Topic
Timoshenko beam theory
About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.
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TL;DR: In this article, a model for dynamic instability of embedded single-walled carbon nanotubes (SWCNTs) is presented, where the motion equations are derived based on Hamilton's principle.
Abstract: In this study, a model for dynamic instability of embedded single-walled carbon nanotubes (SWCNTs) is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory (SSDBT). The modified couple stress theory (MCST) is considered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton’s principle. The differential quadrature method (DQM) in conjunction with the Bolotin method is used in order to calculate the dynamic instability region (DIR) of SWCNTs. The effects of different parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The results depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system (NEMS) and micro-electro-mechanical system (MEMS).
61 citations
TL;DR: In this paper, a finite element (FE) model of an SDB system was developed, and the rubbing between the blade-tip and casing was simulated using contact dynamics theory, where Timoshenko beam elements were adopted to simulate the shaft and the blade.
61 citations
TL;DR: In this article, a dynamic investigation method for the analysis of Timoshenko beams is proposed, which takes into account the shearing deformation and the rotating inertia, and the solution of the problem is obtained through the iterative variational Rayleigh-Ritz method and assuming as test functions an appropriate class of orthogonal polynomials which respect the essential conditions only.
61 citations
TL;DR: In this article, a refined high-order global-local laminated/sandwich beam theory is developed that satisfies all the kinematic and stress continuity conditions at the layer interfaces and considers effects of the transverse normal stress and transverse flexibility, e.g. for beams with soft cores or drastic material properties changes.
Abstract: A refined high-order global-local laminated/sandwich beam theory is developed that satisfies all the kinematic and stress continuity conditions at the layer interfaces and considers effects of the transverse normal stress and transverse flexibility, e.g. for beams with soft cores or drastic material properties changes. The global displacement components, described by polynomial or combinations of polynomial and exponential expressions, are superposed on local ones chosen based on the layerwise or discrete-layer concepts. Furthermore, the non-zero conditions of the shear and normal tractions of the upper and lower surfaces of the beam may also be enforced. In the present C1-continuous shear locking-free finite element model, the number of unknowns is independent of the number of layers. Comparison of present bending and vibration results for thin and thick beams with results of the three-dimensional theory of elasticity reveals efficiency of the present method. Moreover, the proposed model is computationally economic and has a high convergence rate.
61 citations
TL;DR: In this paper, two approaches are used to derive differential equations, stiffness coefficients, and fixed-end forces for the analysis of structural systems composed of Timoshenko beam-columns that may be supported by an elastic foundation.
Abstract: Two approaches are used to derive differential equations, stiffness coefficients, and fixed‐end forces for the analysis of structural systems composed of Timoshenko beam‐columns that may be supported by an elastic foundation. The analysis is for the evaluation of the critical static axial load and buckling mode‐shapes of a structure with consideration of elastic media, bending, and shear deformations. The two approaches differ in terms of the assumed shear component of the static axial load on the cross section. The first approach is based on the assumption that the shear component of the axial load is calculated from the total slope, which consists of the bending and shear slope. In the second approach, the shear component of the axial load, however, is calculated only from the bending slope. Analytical expressions for a typical simple beam are derived to show the influence of a foundation parameter on the buckling modes. It is observed that the critical axial loads are significantly reduced when shear d...
61 citations