Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Rank-Augmented LU-Algorithm for Computing Generalized Matrix Inverses

A rank-augmnented LU-algorithm is suggested for computing a generalized inverse of a matrix. Initially suitable diagonal corrections are introduced in (the symmetrized form of) the given matrix to facilitate decomposition; a backward-correction scheme then yields a desired generalized inverse.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

Use of transverse beam polarization to probe anomalous V V H interactions at a Linear Collider

We investigate use of transverse beam polarization in probing anomalous coupling of a Higgs boson to a pair of vector bosons, at the International Linear Collider (ILC). We consider the most general form of V V H (V = W/Z) vertex consistent with Lorentz invariance and investigate its effects on the process e(+)e(-) -> f (f) over barH, f being a light fermion. Constructing observables with definite C P and naive time reversal ((T) over tilde) transformation properties, we find that transverse beam polarization helps us to improve on the sensitivity of one part of the anomalous Z Z H Coupling that is odd under C P. Even more importantly it provides the possibility of discriminating from each other, two terms in the general Z Z H vertex, both of which are even under C P and (T) over bar. Use of transversebeam polarization when combined with information from unpolarized and linearly polarized beams therefore, allows one to have completely independent probes of all the different parts of a general ZZH vertex.

Studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring

Numerical and experimental studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring are performed. The alloy is electromagnetically stirred to produce semisolid slurry in a cylindrical graphite mould placed in the annulus of a linear electromagnetic stirrer. The mould is cooled at the bottom, such that solidification progresses from the bottom to the top of the cylindrical mould. A numerical model is developed for simulating the transport phenomena associated with the solidification process using a set of single-phase governing equations of mass. momentum, energy. and species conservation. The viscosity variation of the slurry, used in the model, is determined experimentally using a rotary viscometer. The set of governing equations is solved using a pressure-based finite volume technique, along with an enthalpy based phase change algorithm. The numerical study involves prediction of temperature, velocity, species and solid fraction distribution in the mould. Corresponding solidification experiments are performed, with time-temperature history recorded at key locations. The microstructures at various temperature measurement locations in the solidified billet are analyzed. The numerical predictions of temperature variations are in good agreement with experiments, and the predicted flow field evolution correlates well with the microstructures observed at various locations.

On plane-wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient

A theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented. The temperature variation in the pipe is taken to be a linear temperature gradient along the axis. The theoretical studies include the formulation of a wave equation based on continuity, momentum, and state equation, and derivation of a general four-pole matrix, which is shown to yield the well-known transfer matrices for several other simpler cases.

Construction of inverses with prescribed zero minors and applications to decentralized stabilization

We examine the following question: Suppose R is a principal ideal domain, and that F is an n × m matrix with elements in R, with n>m. When does there exist an m × n matrix G such that GF = Im, and such that certain prescribed minors of G equal zero? We show that there is a simple necessary condition for the existence of such a G, but that this condition is not sufficient in general. However, if the set of minors of G that are required to be zero has a certain pattern, then the condition is necessary as well as sufficient. We then show that the pattern mentioned above arises naturally in connection with the question of the existence of decentralized stabilizing controllers for a given plant. Hence our result allows us to derive an extremely simple proof of the fact that a necessary and sufficient condition for the existence of decentralized stabilizing controllers is the absence of unstable decentralized fixed modes, as well as to derive a very clean expression for these fixed modes. In addition to the application to decentralized stabilization, we believe that the result is of independent interest.

Non-linear response of soil N2O emissions to nitrogen fertiliser in a cotton-fallow rotation in sub-tropical Australia

Nitrogen fertiliser is a major source of atmospheric N2O and over recent years there is growing evidence for a non-linear, exponential relationship between N fertiliser application rate and N2O emissions. However, there is still high uncertainty around the relationship of N fertiliser rate and N2O emissions for many cropping systems. We conducted year-round measurements of N2O emission and lint yield in four N rate treatments (0, 90, 180 and 270 kg N ha-1) in a cotton-fallow rotation on a black vertosol in Australia. We observed a nonlinear exponential response of N2O emissions to increasing N fertiliser rates with cumulative annual N2O emissions of 0.55 kg N ha-1, 0.67kg N ha-1, 1.07 kg N ha-1 and 1.89 kg N ha-1 for the four respective N fertiliser rates while no N response to yield occurred above 180N. The N fertiliser induced annual N2O EF factors increased from 0.13% to 0.29% and 0.50% for the 90N, 180N and 270N treatments respectively, significantly lower than the IPCC Tier 1 default value (1.0 %). This non-linear response suggests that an exponential N2O emissions model may be more appropriate for use in estimating emission of N2O from soils cultivated to cotton in Australia. It also demonstrates that improved agricultural N management practices can be adopted in cotton to substantially reduce N2O emissions without affecting yield potential.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.