Showing papers on "Timoshenko beam theory published in 1978"

Debond dynamics of an elastic strip, I: Timoshenko-beam properties and steady motion

Abstract: The paper considers debond of a Timoshenko-beam from a substrate which is rigid during the event. Essential relations expressing support conditions, continuity conditions, conservation of momentum and energy balance are discussed. Details relating to steady motion are exemplified.

Elementary Theory in Linearly Tapered Beams

Abstract: With the use of a generalized Kirchhoff hypothesis in which the transverse shear strain in cylindrical coordinates is assumed to be zero, a beam theory is developed for linearly tapered members. The equations are analogous to those of conventional beam theory but they are applicable to a different class of problems. For a tip loaded, wedge-shaped cantilever beam, the radial stress is identical to the three-dimensional solution. The predicted shear stress distribution in the web of a wide flange web-tapered cantilever beam subjected to a tip force and moment agrees closely with a finite element solution to the same problem. With additional verification, the elementary theory may prove to be extremely useful for the design and analysis of tapered beams under more general conditions.

Distortion of Thin-Walled Open-Cross-Section Members : One-Degree-of-Freedom and Singly Symmetrical Cross-Sections

Abstract: The essential features of the distortional deformation of an open-cross-section member are studied. The analytical models are restricted to the members of one-degree-of-freedom. The assumptions used in the semi-membrane theory are employed, and one dimensional analytical method applicable to distortional deformation is introduced. The concept of two shear centers of distortion can be introduced. This is an extended concept of a centroid and a torsional shear center. The distortional bimoment introduced here should be taken into consideration as a generalized force. According to the results of the calculation of a cantilever, the stress value at the fixed end has the possibility of being about twice as high as the value of the conventional beam theory.

An experimental study of the Timoshenko's shear coefficient for flexurally vibrating beams

Abstract: The validity of the shear coefficient K has been experimentally tested using a large number of rectangular glass beams and cylindrical phosphor-bronze beams. The theoretical expressions of K=(5+5m)/(6+5m) for rectangular beams and K=(6+12m+6m2)/(7+12m+4m2) for cylindrical beams, where m is Poisson's ratio, have been confirmed to yield the best agreement with experiment. For cylindrical beams, Timoshenko's theory has been shown to give good results over a fairly wide frequency range. For rectangular beams, it is suggested that a better expression should be proposed to fit the experimental results.

Wedge loading of a semi-infinite strip with an edge crack

Abstract: The problem of a semi-infinite strip containing an edge crack is considered. It is assumed that the strip is loaded by a frictionless rigid wedge pressed into the crack. The resulting crack-contact problem is formulated in terms of a system of singular integral equations. The behavior of the solution near the singular points is studied in detail. A series of numerical examples is given and the results are compared with those obtained by the method of boundary collocation and by the simple beam theory.

Dynamics of Neutrally Buoyant Inflated Viscoelastic Tapered Cantilevers Used in Underwater Applications

Abstract: The paper investigates statics and dynamics of neutrally buoyant inflated viscoelastic tapered cantilevers used as structural members in underwater platforms. In the beginning, the static flexural behavior of the beam is studied using the three-parameter viscoelastic solid model which yields material properties for the mylar-polyethylene-mylar plastic film used. Results of a detailed experimental program are also presented to substantiate validity of the analytical model. This is followed by free vibration analyses of the inflated cantilevers in the ocean environment. The elementary beam theory is used to predict their natural frequencies. Finally, the dynamical response of the uniform and tapered cantilevers to root excitation, at the fundamental wave frequency and its second harmonic, is studied. The governing nonlinear equations are analyzed by taking two terms of the assumed Fourier series solution. Results suggest that for the case of the simple harmonic excitation, the nonlinear hydrodynamic drag introduces no superharmonic components into the response. For low forcing frequencies typical of the ocean environment, an increase in taper ratio tends to reduce the tip amplitudes. However, for frequencies above the fundamental, the response characteristics are completely reversed. The analysis provides valuable information concerning the system parameters leading to critical response and hence should prove useful in the design of such inflatable members.

Traveling Loads on the Timoshenko Beam.

Abstract: : A transverse force traveling along an infinite string or a beam at critical values of constant velocity generates unbounded amplitudes, in the absence of dissipation. This resonance is analagous to the unbounded amplitudes generated by a stationary force oscillating at one of the natural frequencies. The response of a finite elementary beam to a moving force of constant amplitude can be determined in terms of the eigenfunctions of the beam. Modification of elementary beam theory to take into account the effects of rotatory inertia and shear leads to the Timoshenko beam theory, from which a new set of eigenvalues and eigenfunctions can be determined. These eigenfunctions can be shown to have an orthogonality relationship which, although unusual, permits the solution of initial value and non-homogeneous problems. The procedure for solving such problems is given, and applied to the problem of a traveling load on a finite Timoshenko beam with arbitrary end conditions. Results are obtained for the case of pinned ends, and compared with those from elementary theory. Results of particular significance are that the distribution of critical speeds is altered significantly through inclusion of rotatory and shear effects, and that a shear wave, not present in the results from elementary theory, can be identified and is shown to play a major role in determining the response. (Author)

Waves in Constrained Materials and Thin-Walled Beams

Abstract: The propagation condition for plane infinitesimal waves in constrained elastic materials subjected to arbitrary homogeneous strain is derived and found to be the same as a previously known result for the propagation of acceleration waves. The formal structure of the system of equations leading to the propagation condition is analyzed and extended to include more general situations. In particular, a nonlinear formulation of thin walled beam theory in terms of a constrained multidirected curve is covered by such a generalization. This fact is exploited to derive the frequency equations for small vibrations of thin walled elastic beams of open cross-section about an arbitrary uniformly strained state and to obtain critical loads for Euler and lateral buckling. The results are compared with the classical formulas based on a linearized pre-buckling state and the neglect of shear deformations.

Normal modes of vibration of the vertebral column

Abstract: Publisher Summary This chapter discusses the normal modes of vibration of the vertebral column. Interest in the structure and function of the human vertebral column ranges from its importance in evolution to the more practical aspect of spinal injuries in impulsive ejections or collisions. Damage to the vertebral column may also be caused as a result of repeated low frequency vibrations that correspond to normal mode frequencies. Calculations of the bending vibration frequencies using a simple beam theory were reported by Huijens. For long bones, a finite element method was developed in detail by Orne and Young, and applied to the dog's radius. In the case of the vertebral column, the 24 vertebrae provide a natural set of finite elements in terms of which the system should be studied. The chapter presents a series of models for the vertebral column, in a gradually increasing order of sophistication. It describes the redoing of the simple beam theory by calculating the effective bending stiffness of a disc by making use of the actual cross-sectional areas and Young's moduli as experimentally measured and reported by Yamada.

Dynamic coefficient of an elastically supported, pre-stressed beam

Abstract: An analysis is made of the problem of vibrations of a beam with an axial force resting on eltstic foundation, when the beam is uniform and of finite length and is subjected to an impulsive load. The solution is presented within the framework of a beam theory which includes the effects of shear deformation and rotary inertia. An example is provided where the dynamic coefficient for the bending moment is calculated. From the results of theoretical analysis, it becomes evident that the axial force in the beam and the stiffness of the foundation have considerable effect upon the dynamical behaviour of the system.