Using instrumental inertia in controlled stress rheometry

We describe a new method for characterizing the non-linear behavior of complex fluids at both small and large deformations. For creep measurements, we use the coupling between the instrumental inertia and the material‘s elasticity to follow the rheological behavior of a solution of iota carrageenan both above and below the yield stress. It is shown that this coupling selectively excites one particular frequency of the relaxation spectrum. An analytical calculation is used to quantify the non-linear behavior near the yield stress. The “free“ oscillations observed during the first few seconds allow us to choose the most appropriate mechanical model. Comparison with experiment shows that even above the yield stress, a linear model can still give independently reliable information about the changes in each element of the mechanical model. A comparison of free and forced oscillations in controlled stress rheometry shows both experimentally and theoretically the conditions under which the use of free oscillations is advantageous. Received: 4 September1997 Accepted: 13 January 1998     

Inertia groups and abelian surfaces

This paper classifies the finite groups that occur as inertia groups associated to abelian surfaces. These groups can be viewed as Galois groups for the smallest totally ramified extension over which an abelian surface over a local field acquires semistable reduction. The results extend earlier elliptic curves results of Serre and Kraus.     

Error Analysis in Trifilar Inertia Measurements

Accurate calculation of the moment of inertia of an irregular body is made difficult by the large number of quantities which must be measured. A popular method is to use a trifilar suspension system to measure the period of oscillation of the body in the horizontal plane. In this paper, some sources of error are discussed with particular attention given to the alignment of the test object’s center of mass on the trifilar platform. The procedure is described, the necessary calculations are derived and the relative importance of accuracy in different measurements is assesed. It is determined that the accurate alignment of the centre of mass of the body being tested with the centre of the trifilar plate is insignificant compared to the accuracy of the other measurements required in the calculations.     

微机在用刚体转动仪测刚体转动惯量实验中的应用

用刚体转动仪测量刚体转动惯量实验所要测量的主要物理量是时间,所测量的实验数据繁多,且要求准确,而后续的实验数据处理计算复杂。本介绍了一种测量时间、计算转动惯量数值两项工作全部由PC机来完成的新方法。     

A quasi-velocity-based nonlinear controller for rigid manipulators

The problem of position control in the operational space of a robot manipulator is addressed in the paper. The proposed controller is based on equations of motion expressed in terms of normalized generalized velocity components (NGVC) which result from decomposition of the manipulator inertia matrix. The sufficient conditions for global exponential stability of the system under the controller are given. It is shown that using the controller an further insight into the system dynamics is possible. The proposed control algorithm is tested via simulation on a spatial manipulator with three degrees of freedom.     

Double restricted Co‐Inertia Analysis

In this paper, an extension of the Co‐Inertia Analysis 1 is proposed. This extension is based on an objective function which takes directly into account the external information, as linear restrictions, about parameters of both sets of variables, by rewriting the Co‐Inertia Analysis objective function according to the principle of Restricted Eigenvalue Problem 2 . A restricted extension of Wold's two‐block ‘Mode A’ Partial Least Squares 3 is also proposed. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic Tensile Testing of Soft Materials

Determination of dynamic tensile response of soft materials has been a challenge because of experimental difficulties. Split Hopkinson tension bar (SHTB) is a commonly used device for the characterization of high-rate tensile behavior of engineering materials. However, when the specimen is soft, it is challenging to design the necessary grips, to measure the weak transmitted signals, and for the specimen to achieve dynamic stress equilibrium. In this work, we modified the SHTB on the loading pulse, the equilibrium-monitoring system, and the specimen geometry. The results obtained using this modified device to characterize a soft rubber indicate that the specimen deforms under dynamic stress equilibrium at a nearly constant strain rate. Axial and radial inertia effects commonly encountered in dynamic characterization of soft materials are also minimized.     

Pressure drop and friction factor of steady and oscillating flows in open-cell porous media

Open-cell metal foams are often used in heat exchangers and absorption equipment because they exhibit large specific surface area and present tortuous coolant flow paths. However, published research works on the characteristics of fluid flow in metal foams are relatively scarce, especially for the flow oscillation condition. The present experimental investigation attempts to uncover the behavior of steady and oscillating flows through metal foams with a tetrakaidecahedron structure. In the experiments, steady flow was supplied by an auto-balance compressor and flow oscillation was provided by an oscillating flow generator. The pressure drop and velocity were measured by the differential pressure transducer and hot-wire sensor, respectively. The friction factor of steady flow in metal foam channel was analyzed through the permeability and inertia coefficient of the porous medium. The results show that flow resistance in the metal foams increases with increasing form coefficient and decreasing permeability. The empirical equation obtained by the present study indicates that the maximum friction factor of oscillating flow through the tested aluminum foams with specific structure is governed by the hydraulic ligament diameter-based kinetic Reynolds number and the dimensionless flow amplitude.     

Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium

In this study, laminar boundary layer flow over a flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation, inertia effect and suction/injection is analyzed using the Keller box finite difference method. The flat plate is assumed to be held at constant temperature. The non-Darcian effects of convection, boundary and inertia are considered. Results for the local heat transfer parameter and the local skin friction parameter as well as the velocity and temperature profiles are presented for various values of the governing parameters. The non-Darcian effects are shown to decrease the velocity and to increase the temperature. It is also shown that the local heat transfer parameter and the local skin friction parameter increase due to suction of fluid while injection reverses this trend. It is disclosed that the effect of the viscous dissipation for negative values of Ec (T _w < T _∞) is to enhance the heat transfer coefficient while the opposite is true for positive values of Ec (T _w > T _∞). The results are compared with those available in the existing literature and an excellent agreement is obtained.     

An extended version of Schur-Cohn-Fujiwara theorem in stability theory

This paper is concerned with root localization of a complex polynomial with respect to the unit circle in the more general case. The classical Schur-Cohn-Fujiwara theorem converts the inertia problem of a polynomial to that of an appropriate Hermitian matrix under the condition that the associated Bezout matrix is nonsingular. To complete it, we discuss an extended version of the Schur-Cohn-Fujiwara theorem to the singular case of that Bezout matrix. Our method is mainly based on a perturbation technique for a Bezout matrix. As an application of these results and methods, we further obtain an explicit formula for the number of roots of a polynomial located on the upper half part of the unit circle as well.