Nonlinear airship aeroelasticity

The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.     

The oscillatory squeeze flow rheometer: comprehensive theory and a new experimental facility

In this paper, we give detailed attention to a relatively recent method for the determination of the linear dynamic properties of viscoelastic systems, namely, the so-called oscillatory squeeze flow (OSF) technique. We provide a comprehensive theory for the OSF rheometer, which includes a full discussion of the influence of fluid inertia. In the process, it is argued that, fortuitously perhaps, fluid inertia is more easily accommodated in the OSF rheometer than in the corresponding torsional-flow techniques. A new version of the OSF rheometer is described and experimental results on a set of viscoelastic systems are used to demonstrate the versatility of the technique. In the process, the potential use of the instrument within an industrial quality control environment is stressed.     

Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors

This paper gives a group of expansion formulas for the inertias of Hermitian matrix polynomials A−A², I−A² and A−A³ through some congruence transformations for block matrices, where A is a Hermitian matrix. Then, the paper derives various expansion formulas for the ranks and inertias of some matrix pencils generated from two or three orthogonal projectors and Hermitian unitary matrices. As applications, the paper establishes necessary and sufficient conditions for many matrix equalities to hold, as well as many inequalities in the Löwner partial ordering to hold.     

On the Characters of the Maximal Subgroup <f 1> Sp 4 ( q ) of the Symplectic Group Sp 4(q), q-Even

The aim of this paper is to study the characters of the maximal subgroup of the symplectic group Sp ₄(q)q-even, where is the stabilizer of the one-dimensional space <f ₁> in Sp ₄(q).     

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     

End effects in rotational viscometry I. No-slip shear-thinning samples in the Z40 DIN sensor

Neglect of end effects in Couette rotational viscometry introduces a 10–30% error in the estimate of shear stress at the spindle surface. Actual deviations depend on the shear-thinning level of a given sample. We tackle the end effect for the standard sensor Z40 DIN according to the ISO 3219 by solving the related 2D boundary-value problem for a class of shear-thinning viscosity functions. The pseudosimilarity method of treating the primary data leaves an error of about 0.5% in shear stresses. Further reduction in the errors needs a full numerical simulation for each point of the primary data based on a suitable wide-range representation of the viscosity function. To support a high accuracy of torque calibrations, the effect of inertia on torque for Newtonian liquids in standard sensor Z40 DIN at Re < 500 is calculated using the FLUENT 6.2 commercial software. Paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Towards the generalized purely wild inertia conjecture for product of alternating and symmetric groups

We obtain new evidence for the Purely Wild Inertia Conjecture posed by Abhyankar and for its generalization. We show that this generalized conjecture is true for any product of simple Alternating groups in odd characteristics, and for any product of certain Symmetric or Alternating groups in characteristic two. We also obtain important results towards the realization of the inertia groups which can be applied to more general set up. We further show that the Purely Wild Inertia Conjecture is true for any product of perfect quasi p-groups (groups generated by their Sylow p-subgroups) if the conjecture is established for individual groups.     

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.     

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.     

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.