CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART II: ELEMENTARY STRUCTURE-PRESERVING TRANSFORMATIONS

It has been shown in a previous paper that there is a real-valued transformation from the generalN -degree-of-freedom second order system to a second order system characterized by diagonal matrices. An immediate extension of this fact is that for any second order system, there is a set of real-valued transformations (thestructure-preserving transformations) which transform this system to a different second order system having identical characteristic behaviour. There are several possible reasons why it may be very useful to achieve a particular structure in the transformed system. It is obvious that a diagonal structure is extremely useful and a method has been devised for determining the diagonalizing transformation from the solution of the usual (complex) eigenvalue-eigenvector problem.This paper begins by outlining the usefulness of some other structures. Then it defines a class of elementary structure-preserving co-ordinate transformations that transform from one N -degree-of-freedom second order system to another. The termelementary is applied because any one of these transformations is the minimum-rank modification of the identity transformation. The changes occurring in the system matrices as a result of the application of one such elementary transformation transpire to be very simple in form, they are low rank, and they can be computed very efficiently.This paper provides the fundamental tools to enable the design of structure-preserving co-ordinate transformations which transform a second order system originally characterized by three general matrices in stages into a mathematically similar second order system characterized by three diagonal matrices. The procedure by which the individual elementary transformations are obtained is still under development and it is not discussed in this paper. However, an illustration is given of a five-degree-of-freedom self-adjoint system being transformed into tridiagonal form.     

Effects of lipopolysaccharide-induced inflammation on expression of growth-associated genes by corticospinal neurons

Background  

Inflammation around cell bodies of primary sensory neurons and retinal ganglion cells enhances expression of neuronal growth-associated genes and stimulates axonal regeneration. We have asked if inflammation would have similar effects on corticospinal neurons, which normally show little response to spinal cord injury. Lipopolysaccharide (LPS) was applied onto the pial surface of the motor cortex of adult rats with or without concomitant injury of the corticospinal tract at C4. Inflammation around corticospinal tract cell bodies in the motor cortex was assessed by immunohistochemistry for OX42 (a microglia and macrophage marker). Expression of growth-associated genes c-jun, ATF3, SCG10 and GAP-43 was investigated by immunohistochemistry or in situ hybridisation.     

CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART I: GENERAL TRANSFORMATIONS

When the dynamics of any general second order system are cast in a state-space format, the initial choice of the state vector usually comprises one partition representing system displacements and another representing system velocities. Co-ordinate transformations can be defined which result in more general definitions of the state vector. This paper discusses the general case of co-ordinate transformations of state-space representations for second order systems. It identifies one extremely important subset of such coordinate transformations—namely the set of structure-preserving transformations for second order systems—and it highlights the importance of these. It shows that one particular structure-preserving transformation results in a new system characterized by real diagonal matrices and presents a forceful case that this structure-preserving transformation should be considered to be the fundamental definition for the characteristic behaviour of general second order systems—in preference to the eigenvalue-eigenvector solutions conventionally accepted.     

SIMPLIFIED MODELS FOR THE LOCATION OF CRACKS IN BEAM STRUCTURES USING MEASURED VIBRATION DATA

A new simplified approach to modelling cracks in beams undergoing transverse vibration is presented. The modelling approach uses Euler-Bernoulli beam elements with small modifications to the local flexibility in the vicinity of cracks. This crack model is then used to estimate the crack locations and sizes, by minimizing the difference between the measured and predicted natural frequencies via model updating. The uniqueness of the approach is that the simplified crack model allows the location and damage extent to be estimated directly. The simplified crack model may also be used to generate training data for pattern recognition approaches to health monitoring. The proposed method has been illustrated using the experimental data on beam examples.     

IDENTIFICATION OF SPEED-DEPENDENT BEARING PARAMETERS

Bearing dynamic characteristics have been a major unknown in the modelling and analysis of large turbo-generators. An identification algorithm for bearing dynamic characterization by using unbalance response measurements is developed for multi-degree-of-freedom (m.d.o.f.) flexible rotor-bearing systems. The algorithm identifies the bearing dynamic parameters, consisting of four effective stiffness and four damping coefficients for each bearing, utilizing frequency domain synchronous unbalance response measurements from the accelerometers attached to the bearing housings in the horizontal and vertical directions, for a minimum two different unbalance configurations. The procedure of identifying bearing dynamic coefficients by using the proposed algorithm is presented and demonstrated through a numerical example. Adding noise to the simulated signal checks the robustness of the algorithm against measurement noise. Combinations of regularization and the generalized singular value decomposition (SVD) are used to tackle an ill-posed problem due to the nearly circular orbit of the rotor at the bearings, as a special case for nearly isotropic bearings. It is demonstrated that by measuring noisy bearing responses with the direction of rotation of the rotor both in the clockwise and anticlockwise directions, the bearing estimation problem for circular orbit becomes well-conditioned. The regularization algorithm is tested for an experimental rotor-bearing rig. The response reproduction capabilities are excellent even in the presence of measurement noise.     

Beta-delayed proton emitter kr

The nucleide ⁷³Kr has been identified by on-line mass separation as a precursor of β-delayed proton emission. The proton branch is (6.8 ±1.2) × 10⁻³ proton/decay. The protons populate the ground state and also the first excited 2⁺ state at 866 keV in ⁷²Se with a relative intensity of (35±9) %. The value of Q_EC−B_p, where B_p is the proton separation energy for the nucleus ⁷³Br, is found to be 4.85 ±0.30 MeV based on the fraction of proton events preceded by positron decay.