Variational Equation of Motion for Coupled Flexure and Torsion of Bars of Thin-Walled Open Section Including Thermal Effect

1971 ◽  
Vol 38 (2) ◽  
pp. 502-506 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Thermal Effect ◽  
Structural Dynamics ◽  
Variational Equation ◽  
Equation Of Motion ◽  
Bending Moments ◽  
Open Section ◽  
Thermal Bending ◽  
Axis Of Symmetry ◽  
Thin Walled ◽  
Special Case

Literature on flexure and torsion of bars of thin-walled open section is reviewed. The use of the variational equation of motion in solving problems of structural dynamics is further advocated. The variational equation of motion, together with the associated stress-displacement relations, is then derived for coupled flexure and torsion of the open section. Thermal effect is included, leading to a thermal twisting moment in addition to the usual thermal bending moments. For the special case of an open section with one axis of symmetry and with symmetrical heat input, only flexure is shown to be thermally inducible. The general result then reduces to the simple variational equation of flexural motion used in a separate study of the thermal flutter of a spacecraft boom.

Mathematical Analogy between Non-Uniform Torsion and Transverse Bending of Thin-Walled Open Section Beams

2015 ◽  
Vol 725-726 ◽  
pp. 746-751 ◽  
Author(s):  
Vladimir Rybakov ◽  
Alexander Sergey
Keyword(s):  
Bending Moment ◽  
Maximum Deviation ◽  
Bending Moments ◽  
Distributed Load ◽  
Transverse Bending ◽  
Open Section ◽  
Uniformly Distributed Load ◽  
Thin Walled ◽  
And Function ◽  
Mathematical Analogy

The objective of this work is to identify and make an analysis of correlation between functions of bimoments and function of bending moments arising in the beams under the same loads. This article shows the possibility of using a diagram of bending moment multiplied by a factor as a diagram of bimoment. The maximum deviation between diagram of bending moment and diagram of bimoment made up 3.6 % of maximum bending moment in case of uniformly distributed load on one side of fixed supported beam.

Pretwisted Curved Beams of Thin-Walled Open Section

1972 ◽  
Vol 39 (3) ◽  
pp. 779-785 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
Highway Bridges ◽  
Major Effect ◽  
Curved Beams ◽  
Open Section ◽  
Straight Beam ◽  
Thin Walled ◽  
Bending Modes ◽  
Axes Of Symmetry

Equations of motion are derived for coupled extension, flexure, and torsion of pretwisted curved bars of thin-walled, open section. The derivation is based on energy principles and includes inertia terms. The major effect of initial pretwist is to allow coupling of all possible beam deformation modes; however, if the bar is straight and has two axes of symmetry, pretwist causes coupling only between the two bending modes, and between extension and torsion. The governing equations are presented in first-order form, and a numerical technique is suggested for the case of space varying pretwist. It is suggested that these equations may form the basis for a simplified study of the effect of superelevation on the static and dynamic response of curved highway bridges. Finally, a simple straight beam with uniform pretwist is studied to compare effects of pretwist and restrained torsion in a thin-walled beam of open section.

Stresses in Curved, Circular Thin-Wall Tubes

1963 ◽  
Vol 30 (1) ◽  
pp. 134-135
Author(s):  
E. A. Utecht
Keyword(s):  
Thin Wall ◽  
Bending Moments ◽  
Circular Tubes ◽  
Out Of Plane ◽  
Thin Walled ◽  
Plane Bending

Curves are presented which give stress intensification factors for curved, thin-walled circular tubes under various combinations of in-plane and out-of-plane bending moments.

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

An Evaluation of Material Weight and Contained Fluid Volume for Eccentric Intersecting Cylinders of Arbitrary Size

1989 ◽  
Vol 111 (3) ◽  
pp. 342-347
Author(s):  
Y. J. Chao ◽  
M. A. Sutton
Keyword(s):  
Vessel Diameter ◽  
Fluid Volume ◽  
Wide Range ◽  
Single Integral ◽  
Material Volume ◽  
Thin Walled ◽  
Special Case ◽  
Range Of Values ◽  
Engineering Personnel ◽  
Quantities Of Interest

Engineering personnel in industries which use pressurized containment vessels having attached nozzles are required not only to design portions of the lifting mechanism, but also to estimate the fluid volume which the vessel and nozzles will contain; most designers use simplified formulas for computing the quantities of interest. Typically, these formulas are valid approximations when the nozzle diameter is much smaller than the vessel diameter. The enclosed work develops three single-integral expressions which can be programmed and numerically integrated to obtain accurate estimates for both the material volume and also the containment volume present in a pair of eccentrically, or concentrically, intersecting thin-walled cylinders of arbitrary diameters. A table of such values is presented for a wide range of values of the standard nozzle pipe diameter and vessel diameter, for the special case of a concentric nozzle. In addition, an example is presented which compares the numerically integrated values for both the material volume and the containment volume to simplified upper and lower-bound estimates.

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