Showing papers on "Timoshenko beam theory published in 1975"
TL;DR: In this article, the authors presented a finite element model with nodal degrees of freedom which can satisfy all the forced and natural boundary conditions of a Timoshenko beam, and the mass and stiffness matrices of the element were derived from kinetic and strain energies by assigning polynomial expressions for total deflection and bending slope.
143 citations
TL;DR: In this article, the equations of motion including shear and rotatory inertia are developed for uncoupled lead-lag and flapping vibrations of beams rotating at constant angular velocity in a fixed plane.
70 citations
TL;DR: In this paper, the authors present a method to deal with an inclined crack in an elastic strip, which involves the solutions for a cracked plane and an uncracked strip and results in two coupled singular integral equations with finite interval of integration.
34 citations
TL;DR: In this paper, a direct virtual work formulation of the beam equations is developed by starting with the general Lagrangian form of the three-dimensional virtual displacement equations of solid mechanics and introducing the specializations associated with thin-walled beam theory.
Abstract: A direct virtual work formulation of the beam equations is developed by starting with the general Lagrangian form of the three-dimensional virtual displacement equations of solid mechanics and introducing the specializations associated with thin-walled beam theory. The resulting beam equations are valid, within the limits of thin-walled beam theory, for arbitrary reference axes and are applicable to inelastic beam-column problems. This makes it unnecessary to consider instantaneous centroidal and shear center reference axes for incremental inelastic analysis, or to introduce transformations to these axes in achieving numerical solutions by techniques such as the finite element method.
24 citations
TL;DR: In this article, a more precise approximation for the generalized torsional rigidity of an orthotropic material is presented, which allows a more direct method for the determination of the principal shear moduli.
Abstract: Precise measurements of the free-free resonant frequencies of specimens of unidirectional fibre-reinforced composite material are used to determine the principal elastic moduli and effective specimen moduli of the material. An iterative procedure is described incorporating the Timoshenko beam corrections (1937). A more precise approximation for the generalized torsional rigidity of an orthotropic material is presented. This allows a more direct method for the determination of the principal shear moduli. Discrepancies between the effective specimen shear moduli calculated from the corresponding torsional resonant frequencies and the results predicted using the principal elastic moduli are due to torsion-flexure coupling.
20 citations
TL;DR: In this article, a finite element technique employing transfer matrix calculations is used to calculate the spectrum of flexural and torsional resonant frequencies of specimens of material of orthotropic symmetry, incorporating Lekhnitskii's theory (1963) for static torsion-flexure coupling and the Timoshenko beam corrections (1937) for flexure.
Abstract: For pt.I see ibid., vol.8, no.15, p.1733 (1975). A simple finite-element technique employing transfer matrix calculations is used to calculate the spectrum of flexural and torsional resonant frequencies of specimens of material of orthotropic symmetry. The calculations incorporate Lekhnitskii's theory (1963) for static torsion-flexure coupling and the Timoshenko beam corrections (1937) for flexure. Vibration shapes and nodal contours are also calculated and displayed by computer. The non-crossing rule for the coupled oscillations is verified experimentally.
18 citations
TL;DR: In this paper, a solution for the flexural vibration of an elastically supported Timoshenko beam which is subjected to an axial force and a moving transverse load is obtained.
17 citations
TL;DR: In this article, the minimum cross-section of a vibrating beam is controlled by the introduction of an inequality constraint, and a finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions.
Abstract: Accounting for shear deformations and rotary inertia effects, necessary condition for optimum fundamental frequency of a vibrating beam of constant volume and with a given distribution of non-structural mass, is obtained through the calculus of variations. Minimum cross-section of the beam is controlled by the introduction of an inequality constraint. A finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions. A comparison is then made with the corresponding results of an Euler beam.
14 citations
TL;DR: In this paper, the effect of boundary conditions, via end-fixity and damping, on the overall damping capacity of a flexibly supported cantilever under the condition of steady-state vibrations was investigated.
12 citations
TL;DR: In this article, the authors obtained new information on the order of magnitude of effects which modify the results of elementary beam theory through the influence of transverse shear and normal strain deformations, including the delineation of boundary layer effects.
11 citations
TL;DR: In this paper, the stability of a cantilever beam subjected to a follower force at its free end and rotating at a uniform angular velocity is investigated, where the beam is assumed to be offset from the axis of rotation, carries a tip mass at the free end, and undergoes deflection in a direction perpendicular to the plane of rotation.
TL;DR: In this article, the results of an elastic model study of a post-tensioned three-span slab bridge are presented, which is a 1/36-scale version of a typical straight slab bridge on isolated supports.
Abstract: The results of an elastic model study of a post-tensioned three-span slab bridge are presented. The model is a 1/36-scale version of a typical straight slab bridge on isolated supports. Loading cases considered for the model included both gravity loading and longitudinal prestress. The in-plane and bending stresses resulting from these loading cases were obtained. The observed data were compared with a finite element analysis. Longitudinal moments are generally predictable using elementary beam theory. A two-dimensional finite element analysis is required for transverse moment prediction and support moment prediction. Close agreement was found between the observed and computed data.
Abstract: An analysis is given of the characteristic flexural modes and frequencies of a linearly elastic free-free spheroid in an ideal fluid. The finite element method is used to represent the structural properties of a slender spheroid, employing a special element formulated for this purpose on the basis of Euler-Bernoulli beam theory. A consistent added mass matrix is derived from the exact solution of the infinite fluid potential problem, truncated at a suitable number of terms. A consistent added stiffness matrix is obtained for the buoyancy forces on a spheroid floating with its axis in a free surface, but other free surface effects (associated with wave generation) are assumed negligible. Solutions are computed for different aspect-ratio variable density spheroids in vacuo, deeply submerged, and floating. The results indicate the possibility of considerable distortions in the lowest ('rigid') modes of slender floating bodies vibrating in a vertical plane, and illustrate the difficulty of defining three dimensional reduction factors for use with a simplified two dimensional theory. Derivation of the classical reduction factors for uniform density spheroids is given by way of comparison. The paper provides an illustration of use of a finite element formulation, in conjunction with consistent added mass and stiffness matrices, for a rational analysis of the structural dynamics of ships and other marine vehicles.
TL;DR: In this article, a numerical analysis is presented which takes into consideration both the nonlinear and frictional effects, showing that frictional forces can become significant at large deflections and cause an increase in the measured strength.
Abstract: In testing high strength, elastic materials by the four-point bending method, large deflections can occur. Under these conditions the relationship between load and deflection becomes nonlinear and analyses of results based on simple beam theory may lead to serious errors. Furthermore, friction between the test piece and supports can have an important effect on the results. A numerical analysis is presented which takes into consideration both the nonlinear and frictional effects. The analysis shows that frictional forces can become significant at large deflections and cause an increase in the measured strength. Experimental evidence is given to support these analytical results. Presented at the 29th Annual Meeting in Cleveland, Ohio, April 28–May 2, 1974
Dissertation•
01 Jan 1975
TL;DR: In this paper, the static equilibrium and stability analysis of cylindrical shells subjected to non-uniform external pressures is presented, which is of practical importance in the design of launch vehicles, oil storage tanks, cooling towers and other engineering structures submerged in flowing water.
Abstract: This thesis presents static equilibrium and stability analyses
of cylindrical shells subjected to non-uniform external pressures.
This problem is of practical importance in the design of launch
vehicles, oil storage tanks, cooling towers subjected to wind
loads and other engineering structures submerged in flowing
water. The non-uniform pressure distributions considered are due to: (a) wind at high Reynolds numbers; (b) flow of water on submerged cylinders.
In the static equilibrium analysis for the pre-buckled state both
Donnell and Flugge shell theories are employed. The results of
pre-buckle deformations and stress resultants, when compared
with results obtained using beam or semi-membrane theories show
that the beam theory is inadequate and unsafe, whereas the semi-membrane
theory is conservative and safe for wind loaded structures. [Continues.]
TL;DR: In this paper, a simple technique for introducing the effects due to shear deformation and rotatory inertia in the design of transversely vibrating beams is developed using the state-space analysis of modern control theory.
TL;DR: In this article, a linear elastic analysis of the response of pin-ended rods and tubes in a stationary fluid medium, to random stationary homogeneous surface pressure fluctuations, is presented, where the local pressure spectral density is either band-limited white noise or Gaussian.