Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

A geodesic constant method for computing high-frequency mutual coupling between antennas on general quadric cylinders

A Geodesic Constant Method (GCM) is outlined which provides a common approach to ray tracing on quadric cylinders in general, and yields all the surface ray-geometric parameters required in the UTD mutual coupling analysis of conformal antenna arrays in the closed form. The approach permits the incorporation of a shaping parameter which permits the modeling of quadric cylindrical surfaces of desired sharpness/flatness with a common set of equations. The mutual admittance between the slots on a general parabolic cylinder is obtained as an illustration of the applicability of the GCM.

Yhteisestä toiminnasta yhteiseen kieleen : keskustelunanalyyttinen tutkimus toisen kielen oppimisesta kielikylpypäiväkodin arkitilanteissa

This dissertation examines how Finnish-speaking children learn Swedish in an immersion kindergarten where the method of Canadian immersion is used. Within the framework of conversation analysis, this study explores how second language learning is situated in interaction and evidenced in the participants´ verbal and non-verbal behavior. The database consists of 40 hours of videotaped data collected in naturally occurring situations in a group of 15 four-year-old children during the first two years of their immersion. Due to the immersion method, all the children share the same L1, in this case Finnish, and the teachers understand Finnish. However, they speak only Swedish to the children in all situations and Swedish is learned in interaction without formal teaching. The aim of the study is to discover how the children´s second language competence gradually increases when they participate in interaction with the Swedish-speaking teachers. The study also sheds light on the methodological question of how second language learning can be analyzed with the method of conversation analysis. The focus is on showing how the second language is learned in interaction, especially on how learning is achieved collaboratively. In this study, the emerging second language competence is explored by investigating how the children show understanding of the teachers´ non-verbal and verbal actions during the first and the second semester of the immersion. The children´s use of Swedish is analyzed by investigating how they recycle lexical items and later even syntactic structures from the teachers´ Swedish turns. The results show that the teachers´ actions are largely understood by the children even at the beginning of the immersion. The analyzes of the children´s responsive turns reveal that they interpret the teachers´ turns on the basis of non-verbal cues at first. Especially at the beginning of the immersion, the participants orient to the progress of interaction and not to problems in understanding. Even in situations where the next actions show that the children do not understand what is said, they tend to display understanding rather than non-understanding. This behavior changes, however, when the children´s competence in their second language increases. At the second semester, the children both show understanding of the teachers´ verbal turns and also display their non-understanding by initiating repair when they do not understand. Understanding of the teachers´ verbal turns, including their syntactic structure, is manifested in the ways the children tie their turns to the teachers´ turns. Recycling, on the other hand, proves to be the way by which the children start to speak the second language. In this study, the children´s common L1 is evidenced to be an important resource in interaction. It allows the children to participate in their individual ways and to share their experiences both with each other and with the teachers. It also enables them to co-construct conversations that lead to collaborative learning. Moreover, the uninhibited use of L1 proves to be an important analytic tool that makes the immersion data especially fruitful for conversation analytic research on second language learning, since the children´s interpretations of the second language are in evidence even when they do not speak the second language.

A method for estimation of the radius of elastic-plastic boundary around cold-worked holes

The radius of an elastic-plastic boundary was measured by the strain gage method around the cold-worked region in L72-aluminum alloy. The relative radial expansion was varied from 2.5 to 6.5 percent during the cold-working process using mandrel and split sleeve. The existing theoretical studies in this area are reviewed. The experimental results are compared with existing experimental data of various investigators and with various theoretical formulations. A model is developed to predict the radius of elastic-plastic boundary, and the model is assessed by comparing with the present experiments.

Analysis of continuum using boundary compatibility conditions of integrated force method

Static and vibration problems of an indeterminate continuum are traditionally analyzed by the stiffness method. The force method is more or less non-existent for such problems. This situation is primarily due to the incomplete state of development of the compatibility conditions which are essential for the analysis of indeterminate structures by the flexibility method. The understanding of the Compatibility Conditions (CC) has been substantially augmented. Based on the understanding of CC, a novel formulation termed the Integrated Force Method (IFM) has been established. In this paper IFM has been extended for the static and vibration analyses of a continuum. The IFM analysis is illustrated taking three examples: 1. (1) rectangular plate in flexure 2. (2) analysis of a cantilevered dam 3. (3) free vibration analysis of a beam. From the examples solved it is observed that the force response of an indeterminate continuum with mixed boundary conditions can be generated by IFM without any reference to displacements in the field or on the boundary. Displacements if required can be calculated by back substitution.

An efficient marching algorithm for waterhammer analysis by the method of characteristics

A new fast and efficient marching algorithm is introduced to solve the basic quasilinear, hyperbolic partial differential equations describing unsteady, flow in conduits by the method of characteristics. The details of the marching method are presented with an illustration of the waterhammer problem in a simple piping system both for friction and frictionless cases. It is shown that for the same accuracy the new marching method requires fewer computational steps, less computer memory and time.

Integral method for the calculation of incompressible two-dimensional transitional boundary layers

The method proposed here considers the mean flow in the transition zone as a linear combination of the laminar and turbulent boundary layer in proportions determined by the transitional intermittency, the component flows being calculated by approximate integral methods. The intermittency distribution adopted takes into account the possibility of subtransitions within the zone in the presence of strong pressure gradients. A new nondimensional spot formation rate, whose value depends on the pressure gradient, is utilized to estimate the extent of the transition zone. Onset location is determined by a correlation that takes into account freestream turbulence and facility-specific residual disturbances in test data. Extensive comparisons with available experimental results in strong pressure gradients show that the proposed method performs at least as well as differential models, in many cases better, and is always faster.