The Torsional Vibration of Uniform Thin-Walled Beams of Open Section

1969 ◽  
Vol 73 (704) ◽  
pp. 672-674 ◽  
Author(s):  
J. B. Carr
Keyword(s):  
Torsional Vibration ◽  
Characteristic Functions ◽  
Shear Stresses ◽  
Simply Supported ◽  
Open Section ◽  
Torsional Resistance ◽  
Approximate Frequency ◽  
Thin Walled ◽  
Image Position ◽  
Fixed End

The pure torsional vibration of uniform thin-walled beams of open section, which is governed by the differential equation has been extensively analysed by Gere He derived the exact frequency equations for beams with a variety of end conditions. However, these equations are, in most cases, highly transcendental. This note uses an energy approach to obtain approximate frequency equations for the fixed-fixed and the fixed-simply-supported beams. A fixed end is one which allows no twist and no warping and a simply-supported end allows no twist but permits warping to take place freely. The approximating functions used are those corresponding to the exact solution of the problem if the torsional resistance caused by the St Venant system of shear stresses is zero. These functions are similar to the characteristic functions of simple beams in flexure.

scholarly journals Spectral Dynamic Analysis of Torsional Vibrations of Thin-Walled Open Section Beams Restrained Against Warping at One End and Transversely Restrained at the Other End

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Chellapilla Kameswara Rao 1 ◽  
Lokavarapu Bhaskara Rao 2
Keyword(s):  
Dynamic Analysis ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
The Other ◽  
Graphical Form ◽  
Open Section ◽  
Torsional Frequency ◽  
Thin Walled ◽  
Spectral Frequency

The present paper deals with spectral dynamic analysis of free torsional vibration of doubly symmetric thin-walled beams of open section. Spectral frequency equation is derived in this paper for the case of rotationally restrained doubly-symmetric thin-walled beam with one end rotationally restrained and transversely restrained at the other end. The resulting transcendental frequency equation with appropriate boundary conditions is derived and is solved for varying values of warping parameter and the rotational and transverse restraint parameter. The influence of rotational restraint parameter, transverse restraint parameter and warping parameter on the free torsional vibration frequencies is investigated in detail. A MATLAB computer program is developed to solve the spectral frequency equation derived in this paper. Numerical results for natural frequencies for various values of rotational and transverse restraint parameters for various values of warping parameter are obtained and presented in both tabular as well as graphical form showing the influence of these parameters on the first fundamental torsional frequency parameter.

Nonlinear Torsional Vibrations of Thin-Walled Beams of Open Section

1975 ◽  
Vol 42 (1) ◽  
pp. 240-242 ◽  
Author(s):  
C. Kameswara Rao
Keyword(s):  
Differential Equation ◽  
Large Amplitude ◽  
Torsional Vibrations ◽  
Simply Supported ◽  
Open Section ◽  
Governing Differential Equation ◽  
Thin Walled

An attempt has been made to derive and solve the governing differential equation of large amplitude torsional vibrations of simply supported doubly symmetric thin-walled beams of open section. Graphs indicating the influence of large amplitudes on nonlinear period of torsional vibrations for various nondimensional beam constants are presented.

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.

Computer analysis of thin-walled concrete box beams

1989 ◽  
Vol 16 (6) ◽  
pp. 902-909 ◽  
Author(s):  
Shahbaz Mavaddat ◽  
M. Saeed Mirza
Keyword(s):  
Key Words ◽  
Computer Analysis ◽  
Shear Stresses ◽  
Shear Lag ◽  
Applied Loading ◽  
Box Beam ◽  
Box Beams ◽  
Three Stages ◽  
Thin Walled ◽  
Normal And Shear Stresses

Three computer programs, written in FORTRAN WATFIV, are developed to analyze straight, monolithically cast, symmetric concrete box beams with one, two, or three cells and side cantilevers over a simple span or over two spans with symmetric mid-span loadings. The analysis, based on Maisel's formulation, is performed in three stages. First, the structure is idealized as a beam and the normal and shear stresses are calculated using the simple bending theory and St-Venant's theory of torsion. The secondary stresses arising from torsional and distortional warping and shear lag are calculated in the second and third stages, respectively. The execution times on an AMDAHL 580 system are 0.02, 0.93, and 0.25 s for the three programs, respectively. The stresses arising in each stage of analysis are then superposed to determine the overall response of the box section to the applied loading. The results are compared with Maisel's hand calculations. Key words: bending, bimoment, box beam, computer analysis, FORTRAN, shear, shear lag, thin-walled section, torsion, torsional and distortional warping.

scholarly journals Green's function of the clamped punctured disk

1977 ◽  
Vol 20 (2) ◽  
pp. 175-181 ◽  
Author(s):  
Mitsuru Nakai ◽  
Leo Sario
Keyword(s):  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
American Mathematical Society ◽  
Point Load ◽  
Thin Elastic Plate ◽  
Constant Sign ◽  
Boundary Circle ◽  
Simply Supported ◽  
Image Position

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

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