The dynamics of a spherical pendulum with a vibrating suspension

The motion of a spherical pendulum whose point of suspension performs high-frequency vertical harmonic oscillations of small amplitude is investigated. It is shown that two types of motion of the pendulum exist when it performs high-frequency oscillations close to conical motions, for which the pendulum makes a constant angle with the vertical and rotates around it with constant angular velocity. For the motions of the first and second types the centre of gravity of the pendulum is situated below and above the point of suspension, respectively. A bifurcation curve is obtained, which divides the plane of the parameters of the problem into two regions. In one of these only the first type of motion can exist, while in the other, in addition to the first type of motion, there are two motions of the second type. The problem of the stability of these motion of the pendulum, close to conical, is solved. It is shown that the first type of motion is stable, while of the second type of motion, only the motion with the higher position of the centre of gravity is stable.     

An alternative approach for chaos: A plane pendulum with oscillating torque

The shooting method is applied to obtain chaotic motions for a pendulum with a oscillatory torque excitation on its support. It shows that if the pendulum is placed at certain spots, the corresponding motion will become chaotic. It proves the coexistence of uncountably many non-periodic motions and countably many periodic motions of the pendulum.     

Chelomei's problem of the stabilization of a statically unstable rod by means of a vibration

Chelomei's problem of the stabilization of an elastic, statically unstable rod by means of a vibration is considered. Formulae for the upper and lower critical frequencies for the stabilization of the rod are obtained and analysed. It is shown that, unlike the high-frequency stabilization of an inverted pendulum with a vibrating suspension point, a rod is stabilized by frequencies of a periodic force of the order of the fundamental frequency of the transverse oscillations of the uncompressed rod lying in a certain range.     

On modules with the Kulikov property and pure semisimple modules and rings

For an R-module M let σ[M] denote the category of submodules of M-generated modules. M has the Kulikov property if submodules of pure projective modules in σ[M] are pure projective. The following is proved: Assume M is a locally noetherian module with the Kulikov property and there are only finitely many simple modules in σ[M]. Then, for every n ε , there are only finitely many indecomposable modules of length n in σ[M].

With our techniques we provide simple proofs for some results on left pure semisimple rings obtained by Prest and Zimmermann-Huisgen and Zimmermann with different methods.     

银行存款模型及应用分析

近年来,越来越多的国际知名企业都认识到了从原始数据中寻找规律对决策管理的重要性.一些顶尖级的银行产品企业,象IBM,Oracle,Informix和Sybase等,已经开发了许多用于银行数据挖掘的软件产品,并为国际上的一些著明银行建立了高精度的统计模型以支持银行管理.存款是银行评价业绩的一项重要指标.建立高精度的存款模型有利于银行的日常资金管理,能提高银行的资金利用率,降低成本等.本文以国内某大城市两大银行的实际业务数据为背景,给出了银行存款模型的建立过程,并分析了模型的应用.本文的一些有趣结果对时间序列建模有一定的启示.     

Effect of vertical vibrations on a two-layer system with a deformable interface

The effect of single- and two-frequency vibrations on the behavior of a system consisting of two homogeneous viscous fluids bounded by rigid walls is analyzed. It is assumed that the system as a whole is under vertical vibrations obeying a certain law. An eigenvalue problem is obtained in order to analyze the stability of the relative equilibrium. The case of finite frequencies and arbitrary modulation amplitudes is treated along with the case of high frequencies and small modulation amplitudes. In the former case, the parametric resonance domains are examined depending on the parameters of the system. In the latter case, the high-frequency vibration is shown to create effective surface tension, thus flattening the interface, and can suppress instability when the heavy fluid is over the light one.     

Reduction of vibration due to change in mass configuration

The paper concerns the elimination of vibration due to changing the centre of gravity of a system. It is shown that the damping effect can be generated in an oscillating pendulum by a continuous motion of an auxiliary mass. A simple system in form of a variable length pendulum is considered. It is seen that if the pendulum length function is correctly chosen, the Coriolis force will cause additional damping effect in the system. The Floquet method is used to investigate the linear system stability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shaking table tests of a model-scale building with 2DOF pendulum mass damper

In this paper, the numerical and experimental studies of a tall building's model with 2DOF pendulum mass damper (PMD) are considered. It is assumed that the model excitation is in the form of horizontal and/or torsional motion of the ground caused by earthquake. The construction consists of the main system (tall building's model) and a double pendulum mass damper, which is attuned to the first (bending) and the second (torsional) eigenfrequencies of the main structure. The analysis focuses on reduction of structure vibration caused by horizontal or torsional component of ground motions. Therefore, results presented in this work show efficiency of 2DOF PMD for vibration reduction. The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model-scale building with 2DOF PMD. Model consists of twenty five recurrent storeys (height 2.5m) with a PMD located on the highest one. Shaking table device is used to simulate an earthquake excitation in horizontal and torsional component, independently. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Controllable centrifugal pendulum

The combustion engine produces huge rotational periodic vibrations that could affect the acoustic comfort of the vehicle. An isolating device is placed after the engine and filters the oscillations in order to deliver a clean averaged torque to the rest of the drive train. The centrifugal pendulum is widely used even though its passive version can quench only one order of vibration. We propose in [3] a design allowing to control the tuning of the pendulum. An actuator delivers an additional force that completes the centrifugal force. This is equivalent to changing the stiffness of a classical vibration absorber. In this paper, we apply to the stiffness an optimal feedback control on a neighbouring extremal path as defined in [1]. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

阵的特征根的限界(Ⅱ)

<正> 本文是前文的续作,这里引用的記号与以前是一致的,例如(?)为实或复阵(?)的特征根,A~* 是 A 的共轭转置阵,(?)此外,还引用一些新的记号,(?)     

Resonant triad model for studying evolution of the energy spectrum among a large number of internal waves

Internal waves are generally accepted to be responsible for a large fraction of mixing in the deep ocean. Internal waves interact nonlinearly with one another, exchanging energy among themselves to create the background internal wave spectrum. The most important mechanism resulting in the transfer of energy from one wave to another is believed to be resonant triad interactions. In this paper we consider a large number of resonantly interacting triads in order to investigate the evolution of the energy spectrum due to solely resonant triad interactions. To this end we solve the evolution equations for a large number of resonant triads to determine the temporal evolution of the energy distribution among the various possible wave numbers and frequencies. Our model involves internal waves with frequencies spanning the range of possible frequencies, i.e., between a maximum of the buoyancy frequency N for horizontal wave vectors (vertical motion) to a minimum of the inertial frequency f for vertical wave vectors (horizontal motion) [two limiting cases]. Because of the inclusion of high-frequency waves we cannot make the hydrostatic approximation. We investigate the evolution of the wave’s amplitudes to predict the evolution of the internal wave energy spectrum.     

Oscillations of mechanical systems that do not become linear when the parameter vanishes : PMM vol. 42, no. 6, 1978, pp. 1039–1048

The results of investigations in [1] are extended to multidimensional systems that become nonlinear at μ = 0. Two-dimensional mechanical systems were investigated in [2,3]. The characteristic equations of systems considered here contain in the critical system either a pair of pure imaginary roots or two zero roots with one or two groups of solutions and n roots with negative real parts in the adjoint system. It is shown that the investigation of such systems necessitates the imposition on the system of some constraints that supplement those specified in [1], The auxilliary function u⁽¹⁾_k (θ) used in the determination of Liapunov's function is derived by a different method than in [1 – 3], In two of the three investigated cases the problem is reduced to the determination of roots of some integral real irrational function. An example is presented.     

Bifurcations on a spring-pendulum oscillator

In this paper we study experimentally the dynamics of a non linear system: a spring pendulum coupled to an oscillator. The system was tested using a hybrid technique called Real Time Dynamic Substructuring (RTDS)[1, 2]. RTDS is a testing technique that involves splitting the system under study into two subsystems: one will be physically tested (physical substructure) and the other will be simulated in the computer (numerical model). These substructures interact in real time through a set of transfer systems. RTDS is a very powerful experimental methodology that not only allows full scale and real time testing but also real-time bifurcation tracking in complex engineering systems [3, 4]. In our hybrid experiment the spring pendulum is taken to be the physical substructure while oscillator is the simulated numerical model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A phase field model for martensitic transformations with a temperature-dependent separation potential

Metallic materials often exhibit a complex microstructure with varying material properties in the different phases. Of major importance in mechanical engineering is the evolution of the austenitic and martensitic phases in steel. The martensitic transformation can be induced by heat treatment or by plastic surface deformation at low temperatures. A two dimensional elastic phase field model for martensitic transformations considering several martensitic orientation variants to simulate the phase change at the surface is introduced in [1]. However here, only one martensitic orientation variant is considered for the sake of simplicity. The separation potential is temperature dependent. Therefore, the coefficients of the Landau polynomial are identified by results of molecular dynamics (MD) simulations for pure iron [1]. The resulting separation potential is applied to analyse the mean interface velocity with respect to temperature and load. The interface velocity is computed by use of the dissipative part to the configurational forces balance as suggested in [3]. The model is implemented in the finite element code FEAP using standard 4-node elements with bi-linear shape functions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Translation-invariant monotone systems,I: Autonomous/periodic case

This paper studies autonomous/time-periodic translation-invariant monotone systems without stronger notion. It is proved that every solution is asymptotically periodic if the Poincaré mapping has at least one fixed point. The result gets rid of the “strong” assumption in [1]. Applications are made to chemical reaction networks, especially to enzymatic futile cycles.     

On normal classes of rings

In [6] Lanski,Resco and Small proved that, if I is a non-zero right ideal of a prime ring R then R is right primitive if and only if I is right primitive modulo its prime radical. Considering the opposite ring one gets the left version of this result. It is natural to ask whether the mixed version C left ideal, right primitivity) of the theorem holds as well. Studying this question we concluded that all the results of [6] can be extended to normal classes of rings[7] (of which the classes of left and right primitive rings are examples). It in particular answers positively the question. we also get several new characterizations of normal classes and find a direct proof of the quoted result of [6].     

Vibrational resonance in a time-delayed genetic toggle switch

Biological oscillators can respond in a surprising way when they are perturbed by two external periodic forcing signals of very different frequencies. The response of the system to a low-frequency signal can be enhanced or depressed when a high-frequency signal is acting. This is what is known as vibrational resonance (VR). Here we study this phenomenon in a simple time-delayed genetic toggle switch, which is a synthetic gene-regulatory network. We have found out how the low-frequency signal changes the range of the response, while the high-frequency signal influences the amplitude at which the resonance occurs. The delay of the toggle switch has also a strong effect on the resonance since it can also induce autonomous oscillations.     

The Higher Frequency of Free Vibrations of Thin Annular Plates Made of Functionally Graded Material

Subject of this paper is a thin plate with a characteristic geometry: periodic in one direction and smoothly varying along the other. The aim of the contribution is to formulate and apply the averaged model which can describe higher frequencies of free vibrations. Problem of finding frequencies of free vibrations is very important. It could be applied to many engineering problems such as resonance phenomena, wave propagation, absorption of vibrations and many others. When the considered plate is made of an isotropic material, we can find the first, the second and the others frequencies in simply way. But if we consider plate made of a functionally graded material [1], which have varying properties and which is made of two components, this problem is more complicated. In this cause, apart from family of the base frequencies (first, second, etc), which depend on macroscopic properties of the plate, we have the higher frequency, which depends on a microscopic structure. We can find many papers describing the base frequencies of free vibrations for many different types of structures (for example [2] for considered type of plate). In this paper, we find the higher frequency. For solving this problem, we use the tolerance averaging technique described in [3]. This theory allows to take into account the microstructure size and to find the higher frequency of free vibrations. The equations have smooth coefficients. They can be solved numerically with help of the finite difference method, in polar coordinates for an annular plate. Next, we use special procedure for selecting of the higher frequencies of free vibrations, which depend on the microstructure size, from the list of all frequencies. After that we analyze an influence of ratios of material properties and the microstructure size on the higher frequency of free vibrations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance

In many of the known sports disciplines, especially in athletics, the criterion which determines the positions of the competitors is a simple physical value, mostly a time or a distance, and the athlete with the minimum or maximum, respectively, takes the first place. Moreover, sports science explains this criterion by a set of the so-called basic abilities. Compensation means the balance of the inferiority of such a basic ability by the superiority of another one. In the following paper, a general abstract concept to analyse compensation in a quantitative way is presented first. It can be applied to any discipline with a measurable criterion, if, in addition, the performance can be described by a kinematic function. Second, the proceeding is worked out in detail for the short sprint based on the modelling of the velocity function of a sprinter and the indicators for his basic abilities in [6]. The two aspects of compensation, namely the set of indicators which belong to the same criterion and the improvement of the criterion caused by the improvement of a basic ability, are discussed in a quantitative way. They turn out to be describable by the mathematical structures of ‘surfaces of constant pure running time’ and certain gradients, respectively.     

Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance

Two-frequency parametric resonance in nonlinear dynamical systems is studied by analyzing a delay differential equation with the delay obeying a two-frequency law, which arises in the mathematical simulation of some physical processes. It is shown that the system can exhibit chaotic oscillations (strange attractors) when the parametric excitation frequencies are both close to the doubled eigenfrequency of the system (degenerate case). The formation mechanisms of chaotic attractors are discussed, and the Lyapunov exponents and the Lyapunov dimension are calculated for them. If only one of the parametric excitation frequencies is close to the double eigenfrequency, a two-frequency regime occurs in the system.