Showing papers on "Timoshenko beam theory published in 1971"
TL;DR: In this paper, the dynamic equations of orthotropic laminated plates are derived from the concepts of Timoshenko's beam theory to include the effects of transverse shear and rotatory inertia.
Abstract: The dynamic equations of orthotropic laminated plates are derived from the concepts of Timoshenko's beam theory to include the effects of transverse shear and rotatory inertia. The propagation of flexural waves is discussed. The transient response of a rectangular plate to a normal impact is investigated. We also consider briefly the influence of internal friction related to the damping on the response of the plate.
174 citations
TL;DR: In this paper, a portal frame subjected to free and forced vibrations is used to illustrate the application of the proposed method and to show the rotary inertia and shear effects, including the effect of transverse-shear deformation.
46 citations
TL;DR: In this paper, a non-linear thin-walled beam theory for elastic beams of open section is presented, which takes into account geometric nonlinearities and longitudinal deformations caused by large cross-sectional rotation of the beam.
42 citations
TL;DR: In this paper, the transient response of the Euler-Bernoulli beam and the Timoshenko beam on elastic foundations due to moving loads is reviewed, using a considerably simpler vector formulation with a Laplace rather than Fourier transformation.
24 citations
TL;DR: In this article, the correspondence principle was applied to derive the differential equations of viscoelastic Timoshenko beams with external viscous damping, and these equations were solved by Laplace transform and boundary conditions were applied to obtain complex frequency equations and mode shapes for beams of any combination of end conditions.
Abstract: The correspondence principle has been applied to derive the differential equations of viscoelastic Timoshenko beams with external viscous damping. These equations are solved by Laplace transform and boundary conditions are applied to obtain complex frequency equations and mode shapes for beams of any combination of end conditions. For beams without external damping, the correspondence principle can be applied directly to the available solutions of elastic Timoshenko beams. Numerical illustration is given.
22 citations
01 May 1971
TL;DR: In this article, the dynamic buckling of a hinged bar under harmonic axial load was studied using Timoshenko's beam theory and considering the effects of longitudinal vibrations, and several new types of parametric resonances were found.
Abstract: The dynamic buckling of a hinged bar under harmonic axial load is studied using Timoshenko's beam theory and considering the effects of longitudinal vibrations. Several new types of parametric resonances were found. The influences of the more accurate Timoshenko beam theory on the instability regions found with the Bernoulli-Euler theory is also discussed.
17 citations
TL;DR: In this article, a beam theory solution is obtained for the bimetallic element, which shows that the deflection and snap-through response of the beam, to increasing temperature, is considerably different from the approximate solutions obtained by Timoshenko and by Burgreen.
Abstract: An analysis is made of the thermal buckling and snap-through action of an initially curved bimetallic beam, supported by two hinges at the extremities. A beam theory solution is obtained for the bimetallic element, which shows that the deflection and snap-through response of the bimetallic beam, to increasing temperature, is considerably different from the approximate solutions obtained by Timoshenko and by Burgreen. The validity of the earlier treatments is dependent upon the maintenance of a first mode deflected shape, whereas in the present analysis this restriction is removed. It is found that thermostatic snap-through is obtainable at low temperatures, only when there is a large difference in the coefficients of expansion of the bimetallic constituents, but that snap-through will always take place at sufficiently high temperatures. This high temperature behavior of the beam was not obtained in the approximate one-mode solutions.
16 citations
TL;DR: In this paper, the coupled equations of motion for a thin-walled shear wall of monosymmetric cross section are presented based on thinwalled beam theory, and an exact coupled solution is obtained by simultaneously solving a coupled polynomial and set of homogeneous linear algebraic equations, in order to obtain the natural frequencies and mode shapes.
Abstract: The coupled equations of motion for a thin-walled shear wall of monosymmetric cross section are presented based on thin-walled beam theory. An exact coupled solution is obtained by simultaneously solving a coupled polynomial and set of homogeneous linear algebraic equations, in order to obtain the natural frequencies and mode shapes. An approximate solution is obtained by using the uncoupled flexural and torsional mode shapes in applying the virtual work principle in order to obtain the appropriate eigenvalues. A comparison of the exact and approximate solutions for a single shear wall of E-shaped cross section indicates extremely close agreement for both frequencies and mode shapes. The approximate solution requires considerably less computer time than the exact solution and consequently provides a valuable alternative.
13 citations
TL;DR: In this article, the first spatial and temporal modes of cantilevered columns having longitudinal inertia and end mass have been determined experimentally and analytically in the parametric space.
12 citations
01 Aug 1971
TL;DR: In this paper, a second order solution is presented for sandwich beams consisting of an arbitrary number of midplane symmetrical layers subjected to any type of transverse and shear loading and bounded by any combinations of free, pinned, and clamped end conditions.
Abstract: : A second order solution is presented for sandwich beams consisting of an arbitrary number of midplane symmetrical layers subjected to any type of transverse and shear loading and bounded by any combinations of free, pinned, and clamped end conditions. The solution includes transverse shear deformation and is shown to be a very good approximation to exact elasticity solutions. The distributions of shear stresses, normal stresses, horizontal displacements, and transverse deflections have been computed for various beams and the pronounced deviations of these distributions from similar results using classical beam theory ar explained. (Author)
8 citations
TL;DR: In this paper, the effect of shear deformation on the optimal design of elastic beams is illustrated by a problem of a circular ring, where the cross section of the ring is assumed to be rectangular with given depth and variable width.
TL;DR: In this paper, a generalized beam theory was proposed for beam-like trusses, where the equations of motion were deduced including the effect of rotatory inertia and the resulting eigenvalue problem, which consists of two simultaneous second order differential equations and four boundary conditions, was solved by a conventional technique using successive approximations.
01 Jan 1971
TL;DR: In this article, the dynamic buckling of a hinged bar under harmonic axial load is studied using Timoshenko's beam theory and considering the effects of longitudinal vibrations, and several new types of parametric resonances are found.
Abstract: SummaryThe dynamic buckling of a hinged bar under harmonic axial load is studied using Timoshenko's beam theory and considering the effects of longitudinal vibrations. Several new types of parametric resonances were found. The influences of the more accurate Timoshenko beam theory on the instability regions found with the Bernoulli-Euler theory is also discussed.ÜbersichtDie dynamische Stabilität eines gelenkig gelagerten Balkens mit harmonischer Axiallast wird mit Hilfe der Timoshenkoschen Balkentheorie und unter Berücksichtigung der Längsschwingungen untersucht. Verschiedene neue Arten von parametrischen Instabilitäten konnten gefunden werden. Der Einfluß der genaueren Timoshenkoschen Balkentheorie auf die sich aus der Bernoulli-Eulerschen Theorie ergebenden Instabilitätsbereiche wird diskutiert.
01 Apr 1971
TL;DR: In this paper, a finite element model for representation of a Timoshenko beam segment is derived, which is a massless beam, having bending and shear flexibility, carrying concentrated masses on rigid arms to account for translatory and rotary inertia.
Abstract: : A finite element model for representation of a Timoshenko beam segment is derived. The model is a massless beam, having bending and shear flexibility, carrying concentrated masses on rigid arms to account for translatory and rotary inertia. The accuracy of the model is domonstrated by comparing its impedance and ground shock response to those of the exact Timoshenko beam, the exact Bernoulli-Euler beam, and center-of-gravity lumped mass models. (Author)
TL;DR: In this article, a generalized beam theory is applied to a rotationally symmetrical shell structure consisting of cylindrical and conical sections, and it is shown that this theory, in which the flexibility of the beam is specified by four functions, is adequate for treating the shell structure as a beam in bending.