Theoretical analysis of transient waves in a simply-supported Timoshenko beam by ray and normal mode methods

Forced vibration analysis of two dimensional bridge deck structures involves complex mathematical procedures and therefore analysis is often based on beam idealization of equivalent plates. This simplification yields close agreement only for long span bridges where plate action is relatively insignificant. However, such a concept of beam idealization cannot be successfully utilized in the case of short span bridges where plate action is predominant and where the determination of the distribution of dynamic deflections and amplification factors at critical sections of such plates is of prime concern. The principal objective of the present investigation is the forced vibration analysis of longitudinally stiffened, simply supported orthotropic bridge decks utilizing a new concept of interconnected beam idealization. The theoretical analysis deals with determination of amplification factors and dynamic deflections along critical sections of the plate treated as a series of interconnected beams. The aspect ratios of the plates under investigation as series of interconnected beams are designed to cover a wide range of plate to beam transition. The theoretical analysis is supplemented by an extensive experimental programme.In conclusion, it is seen that this concept of interconnected beam idealization not only takes into account the plate action of the deck structure but also reduces greatly the complexity of mathematical formulation. A good comparison between the theoretical and the experimental results indicates that this concept can be used to advantage for analysis and, within certain limitations, for design purposes.

Download Full-text

Response of a Simply Supported Timoshenko Beam to a Purely Random Gaussian Process

Journal of Applied Mechanics ◽

10.1115/1.4011862 ◽

1958 ◽

Vol 25 (4) ◽

pp. 496-500

Author(s):

J. C. Samuels ◽

A. C. Eringen

Keyword(s):

Timoshenko Beam ◽

Beam Theory ◽

Beam Equation ◽

Mean Square ◽

Bending Stress ◽

Random Loading ◽

Simply Supported ◽

The Mean ◽

Timoshenko Beam Equation ◽

Classical Beam Theory

Abstract The generalized Fourier analysis is applied to the damped Timoshenko beam equation to calculate the mean-square values of displacements and bending stress, resulting from purely random loading. Compared with the calculations, based on the classical beam theory, it was found that the displacement correlations of both theories were in excellent agreement. Moreover, the mean square of the bending stress, contrary to the results of the classical beam theory, was found to be convergent. Computations carried out with a digital computer are plotted for both theories.

Download Full-text

Experiments on the Buckling of Simply-Supported Rectangular Plates

The Aeronautical Journal ◽

10.1017/s0001924000052180 ◽

1969 ◽

Vol 73 (703) ◽

pp. 607-608 ◽

Cited By ~ 1

Author(s):

A. C. Mills

Keyword(s):

Experimental Investigation ◽

Theoretical Analysis ◽

Boundary Conditions ◽

Buckling Load ◽

Theoretical Solution ◽

Rectangular Plates ◽

Uniform Load ◽

Simply Supported

In ref. (1) Pope presents a theoretical analysis of the buckling of rectangular plates tapered in thickness under uniform load in the direction of taper. An experimental investigation into the end load buckling problem for a plate having simply-supported edges with the sides prevented from moving normally in the plane of the plate is described in ref. (2). For these boundary conditions the theoretical solution is exact. However, the compatability equation is not satisfied exactly when the sides are free to move in the plane of the plate. This experimental investigation demonstrates that the buckling load is nevertheless adequately predicted by the analysis in these circumstances.

Download Full-text

Thermal Effects on Internal and External Resonances of a Nonlinear Timoshenko Beam

Volume 8: 26th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2014-34078 ◽

2014 ◽

Cited By ~ 1

Author(s):

Anna Warminska ◽

Jerzy Warminski ◽

Emil Manoach

Keyword(s):

Timoshenko Beam ◽

Thermal Effects ◽

Internal Resonance ◽

Structural Parameters ◽

Effect Of Temperature ◽

Simply Supported ◽

Thermal Fields ◽

Large Amplitude Vibrations ◽

The Galerkin Method ◽

The Mathematical Model

Large amplitude vibrations of a Timoshenko beam under an influence of thermal and mechanical loadings are studied in the paper. The structural parameters of the beam are considered enabling internal resonance conditions. Moreover, it is assumed that the beam gets instantly temperature which is distributed along its length and thickness. The mathematical model represented by a set of partial differential equations takes into account coupled mechanical and thermal fields. The problem is transformed to a set of ODEs by the Galerkin method and three modes of a simply supported beam at both ends are studied. The effect of temperature on internal and external resonances is analysed on the basis of the proposed reduced model.

Download Full-text

Mechanical Characters of Six Engineering Timoshenko Beams

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.668-669.201 ◽

2014 ◽

Vol 668-669 ◽

pp. 201-204

Author(s):

Hong Liang Tian

Keyword(s):

Timoshenko Beam ◽

Analytic Solutions ◽

Timoshenko Beams ◽

Bernoulli Beam ◽

Simply Supported ◽

Normality Assumption ◽

Length Direction ◽

The Right ◽

Euler Bernoulli Beam ◽

Mechanical Characters

Timoshenko beam is an extension of Euler-Bernoulli beam to interpret the transverse shear impact. The more refined Timoshenko beam relaxes the normality assumption of plane section that remains plane and normal to the deformed centerline. The manuscript presents some exact concise analytic solutions on deflection and stress resultants of NET single-span Timoshenko beam with general distributed force and 6 kinds of standard boundary conditions, adopting its counterpart Euler-Bernoulli beam solutions. Engineering example shows that scale impact would not unveil itself for micro structure with micrometer μm-order length, yet will be prominent for nanostructure with nanometer nm-order length. When simply supported CNTs is undergone to a concentrative force at the median and complete bend moment, scale action is observed along the ensemble CNTs, while it unfurls itself the most at the position of the concentrated strength. When a clamped-free CNTs is exposed to a centralized force at the mesial and distributed force, there is no scale impact about the deflection at all positions on the left border of the concentrated strength position, while such operation inspires at once at all positions on the right margin of the concentrated strength position. When a clamped-clamped CNTs is lain under a concentrative strength at the middle, the deflection of NET Euler-Bernoulli CNTs reflects scale effect completely. Notable differences between the deflection of Euler-Bernoulli CNTs and that of Timoshenko CNTs are reflected at large ratio of diameter versus length. The deflection of NET clamped-free and simply supported Timoshenko beam doesn’t introduce surplus scale process in terms of its counterpart, NET Euler-Bernoulli beam. However, the deflection of NET clamped-clamped Timoshenko beam does involve additional scale impact solely including the method when the concentrated strength position is at the midway in the beam-length direction.

Download Full-text

The Control of Parametric Vibration in a Simply Supported Beam

Journal of Vibration and Acoustics ◽

10.1115/1.3269437 ◽

1987 ◽

Vol 109 (3) ◽

pp. 315-318

Author(s):

J. S. Burdess

Keyword(s):

Numerical Simulation ◽

Theoretical Analysis ◽

Perturbation Method ◽

Natural Frequency ◽

Multiple Scales ◽

Equation Of Motion ◽

Control Law ◽

Parametric Vibrations ◽

Simply Supported ◽

Multiple Scales Perturbation Method

The paper shows how unstable parametric vibrations of a uniform beam can be controlled. A control law is proposed and it is shown that the beam can be made to vibrate at a present amplitude at its natural frequency. The beam is modelled by its first mode and a solution to the governing equation of motion is derived by applying the multiple scales perturbation method. The results of the theoretical analysis are verified by a numerical simulation.

Download Full-text