Closure to “Discussion of ‘Transverse Vibration of a Uniform Simply Supported Timoshenko Beam Without Transverse Deflection’” (1977, ASME J. Appl. Mech., 44, p. 362)

1977 ◽  
Vol 44 (2) ◽  
pp. 362-362
Author(s):  
B. Downs
Keyword(s):  
Timoshenko Beam ◽  
Transverse Vibration ◽  
Simply Supported ◽  
Transverse Deflection

Transverse Vibration of a Uniform, Simply Supported Timoshenko Beam Without Transverse Deflection

1976 ◽  
Vol 43 (4) ◽  
pp. 671-674 ◽  
Author(s):  
B. Downs
Keyword(s):  
Timoshenko Beam ◽  
Transverse Vibration ◽  
Simply Supported ◽  
Transverse Deflection

An additional solution is obtained for the vibrational behaviour of a uniform, simply supported Timoshenko beam. The characteristics of the mode are explained in physical terms.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

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

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.

Forced Flexural Vibrations of Sandwich Plates in Plane Strain

1960 ◽  
Vol 27 (3) ◽  
pp. 535-540 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Plane Strain ◽  
Sandwich Plate ◽  
Classical Method ◽  
Separation Of Variables ◽  
Flexural Vibration ◽  
Time Dependent ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Transverse Deflection ◽  
Plane Strain Case

On the basis of the new flexural theory of elastic sandwich plates recently developed [1–3], the problem of general forced flexural vibration of sandwich plates in the plane-strain case is solved. The classical method of separation of variables combined with the Mindlin-Goodman procedure [4] for treating time-dependent boundary conditions is used. As an example, the results are made use of in solving the problem of a simply supported sandwich plate in plane strain with one of the two end sections prescribed a transverse deflection varying with time.

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

2014 ◽  
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.

Mechanical Characters of Six Engineering Timoshenko Beams

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.

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