Torsional Rigidity of Beams of given areas with different Cross sections

This paper is aimed at determining among beams with different cross sections whose torsional rigidity is the greatest. That is, to determine the beam, with a particular cross section, that gives the greatest resistance to the twisting moment. The Torsional Rigidity is obtained as the ratio of twisting moment to the angle of twist per unit length. From the table of value of the maximum torsional Rigidity of beams with different cross sections, it is observed that the beam with circular cross sectional area has the greatest torsional rigidity. It is also observed that maximum torsional rigidity of beams with different cross-sectional area is a function of their areas

SOLVING NON-LINEAR DAMPED DRIVEN SIMPLE PENDULUM WITH SMALL AMPLITUDE USING A SEMI ANALYTICAL METHOD

In this paper, we present a semi analytical solution for a damped driven pendulum with small amplitude, by using the differential transformation method. We begin by showing how the differential transformation method applies to the non-linear dynamical system. The method transformed the differential equation governing the motion of the pendulum into its algebraic form. The results obtained are in good agreement with the solution in the literature. The results show that the technique introduced is easy to apply to such dynamical syste

Dynamic Analysis of Railway Bridges Supported by Winkler Foundation under Uniform Partially Distributed Moving Railway Vehicle

Transport structure such as railway bridges (plates), are subjected to moving railway vehicles (loads) which vary in both space and time. This branch of transport has experienced great advances, characterised by increasing high speed and weights of railway vehicles. Structures and media on which the railway vehicles move have, therefore, been subjected to vibration and dynamic stress more than ever before. The motivation for this paper is the observation that most of the works available in the literature are concerned with plates for which the effects of both rotatory inertia and shear deformation are neglected. Also the plates are assumed not resting on any foundation. In this paper, the dynamic response of railway track, modelled as an elastic rectangular plate, continuously supported by an elastic foundation and traversed by moving railway vehicle is investigated. Finite difference method is used to transform the set of coupled partial differential equations to a set of algebraic equations. The desired solutions are obtained with the aid of computer programs developed in conjunction with MATLAB. This shows that the elastic foundation, rotatory inertia and shear deformation have significant effect on the dynamic response of the railway bridge, to the moving railway vehicle (modelled as partially distributed moving load). In particular, it is observed that the deflection of the railway bridge decreases as the foundation moduli increas

Application of Unified Number to Temperature Profiles of Pipe Walls and Fluids Using Mathematical Experimentation

The equations of energy balance and heat conductivity was queried by introducing known parameters and expanded using virtual mathematical experimentation. Distribution of temperature of the pipe wall, fluid flow and surrounding air were accounted for via mathematical expressions. A new dimensionless parameter was introduced with the aim of solving future problems in hydraulic engineering. Keywords: dimensionless parameters, heat conductivity equations, fluid, Bessel polynomial scheme, Unified numbe

Finite Difference Dynamic Analysis of Railway Bridges Supported by Pasternak Foundation under Uniform Partially Distributed Moving Railway Vehicle

Rail transport has experienced great advances in recent times, characterised by increasing high speed and weights of railway vehicles. The vibration and dynamic stress being subjected to by the transport structures, such as road or railway bridges, have increased due to these factors. In this paper, the dynamic response of railway bridges, modelled as an elastic rectangular plate, continuously supported by Pasternak foundation and traversed by moving railway vehicle is investigated. Finite difference method is used to transform the set of coupled partial differential equations to a set of algebraic equations. The desired solutions are obtained with the aid of computer programs developed in conjunction with MATLAB. It is observed that the deflection of the railway bridge decreases as the foundation moduli increase. The rotatory inertia and shear deformation have significant effect on the deflection of the railway bridge under a moving railway vehicle (modelled as partially distributed moving load)

Analysis of Hermite’s equation governing the motion of damped pendulum with small displacement

This paper investigates simple pendulum dynamics, putting damping into consideration. The investigation begins with Newton’s second law of motion. The second order differential equation governing the motion of a damped simple pendulum is written in form of Hermite’s differential equation and general solution obtained by means of power series. The results obtained are in agreement with the existing ones, and converge fast

ANALYSIS OF TORSIONAL RIGIDITY OF CIRCULAR BEAMS WITH DIFFERENT ENGINEERING MATERIALS SUBJECTED TO ST. VENANT TORSION

Many engineering structures, such as airplane wings, beams and shafts are subjected to higher torsional forces today due to advancement in Structural Engineering, in terms of size and technology. In this paper, we analyzed the resistance of circular beams, of different engineering materials, to their corresponding twisting moments. We obtained the torsional rigidity for the different beams as the ratio of twisting moment to the angle of twist per unit length. It is observed that torsional rigidity of the beams is a function of their areas and the engineering material they are made up of. Specifically it is observed that the circular beam made up of brass engineering material has the greatest torsional rigidity among the twelve engineering materials considered

Dynamic Response of Mindlin Elastic Plate Supported by Pasternak Foundation under Uniform Partially Distributed Moving Load

Various transport structures, ranging from railways, roads and bridges to space vehicles and submarines, are usually subjected to moving loads which vary in both space and time. All branches of transport have experienced great advances, characterised by increasing high speed and weights of railway vehicles. Structures and media on which the railway vehicles move have, therefore, been subjected to vibration and dynamic stress more than ever before. The motivation for this paper is from the observation that most of the works available in the literature are concerned with plates for which the effects of both rotatory inertia and shear deformation are neglected. Also the plates are assumed not resting on any foundation. In this paper, the dynamic response of Mindlin plate, continuously supported by Pasternak foundation and traversed by moving load is investigated. Finite difference method is used to transform the set of coupled partial differential equations to a set of algebraic equations. The desired solutions are obtained with the aid of computer programs developed in conjunction with MATLAB. This shows that the elastic foundation, rotatory inertia and shear deformation have significant effect on the dynamic response of the plate, to the moving load. In particular, it is observed that the deflection of the plate decreases as the foundation moduli increas

A Comparison of Dynamic Behaviours of Mindlin, Shear, Rotatory and Kirchoff Plates Supported by Subgrade under Moving Load

Various Plates and Plate-like transport structures, such as roads, railway bridges, space vehicles and submarines, are usually subjected to different types of loads. These loads include cars, Railway vehicles and human beings. In this paper we made an attempt to analyse the dynamic responses of some specific plates to moving load. Four types of plates were considered, namely: Mindlin plate, Shear plate, Rotatory plate and Kirchoff plate. The moving load is assumed to be uniform partially distributed, while the plates are isotropic and supported by Winkler foundation. Finite difference technique was used to transform the set of dimensionless first order partial differential equations to a set of algebraic equations. Computer programs were developed and used in conjunction with MATLAB in order to obtain the desired solution. It was observed that the solution obtained were consistent with the ones in literature. Specifically, it was observed that for fixed values of velocity, contact area and foundation constant, the values of the maximum deflection are higher for Mindlin plates when compared to shear, rotatory and Kirchoff plates