Showing papers on "Timoshenko beam theory published in 1992"
TL;DR: In this paper, a general high-order theory based on variational principles is presented for the bending behavior of a sandwich beam with a core that is vertically flexible, which embodies a rigorous and systematic approach to the analysis of such structures, which have highorder effects caused by the nonlinearity of the longitudinal and the transverse deformations of the core through the height.
Abstract: A general high-order theory based on variational principles is presented for the bending behavior of a sandwich beam with a core that is vertically flexible. The theory embodies a rigorous and systematic approach to the analysis of such structures, which have high-order effects caused by the nonlinearity of the longitudinal and the transverse deformations of the core through the height. As such, it improves on the available classical and superposition theories. Beam construction consists of the upper and lower skin, metallic or composite laminated symmetric, with nonidentical mechanical and geometrical properties, and a soft core made of foam or honeycomb. The formulation uses a beam theory for the skins and a two-dimensional elasticity theory for the core. The behavior is presented in terms of internal resultants and displacements in skins, peeling and shear stresses in skin-core interfaces, and stress and displacement fields in the core, even in the vicinity of concentrated loads. The method is applicable to any type of loading exerted on the skins and to any type of boundary or continuity conditions, including cases in which at the same section the conditions at the upper skin are different from those at the lower. Some typical cases are studied numerically.
434 citations
TL;DR: In this article, a generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips, which is accomplished by introducing a "crack function" into the beam's compatibility relations.
Abstract: Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.
262 citations
TL;DR: In this article, a finite element model based on a higher-order shear deformation theory is developed to study the free vibration characteristics of laminated composite beams and the effects of in-plane inertia and rotary inertia are considered in the formulation of the mass matrix.
130 citations
TL;DR: In this paper, the dynamics of the Timoshenko beam is recast such that the description requires information only at the end points, and a dynamic stiffness relation suitable for assembling is presented in the form of a dynamic stiff relation.
120 citations
TL;DR: In this paper, the bending behavior of a general sandwich beam, delaminated (debonded) at one of the skin-core interfaces, with transversely flexible core, based on variational principles is analytically investigated.
119 citations
TL;DR: In this article, analytical expressions for the coupled bending-torsional dynamic stiffness matrix elements of a uniform Timoshenko beam element are derived in an exact sense by solving the governing differential equations of motion of the element.
110 citations
TL;DR: In this paper, the free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analyzed and presented for the first time, and expressions for computing natural frequencies and mode shapes are given.
Abstract: A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.
94 citations
TL;DR: In this article, a simplified improved beam model is proposed to analyze the cracked part of a double cantilever beam by means of shear-corrected classical beam theory and the uncracked part is analysed by considering Saint Venant effects and deformation of a beam on an elastic foundation.
90 citations
TL;DR: In this article, a beam model is used to model a thin film segment bonded to an elastic half space, and a cohesive zone model is employed to determine the cohesive zone size at a given value of the yield stress.
72 citations
TL;DR: In this article, the coupling of vibration modes of vibration of a clamped-free circular cross-section Timoshenko beam with a transverse crack was investigated and a 6 × 6 local flexibility matrix was used to simulate the crack.
Abstract: The coupling of vibration modes of vibration of a clamped-free circular cross-section Timoshenko beam with a transverse crack is investigated in this paper. A 6 × 6 local flexibility matrix is used to simulate the crack. The nondiagonal terms of this matrix cause coupling between the longitudinal, torsional, and bending vibrations. Coupling is apparent in all spectra obtained with a harmonic sweeping excitation throughout the frequency range. The method is very sensitive even for small cracks.
63 citations
TL;DR: In this paper, the free vibration of symmetrically laminated composite beams is studied based on Timoshenko type equations, where shear deformation and rotary inertia are included in the analysis, but with the term representing the joint action of these effects omitted in the Timoshenko equations.
TL;DR: In this article, a finite element model is developed for free lateral vibration analyses of linearly tapered Timoshenko beams, where shape functions are obtained from the homogeneous solution of the governing equations for static deflections.
TL;DR: It is proved that with the proposed dynamic boundary control law applied at the free end of the beam, the beam vibrations uniformly and exponentially decay to zero.
TL;DR: In this article, the authors present a consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load.
Abstract: The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.
TL;DR: In this paper, a generalized modal approach is presented to solve the equations of motion of a laminated composite beam obtained with a third-order shear deformation theory, where the biorthonormal eigenfunctions of the differential equations expressed in the state form are used to decouple the equations.
Abstract: A generalized modal approach is presented to solve the equations of motion of a laminated composite beam obtained with a third-order shear deformation theory. The biorthonormal eigenfunctions of the differential equations expressed in the state form are used to decouple the equations. To obtain these eigenfunctions for beams with any arbitrary beam boundary conditions, a method is presented. The solution obtained by this approach is used to calculate the beam response for spatially and temporally correlated random loads. Several sets of numerical results are presented to demonstrate the importance of shear deformations in the dynamic analysis of composite beams.
TL;DR: In this paper, a simple one-dimensional mechanical model for curved laminated beams is presented, where the laminae composing the beam are modelled as Timoshenko beams, perfectly bonded at the interfaces.
TL;DR: In this article, the structural characteristics of spinning pretwisted orthotropic beams by the finite element method were investigated. And the effect of pretwist angle on the elastic stability was also studied.
TL;DR: In this paper, a finite beam element for vibration analysis of a rotating tapered beam including shear deformations and rotary inertia is derived, and numerical solutions are generated for a wide range of rotational speed and taper ratios.
TL;DR: In this article, a simple finite element model for the analysis of arbitrary thin-walled beams under general loadings and boundary conditions is presented. But the model is limited to both open-and closed-type sections, and it does not account for both flexural and warping torsional effects.
TL;DR: In this article, the beam theory was used to compute stress intensity factors for a circumferentially cracked cylindrical pipe in bending and tension and find good agreement with the exact solutions obtained from complete shell analysis.
TL;DR: In this paper, the exact solution for the free vibration of a symmetric nonuniform Timoshenko beam with tip mass at one end and elastically restrained at the other end of the beam is derived.
Abstract: The exact solution for the free vibration of a symmetric nonuniform Timoshenko beam with tip mass at one end and elastically restrained at the other end of the beam is derived. The two coupled governing characteristic differential equations are reduced into one complete fourth-order ordinary differential equation with variable coefficients in the angle of rotation due to bending. The frequency equation is derived in terms of the four normalized fundamental solutions of the differential equation. It can be shown that, if the coefficients of the reduced differential equation can be expressed in polynomial form, the exact fundamental solutions can be found by the method of Frobenius. Finally, several limiting cases are studied and the results are compared with those in the existing literature. A (x) E(x) G(x) I(x) J(x)
TL;DR: In this article, the authors presented the complete force displacement relationship for a Timoshenko beam element resting on a two-parameter elastic foundation and derived the stiffness matrix and nodal-action column vector coefficients from the transport matrix based on the exact solution of two differential equations governing the problem concerned herein.
Abstract: The objective of this paper is to present the complete force-displacement relationship for a Timoshenko beam element resting on a two-parameter elastic foundation. Both the stiffness matrix and nodal-action column-vector coefficients are derived from the transport matrix based on the exact solution of two differential equations governing the problem concerned herein. Explicit expressions for the element stiffness matrix and the nodal-action column vectors are
TL;DR: In this article, the lateral deflection and the cross-sectional rotation are represented by B-spline functions of equal order and the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams.
Abstract: B-spline functions are used as trial functions in a Rayleigh-Ritz analysis of the free vibration of shear-deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross-sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear-locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B-spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear-locking difficulty is completely eliminated. This has clear significance for the analysis of shear-deformable plates and shells when using B-spline functions.
TL;DR: In this article, the non-linear differential equations of motion of a fluid conveying pipe, the no-flow configuration of which is in the shape of a one-dimensional line arbitrarily curved and twisted in space, are derived by making use of the Newtonian approach.
TL;DR: In this article, a flexural theory of elastic sandwich beams is derived which renders quite precise results within a wide range of ratios of dimensions, mass densities, and elastic constants of the core and faces.
Abstract: A flexural theory of elastic sandwich beams is derived which renders quite precise results within a wide range of ratios of dimensions, mass densities, and elastic constants of the core and faces. The assumptions of the Timoshenko theory of shear-deformable beams are applied to each of the homogeneous, linear elastic, transversely isotropic layers individually. Core and faces are perfectly bonded. The principle of virtual work is applied to derive the equations of motion of a symmetrically designed three-layer beam and its boundary conditions. By definition of an effective cross-sectional rotation the complex problem is reduced to a problem of a homogeneous beam with effective stiffnesses and with corresponding boundary conditions. Thus, methods of classical mechanics become directly applicable to the higher-order problem. Excellent agreement of the results of illustrative examples is observed when compared to solutions of other higher-order laminate theories as well as to exact solutions of the theory of elasticity.
TL;DR: In this article, the influence of rotary inertia and shear deformation on the natural frequencies of a cantilever beam with translational and rotational springs at an arbitrary point along the beam, carrying a tip mass the center of gravity of which does not coincide with the point of attachment was investigated.
TL;DR: In this article, a modal expansion technique is used to analyze a spinning Timoshenko beam subjected to a constant moving load using a body-fixed axis reference system, and closed form expressions for natural frequencies and system transient response are derived.
TL;DR: In this paper, the influence of Winkler elastic foundation modulus, slenderness ratio and elastically restrained boundary conditions on the critical load of a Timoshenko beam subjected to an end follower force is investigated.