortices. With increasing of Re the process continues. Finally, a configuration is obtained with an odd number of vortices in the annulus at about Re = 700, which confirms the experimental observation. Moreover, the local extreme values of pressure and velocity are achieved at the adjacent lines between neighboring vortices or at the medium lines of vortices. The effect of gap size on vortices is also considered. It is shown that the number of vortices increases with decreasing of the gap size and the end plates play an important role in the parity of the number of the vortices.     

Analytic discs attached to a generating CR-manifold

Perturbations by analytic discs along generating CR-submanifolds of Cⁿ are considered. In the case all partial indices of a closed pathp in a generating CR-fibration {M(ξ)}_ξ∈∂D are greater or equal to −1 we can completely parametrize all small holomorphic perturbations of the pathp along the fibration {M(ξ)}_ξ∈∂D . In this case we also study the geometry of perturbations by analytic discs and their relation to the conormal bundle of the fibration.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part II: Nonlinear system simulation and control

As was stated in Part I, the linear control models of a radically rotating elastic rod in all the analysis and design procedures for lead with closed-loop system compensation is presented. For a given linear system model, if the model is accurate, it will be accurate only over a very limit range of operation of the system. However, all the effort of design comes to be meaningful until it is tested using the nonlinear system model. On the other hand, the response of the nonlinear system model will not be as good as that of the linear model. In fact, some iterations on the design and on improving the design based-model are often needed before there is even a resemblance between the linear model response and the nonlinear system response. The present paper is a continuation of [1] and nonlinear control system simulation and a tuning process are presented. While almost all design procedures for physical system contain some tuning process, the development of an analytic design procedure for models of distributed-parameter control system can be evidently shown through this paper.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part I: A unified approach to the design of Llnear control system

Due to difficulties in modeling and poor knowledge of parameters, the behavior of flexible structures is subject to significant uncertainty. Hence it is essential that the control system provide an absolutely stable property in the presence of large variations. Over the years, many control laws—proportion and derivative (PD) control, nonlinear, linear-quadratic, adaptive, and linear quadratic Gaussian (LQG)—have been synthesized for flexible structures. The most commonly applied are the LQG controllers. In spite of its attractive qualities, the LQG controller is sensitive to parameter variations, and therefore its performance will deteriorate when the payload or typical parameters of the system vary with time. At the same time, the LQG controller does not guarantee general stability margins, and this is, perhaps, its main drawback. On the other hand, the PD is one kind of controller that ensures system stability to parameter variations within a certain bound. But a problem with the PD controller is evident; when high-frequency noise is present in the system, this noise will be amplified by the PD controller, which is generally unacceptable. In this paper, instead of using a PD controller, a passive lead compensator is employed, so that

• 1.(1) no additional power supplies are required and
• 2.(2) noise due to differentiation is reduced.

This lead compensator, together with a composite control strategy designed by the most popularly used sensors, potentiometer and tachometer, for the corresponding closed-loop system, has been shown with very good agreement in terms of system performance requirement. For the design of control system, it is practical to first design the controller based on the linear system model by neglecting the nonlinearities of the system. In Part I, the lead compensator, together with complementary control strategy and computer simulation modeling for a rotating flexible structure, with particular application to elastic rod system, is presented for the linear control system. Then the designed controller is applied to the nonlinear system model for evaluation and redesigned by computer simulation. This will be presented in Part II.     

A Lie algebra attached to a projective variety

Abstract. Each choice of a K?hler class on a compact complex manifold defines an action of the Lie algebra sl(2) on its total complex cohomology. If a nonempty set of such K?hler classes is given, then we prove that the corresponding sl(2)-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori, hyperk?hler manifolds and flag varieties. We pay special attention to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra. Oblatum 21-V-1996 & 15-X-1996     

Regularity of discs attached to a submanifold ofC n

Letp be an analytic disc attached to a generating CR-submanifoldM of C ⁿ . It is proved that some recently introduced conditions onp andM which imply that the family of all smallC ^α holomorphic perturbations ofp alongM is a Banach submanifold of (A^α(D))ⁿ are equivalent. These conditions are given in terms of the partial indices of the discp attached toM and “holomorphic sections” of the conormal bundle ofM along p(∂D). Also, a sufficient geometric conditionon p andM is given so that the family of all smallC ^α holomorphic perturbationsof p alongM, fixed at some boundary point, is a Banach submanifold of (A ^α (D))ⁿ.     

Spectra of generalized Bethe trees attached to a path

A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let P_m be a path of m vertices. Let {B_i:1?i?m} be a set of generalized Bethe trees. Let P_m{B_i:1?i?m} be the tree obtained from P_m and the trees B₁,B₂,…,B_m by identifying the root vertex of B_i with the i-th vertex of P_m. We give a complete characterization of the eigenvalues of the Laplacian and adjacency matrices of P_m{B_i:1?i?m}. In particular, we characterize their spectral radii and the algebraic conectivity. Moreover, we derive results concerning their multiplicities. Finally, we apply the results to the case B₁=B₂=…=B_m.     

Long-wave dispersion phenomena in a layer subject to elastically restrained boundary conditions

A generalisation of the usual free and fixed-face boundary conditions for an elastic layer is considered. Specifically, this is in the context of a linear isotropic elastic layer and involves an investigation into long-wave motion. Elastically restrained boundary conditions are introduced, with both a numerical investigation and a multi-parameter asymptotic analysis employed to elucidate dispersion phenomena in a layer subject to such boundary conditions. The characteristics of mode transformations associated with the change from traction-free to fixed-face boundary conditions are described, focusing particularly on the fundamental modes which are known to not occur in the case of fixed faces. All possible asymptotic regimes are grouped into six classes, with the corresponding expansions of frequency in respect of wave number derived.     

Existence of energy minimizing vortices attached to a flat-top seamount

The existence of an energy minimizer relative to a class of rearrangements of a given function is proved. The minimizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable anticyclonic vortices with cyclonic potential vorticity over a seamount, and a corresponding family of cyclonic vortices with anticyclonic potential vorticity over a localized depression. The seamount is described by a characteristic function (corresponding to a flat top) with arbitrary shape.     

Heat transfer due to the flow through a conical tube

Résumé On étudie la distribution de la température dans un fluide visqueux incompressible s'écoulant dans un tube conique. On fait également la comparaison de la distribution de température entre deux parois inclinées non-parallèles à celle du tube conique précédemment étudiée.     

On a series of Koecher-Maass type attached to Siegel cusp forms

Under the hypothesis of the Resnikoff-Saldaña conjecture, we give a precise formula for the abscissa of convergence of a series of Koecher-Maass type attached to a Siegel cusp form of arbitrary genus.