Procedia IUTAM最新文献

The engineering problem of successive construction of a heavy circular vault (a cylindrical arch) on a smooth rigid horizontal base is studied. The constructed vault manifests properties of creep and aging. The construction goes by layer-by-layer buildup of a prefabricated residual stress-free vaulted preform originally installed on the base. A buildup process in which a large number of thin layers of additional material are successively attached to the interior cylindrical surface of the arch is considered. The process is modeled as a continuous accretion process, that is, an infinitely thin material layer is added to the solid on every infinitesimal time interval. The added material is assumed not to be prestressed. The sliding mounting of the vault to the base is assumed. The case of plane strain of the vault is examined. The initial-boundary value problems describing deformation process of the structure in question before, during and after its accretion within the framework of the linear theory of viscoelasticity of accreted solids are stated and solved analytically in series and quadratures. Numerous numeral calculations for different time modes of the viscoelastic vault constructing process are performed. The influence of the temporal characteristics of the process on obtained stress state of the constructed vault is investigated. Some practically relevant phenomena are discovered. Requirement of taking into account the gravity forces in the course of the whole constructing process but not only in the terminal structure configuration is shown convincingly.

A classical viscoelastic rod subjected to longitudinal vibrations is considered. The boundary conditions are so that the left end of the rod is fixed and the right end is free. Moreover it is assumed that the rod is growing and hence, its length is changing in time. The function of growth is assumed to be twice continuously differentiable with respect to time. A particular case of rod's growth proportional to time is of special interest. The change of variables is introduced so that in new variables the rod length becomes constant. The new partial differential equation describing the rod's dynamics is derived in these variables. This equation is simplified using assumptions on slow rate growth constant and small viscoelastic damping factor. A special representation of solution is introduced which uses eigenfunctions of the generating problem, when growth and damping are neglected, and satisfy the boundary conditions. By means of this representation the governing partial differential equation is converted in infinite system of ordinary differential equations. It is shown that solutions of truncated systems converge to solution of the original system of equations. Three major problems of the growing rod vibrations are formulated and solved. In the first problem free undamped vibrations are considered. It is shown that at linear growth of rod length amplitudes of all its modes are also growing linearly in time. The simplified model neglecting the modes cross-coupling is composed for the explanation of this effect. The corresponding differential equation is solved exactly in elementary functions and it is shown that amplitudes of vibration of any modes grow linearly and almost-periods of vibrations have logarithmic dependence on time. In the second problem free damped vibrations of linearly growing rod are considered. It is shown that time behaviour of the rod has two characteristic domains: in the first the vibration amplitudes decay exponentially due to domination of the viscoelastic damping effects; in the second domain these amplitudes start to grow linearly in time due to domination of the effects considered in the first problem. The simplified model describing this effect and neglecting the modal cross-coupling is developed. The exact solution of the corresponding differential equation is obtained in the confluent hypergeometric functions, which qualitatively explain the abovementioned behaviour of the rod. In the third problem the forced damped vibrations of the rod are considered. It is shown that at fixed frequency of excitation the resonant effects are manifested subsequently in all modes of the rod in the process of its growing.

The effective influence on exothermic reaction behavior is possible if the thermite mixture contains chlorinated components such as NaCl and KCl. Their content in the thermite mixture less than 7% and 7.25%, respectively, permits one to improve the efficiency of the aluminothermic process by increasing in the bulk of obtained metal melt, to decrease a number of nonmetallic inclusions is steel structure owing to the reduction of exothermic process intensity, to control the physical-mechanical properties of the produced steel.

A pendulum on a movable support has been used widely in the modeling of many mechanical systems, say, as the simplest model of gantry cranes. This paper presents a comparison study of the stability of the controlled pendulum with a delayed proportional- derivative feedback controller or a delayed derivative-acceleration feedback controller for sway reduction. Numerical calculation shows that the delay combinations and the sign combinations of the gains have important impact on the stability of the controlled pendulum. Although acceleration feedback is used few in applications compared with the widely used proportional-derivative feedback, the case when the delay in the acceleration feedback is double of the one in the derivative feedback can be particularly useful in enlarging the stable region in the gain plane, or in enlarging the stable delay interval if the feedback gains are fixed.

Initiation of period-1 rotation of a vertically or horizontally excited parametric pendulum from arbitrary initial conditions has been studied using a switch delayed feedback control. We also study the possibility of controlling the preferential direction of rotation. In order to choose the control parameters, a systematic linear stability analysis of the various periodic solutions is performed using the Floquet theory. The control gains are obtained using the variation of the dominant Floquet multipliers with the control gain. Our procedure has been verified to work well with both the case of vertical and horizontal excitation.

One of the important questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose a unique self-consistent experimental and numerical set up that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multi-scale internal wave motion. We show how this set-up can be used to tackle the open question of studying internal wave turbulence in a laboratory, by providing, for the first time, explicit evidence of a wave turbulence framework for internal waves. Finally, beyond this regime, we highlight a clear transition to a cascade of small-scale overturning events which induce mixing.

Similarity theory of isotropic turbulence induced by waves on the water with free surface is proposed. Scaling is obtained from experimental and numerical observations of dissipation rates for surface waves, and then used to estimate the turbulent viscosity of the locally-isotropic turbulence.

The concept of equivalent inhomogeneity has been introduced to analyze the effective properties of composites with interphases using techniques devised for problems without interphases. The basic idea is to replace the inhomogeneity and the surrounding it interphase by a single equivalent inhomogeneity with constant stiffness tensor, combining properties of both, which is then perfectly boned to the matrix. In this presentation a new definition of equivalent inhomogeneity is discussed. It is based on Hill's energy equivalence principle, applied to the problem consisting only of the original inhomogeneity and its interphase. It is more general than the definitions proposed in the past in that, conceptually and practically, it allows to consider inhomogeneities of various shapes and various models of interphases. This is illustrated considering spherical and cylindrical particles with two models of interphases, Gurtin-Murdoch material surface model and spring layer model. The resulting equivalent inhomogeneities are subsequently used to determine effective properties of randomly distributed unidirectional particulate composites. Properties of the equivalent cylindrical inhomogeneities are transversely isotropic, thus the method of conditional moments, which is a statistical method capable of handling anisotropy and randomness, has been employed for that purpose. Closed-form formulas for the effective stiffness tensor have been developed in all cases considered here. Comparisons with solutions available in the literature are made and other possible applications are discussed.

Skins of water and ice perform anomalously in capacities of hydrophobicity, lubricity, mass density, thermal stability, viscoelasticity, and phonon frequency with yet little knowledge about the mechanism behind these anomalies. We present the recent progress in this regard from the perspective of molecular undercoordination induced O:H-O bond segmental cooperative relaxation and nonbonding electron polarization. The skin molecular undercoordination shortens the intramolecular H-O covalent bond spontaneously from 1.0 to 0.84 Ǻ, while the Coulomb repulsion between oxygen anions lengthens the intermolecular O:H nonbond from 1.70 to 2.71 Ǻ associated with strong polarization. The O:H-O resultant elongation depresses the mass density to 0.75 g/cm³; the polarization results the skin high stress, hydrophobicity, lubricity, viscoelasticity; the H-O contraction shifts its stretching vibration frequency from the bulk value of 3150 to 3450 cm^-1 at skin and to 3650 cm^-1 of vapor; the O:H elongation shifts its stretching mode from 210 of bulk to 180 cm^-1 at skin. Therefore, molecular undercoordination induced O:H-O bond relaxation and the associated polarization govern the performance of molecules at the skins of water and ice.

Modal interactions, stability analysis and time delay control of a composite column loaded by axial periodic force is presented in the paper. The simply supported column is composed of channel sections made of layers of a laminate with an arrangement which couples bending and twisting of the structure. The laminate coupling, together with a nonlinear geometrical displacement field result in a nonlinear model with parametric excitation. It is shown that for the selected configuration different mode couplings and parametric instability zones may occur. In order to stabilise the system a time delay displacement feedback control is proposed. An effect of the time delay control on the first principal parametric resonance zone is studied analytically and numerically.