Effects of TLCD with maneuverable flaps on vibration control of a SDOF structure

Tuned liquid column damper (TLCD) is a class of auxiliary damping device which is used to dissipate vibrational energy of structures when excited by dynamic loading. Damping control of TLCDs is an important parameter to achieve the maximum benefit of TLCDs when attached to the structure. Herein, a new method of controlling damping is proposed by installing maneuverable flaps into TLCD (TLCD + MF). The damping value of the TLCD is controlled by the closing angle of the flaps. This method is simple in concept, more applicable in construction, and it is an effort to make the TLCD more controllable, (i.e. semi-active). Dynamic characteristics of such TLCD + MF system are investigated in this study. It is observed that by increasing the closing angle, the damping ratio of the TLCD + MF system increases. In addition, it is found that the mistuning of frequency becomes ignorable below the closing angle of 50°. The efficiency of the TLCD + MF in reducing response of structures under harmonic excitation is also studied. It is shown that existence of the flaps improves the performance of combined structure and the TLCD + MF system in terms of damping ratio and structural responses. The TLCD + MF system with the closing angle of 50° reduces the acceleration and displacement responses about 20 % more than conventional TLCDs.     

Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes

Passive control of structural vibrations has received in recent years a great attention from researchers concerned with vibration control. Several types of devices have been proposed in order to reduce the dynamic responses of different kinds of structural systems. Among them, the Tuned Liquid Column Damper (TLCD) proved to be very effective in reducing vibration of structures. Since the increasing use of TLCDs in practical realizations, this paper aims at developing an approximate formulation, by means of a statistical linearization technique, able to estimate the parameters of a structure equipped with a TLCD subjected to random loads for pre-design purposes. Moreover, it is shown that results obtained via Monte Carlo approach on the non-linear system are in good agreement with those obtained by means of the proposed formulation.     

Comparison of methods for calculating the shock hugoniot of mixtures

Various methods used to determine the shock Hugoniot of condensed phase multi-component mixtures are reviewed and compared to available experimental data. The assumptions inherent in the different models are presented in this overview and their implications are discussed. The comparisons of the various models demonstrate that the predicted shock Hugoniots are in good agreement with published data despite the simplifying assumptions that are associated with the models. Averaging models are shown to be among the simplest methods to implement and result in the closest agreement with experimental data.     

Evolution of the Theory of Laminated Plates and Shells

The theory of laminated plates and shells is considered. Three-dimensional models of layered systems and methods of reducing them to two-dimensional models are elucidated. An analysis is made of how two-dimensional models are constructed by the method of hypotheses. Two basic approaches to the construction are presented: one leads to the discrete structural theory of laminated systems and the other to continuous structural theory. Attention is drawn to transverse shear and reduction in nonclassical theories of high approximation. The finite-element implementation of the theory is described. Examples of analysis by various models are given. Results of an applicability analysis of various theories and experimental data supporting them are presented. New research areas for the theory of laminated structures are pointed out.     

Diagonalization of a three-dimensional system of equations in terms of displacements of the linear theory of elasticity of transversely isotropic media

A dynamic three-dimensional system of linear equations in terms of displacements of the theory of elasticity of transversely isotropic media is given explicit expressions for phase velocities and polarization vectors of plane waves. All the longitudinal normals are found. For some values of the elasticity moduli, the system of equations is reduced to a diagonal shape. For static equations, all the conditions of the system ellipticity are determined. Two new representations of displacements through potential functions that satisfy three independent quasi-harmonic equations are given. Constraints on elasticity moludi, at which the corresponding coefficients in these representations are real, different, equal, or complex, are determined. It is shown that these representations are general and complete. Each representation corresponds to a recursion (symmetry) operator, i.e., a formula of production of new solutions.     

旋转弹性体的有限元线法分析

本文将有限元线法应用于一般荷载作用下的旋转弹性体的分析。文中将任意荷载沿环向展开为Ｆｏｕｒｉｅｒ级数，利用正交性，将问题转变为一系列旋转子午面上二维问题的叠加。文中对任一环向谐波建立了旋转面上的曲线曲边单元，导出了相应的常微分方程体系，并对由柱坐标引起的ｒ＝０处的奇异性问题做了完备合理的处理。文中给出了具有代表性的数值算例，用以展示本法的出色的表现     

悬索非线性动力学中的直接法与离散法

以悬索为例对结构非线性动力学中直接法与离散法的应用进行了研究. 针对悬索面内运动的第$n$阶模态的主共振，分别利用这两种方法对悬索的非线性响应进行求解，得到悬索非线性响应的二次近似解以及相应的幅频响应曲线，并比较和讨论了这两种方法得到的结果及其差异. 通过分析得知：离散法在用于非对称结构非线性动力学的求解时可能导致错误的结果.     

On a Model of Heterogenous Deformation of Elastic Bodies by the Mechanism of Multiple Appearance of New Phase Layers

A model describing a possible scenario of martensite type phase transformations is examined. A new phase is supposed to nucleate in the form of plane parallel layers. As the boundary condition, average strains are imposed. Then, the governing parameters of the two-phase structure are the concentration of new phase layers, their orientation and also the orientation of anisotropy axes. The parameters depend on the average strains and are determined by the requirement to minimize the average Helmholtz free-energy function. Once a general procedure has been discussed, average strain–stress diagrams are constructed for two cases. In the first case, for the simplicity sake, both phases are assumed to be isotropic. In the second case anisotropy is produced by a non-spherical phase transformation strain tensor. For both cases phase transition zones (PTZs) are constructed. The PTZ is formed in the space of strains by those which can exist on equilibrium interfaces. Loading and unloading paths, corresponding to uniaxial stretching and plane stretching/compression, are examined and related with the PTZ. Effects of internal stresses induced by the nucleation of new phase areas and the anisotropy of new phase are discussed.     

Approximate symmetries of creeping flow equations of a second grade fluid

Creeping flow equations of a second grade fluid are considered. Two current approximate symmetry methods and a modified new one are applied to the equations of motion. Approximate symmetries obtained by different methods and the exact symmetries are contrasted. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.     

Experimental Study of the Dynamic Flexural Strength of Concrete

In this paper, we analyze the increase in the dynamic flexural strength of concrete according to strain rate. A simple beam with center-point loading and a classical electro-mechanical testing machine are used to determine the static flexural strength. The dynamic measurements are conducted using a split Hopkinson pressure bar (SHPB) device in the same three-point bending configuration. The outer faces of the beams are instrumented with strain gauges to record the extreme tensile strains. Moreover, full-field displacement measurements are obtained using digital image correlation (DIC) on images recorded by a very high-speed camera. The strain gauge and DIC measurements are compared and used to determine the onset of failure and to evaluate the rate-related tensile strength. Several tests are performed at strain rates in the range from 1/s to 15/s. As expected, a significant increase in the flexural tensile strength with strain-rate is observed, which is consistent with results from the literature.     

Measurement of the Viscoelastic Properties of Bitumen Using Instrumented Spherical Indentation

Indentation testing as a tool for determination of the viscoelastic mechanical properties of bitumen is examined in some detail using theoretical, numerical as well as experimental methods. In particular Brinell indentation is analysed and simple but rigorous formulae for a complete characterization of linear viscoelastic materials are presented. Numerical methods (finite element methods) are used in order to verify and substantiate these relations for an experimental situation. Indentation experiments are then performed on bitumen and special efforts are made in order to avoid size effects, i. e. anomalous results due to the fact that the indented specimens are too small and as a result, far field boundary conditions will influence the interpretation of the experimental output. The mechanical properties determined experimentally by indentation are compared with corresponding results from standard mechanical tests, and the results are encouraging considering the fact that non-linear effects are also influencing the outcome of the experiments.     

Influence of surface effects on fatigue of microcracks nucleation

Cyclic plastic slips in persistent slip bands (PSBs) at the free surface and in the bulk are evaluated for high-cycle fatigue of polycrystals. Analytical results are obtained for PSBs in the bulk and for surface type A PSBs, but the finite element method is used for surface type B PSBs. For practical applications, the results are presented in the form of amplification factors, which are almost insensitive to the PSB aspect ratio and other material parameters. These values are then used to include surface effects in an evaluation of the post-saturation number of cycles to crack nucleation. Some environmental effects are also taken into account. An energy balance criterion is used, and the effect of microslip irreversibilities is evaluated on a statistical basis.     

On the orthogonality of natural modes of vibration

The natural modes of a discrete linear system are orthogonal with respect to the mass and stiffness matrices in a generalized sense. However, these modes are usually not orthogonal to each other in the ordinary sense. The purpose of this paper is to document a number of conditions under which the modes are also orthogonal in an ordinary fashion.     

Identification of regions of fastest mixing in a system of point vortices

This paper describes a numerical method for efficiently identifying the regions of fastest mixing of a passive dye in a flow due to a system of point vortices. Results obtained from computations are presented for systems of three and four point vortices, both in the unbounded domain and inside a circular cylinder. The flow is two‐dimensional and the fluid is incompressible. The regions where mixing is possible are found by studying the largest Lagrangian Lyapunov exponent distribution with respect to various initial positions of tracer particles. The regions of fastest mixing are then identified from the Lyapunov exponent distribution at small times. The results of the method are verified by quantifying the mixing by using a traditional box counting technique. The technique is then applied to several different initial configurations of vortices and some interesting results are obtained. Some numerical findings about the nature of the exponents computed are also discussed. Copyright © 2002 John Wiley Sons, Ltd.     

Ellipticity conditions of the static equations of nonlinear elasticity

The relations of the nonlinear model of the theory of elasticity are considered. The Cauchy and the strain gradient tensors are taken to be the characteristics of the stress-strain state of a body. Sufficient conditions under which the static equations of elasticity are of elliptic type are established. These conditions are expressed in the form of constraints imposed on the derivatives of the elastic potential with respect to the strain-measure characteristics. The cases of anisotropic and isotropic bodies are treated, including the case where the Almansi tensor is taken to be the strain measure. The plane strain of a body is investigated using actual-state variables. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 196–203, March–April, 1999.     

Global smooth solutions of the equations of motion of a nonlinear fluid with fading memory

The initial value problem associated with the equation of motion of an incompressible simple fluid with exponentially fading memory is studied. Suitable function spaces are constructed and a local existence theorem is established by the method pf artificial viscosity. Several energy integrals are obtained in order to estimate the size of solutions in suitable function spaces. It is shown that the solution are globally defined when the intial data are small and that they decay to equilibrium are time tends to infinity.This research has been supported in part by the National Science Foundation under grant Eng.-CME 80-23824.     

Analysis of Isolation Effectiveness of Shear Waves by a Row of Hollow Pipe Piles in Saturated Soils

Wave numbers about the three types of waves in saturated soils are firstly given in this paper. The lengths of the pipe piles are much larger than their diameters, so the isolation problem about SV waves by discontinuous barriers composed of a row of pipe piles can be simplified as a two-dimensional scattering problem. The expansion method of wave functions is adopted, the stresses and displacements at the boundaries between the pipe piles and adjacent soils are considered as continuous and the inner sides of the pipe piles are free, and then the theoretical solutions are obtained about this two-dimensional scattering problem. Normalized displacements are introduced, which are the displacements behind the barriers caused by both the incident and scattered waves to those only by the incident SV waves, contours and curves of the normalized displacements are drawn, and the influences of wall thickness of pipe piles, modulus ratio of pipe piles to soils, spacing distance between the pipe piles and pipe pile numbers on the isolation effectiveness are analyzed.     

Two-dimensional elastica analysis of equilibrium shapes of single-anchor inflatable dams

Several types of inflatable dams are considered. These are long, air-inflated, cylindrical structures on a rigid foundation. Sometimes one of the long edges of a sheet is folded back to the other edge, and then the two edges are clamped to the foundation along a single anchoring line. A second configuration can be modeled as two sheets attached along two long edges, with one edge anchored and the other free to lift as air pressure is applied between the sheets. Another device treated here is a hinged spillway gate lifted by an inflatable bladder. The cross section of the dam or bladder is analyzed as an inextensible elastica. The governing equations and boundary conditions are formulated for each case, and shooting methods are utilized to obtain numerical solutions for the equilibrium shapes. The effects of the internal air pressure and the external water height are investigated.     

Analysis and application of ellipticity of stability equations on fluid mechanics

By using characteristic analysis of the linear and nonlinear parabolic stability equations ( PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub- characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic., respectively . The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories , the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time , the methods of removing the remained ellipticity are further obtained from the nonlinear PSE .     

Thermal bending of thick rectangular plates of bimodulus composite materials

Wiighted residual solutions are presented for thermal bending of laminated composite plates. The material of each layer is assumed to be clastically and thermoelastically orthotropic and bimodular. The formulations are based on the thermoclastic version of the theory of Whitney-Pagano laminated plate, which includes thickness shear detormations. The results are obtained for deflections and neutral-surface positions and are found to be in good agreement with the closed-form solution.