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.     

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.     

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.     

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.     

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.     

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     

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.     

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.     

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.     

Compression stiffness of infinite-strip bearings of laminated elastic material interleaving with flexible reinforcements

The closed-form solutions to the compression stiffness of the laminated elastomeric bearings of infinite-strip shape with flexible reinforcements are derived. The effect of bulk compressibility in the elastic layer and the effect of boundary condition at the ends of the bearing are considered. Three types of the elastic layers bonded to flexible reinforcements are studied. The first type simulates the interior elastic layers of the bearings with shear-free ends. The second type simulates the exterior elastic layers of the free-end bearings. The third type simulates the elastic layers in the bearings which ends are bonded to rigid plates. The theoretical solutions to the compression stiffness of the bearings are extremely close to the results obtained by the finite element method, which proves that the displacement assumptions utilized in the theoretical derivation are reasonable.     

Non-linear temporal dynamics of two-mode interactions of magnetized flow

This paper considers, in the frame work of the model of two superposed layers of viscous-potential incompressible magnetic fluids, the problem on formation of resonant waves of two modes on the interface between fluids that arisen as a result of second-harmonic resonance. The fluids moving with uniform velocities parallel to their interface are stressed by a tangential magnetic field. The analysis includes the linear, as well as the non-linear effects where the analytical solutions are constructed using the method of multiple scales, in both space and time, and hence the solvability conditions correspond to the uniform (convergent) solutions are obtained. The solvability conditions are then exploited to derive a more general system of non-linear partial differential equations with complex coefficients governing the amplitudes of the resonant waves. These equations are examined for solutions corresponding to sinusoidal wavetrains consequently different kinds of instabilities are demonstrated. The stability criterion in each case is derived and discussed both analytically and graphically.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Implicit boundary method for determination of effective properties of composite microstructures

A method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented. This approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite. Implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries. In this method, solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied, even if there are no nodes on the material interface boundary. Since a structured grid does not conform to the geometry of the analysis domain, the geometry of the microstructure is defined independently using equations of the interface boundary curves/surfaces. Structured grids that overlap the geometry are easy to generate, and the elements in the grid are regular shaped and undistorted. A numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface, and convergence analysis is performed to show that the method converges as the grid density is increased. Fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2D and 3D models to show that the results match closely with the ones available in the literature.