A new approach for fixed point smoothing in linear distributed parameter systems

In this paper, we solve the distributed parameter fixed point smoothing problem by formulating it as an extended linear filtering problem and show that these results coincide with those obtained in the literature using the forward innovations method.

The elastic constants of isomorphous sodium bromate and sodium chlorate from 77 to 350 K

The elastic constants of NaBrO3 and NaClO3 are evaluated from ultrasonic velocity measurements using pulse superposition techniques. The values of C11, C12 and C44 for NaBrO3 at 298°K are 5.578, 1.705, 1.510 (x 1010 N/m2) and for NaClO3 the values are 4.897, 1.389, 1.174. The values at 77°K are respectively 6.35, 1.98 and 1.65 for NaBrO3 and 6.15, 2.16 and 1.32 for NaClO3.

Influence of Joint Thickness and Mortar-Block Elastic Properties on the Strength and Stresses Developed in Soil-Cement Block Masonry

Soil-cement blocks are employed for load bearing masonry buildings. This paper deals with the study on the influence of bed joint thickness and elastic properties of the soil-cement blocks, and the mortar on the strength and behavior of soil-cement block masonry prisms. Influence of joint thickness on compressive strength has been examined through an experimental program. The nature of stresses developed and their distribution, in the block and the mortar of the soil-cement block masonry prism under compression, has been analyzed by an elastic analysis using FEM. Influence of various parameters like joint thickness, ratio of block to mortar modulus, and Poisson's ratio of the block and the mortar are considered in FEM analysis. Some of the major conclusions of the study are: (1) masonry compressive strength is sensitive to the ratio of modulus of block to that of the mortar (Eb/Em) and masonry compressive strength decreases as the mortar joint thickness is increased for the case where the ratio of block to mortar modulus is more than 1; (2) the lateral tensile stresses developed in the masonry unit are sensitive to the Eb/Em ratio and the Poisson's ratio of mortar and the masonry unit; and (3) lateral stresses developed in the masonry unit are more sensitive to the Poisson's ratio of the mortar than the Poisson's ratio of the masonry unit.

Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m times n) matrix with non-negative elements, x and g are respectively (n times 1) and (m times 1) vectors with positive components.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

A simple non-linear D/A converter

A simple generalized technique for realizing a non-linear digital to analogue converter (N-DAC), based on the principles of ' segment of equal digital interval ' is described. The simplicity of the proposed technique is demonstrated by realizing an N-DAC having a square law transfer function.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC 11,C 12 and C 44 of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values are C 11=4.90,C 12=1.39,C 44=1.17 (× 1010 N/m 2) at 298 K and 6.15, 2.16, 1.32 (×1010 N/m 2) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.

Constrained linear filter and its relation to singular optimal control

This paper presents an analysis of an optimal linear filter in the presence of constraints on the moan squared values of the estimates from the viewpoint of singular optimal control. The singular arc has been shown to satisfy the generalized Legcndrc-Clebseh condition and Jacobson's condition. Both the cases of white measurement noise and coloured measurement noise are considered. The constrained estimate is shown to be a linear transformation of the unconstrained Kalman estimate.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Vibrations of annular plates with linear thickness profiles

Abstract is not vailable.