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 paper, a single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal Euler-Bernoulli, Timoshenko, and higher order beams.
98 citations
TL;DR: In this paper, the exact dynamic stiffness matrix for a straight and uniform beam element whose elastic and inertial axes are not coincident is derived for planar assemblages of connected bending-torsion beams.
98 citations
TL;DR: In this article, the authors compare early and very recent approaches to static analysis of reinforced-shell wing structures based on a hierarchical, one-dimensional formulation of the displacement field above the cross-section of the structure.
Abstract: This paper compares early and very recent approaches to the static analysis of reinforced-shell wing structures. Early approaches were those based on the pure semimonocoque theory along with the beam assumptions of the Euler–Bernoulli and Timoshenko type. The recent approaches are based on a hierarchical, one-dimensional formulation. These are obtained by adopting various polynomial expansions of the displacement field above the cross-section of the structure according to the unified formulation which was recently proposed by the first author. Two classes were developed in the unified formulation framework. In the first class, Taylor expansion models were developed by exploiting N-order Taylor-like polynomials; classical beam theories (Euler–Bernoulli and Timoshenko) were obtained as special cases of Taylor expansion. In the second class, Lagrange expansion models were built by means of four- and nine-point Lagrange-type polynomials over the cross-section of the wing. The component-wise approach was obtai...
98 citations
TL;DR: In this article, the eigenvalue and lateral deflection of both the surface and middle plane of the plate, as well as the bending strains, are obtained in the form of series expansions in even powers of plate thickness.
98 citations
TL;DR: In this article, a Lyapunov-based control strategy is proposed for the regulation of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam with a translational base support.
Abstract: A Lyapunov-based control strategy is proposed for the regulation of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam with a translational base support. The beam (arm) cross-sectional area is assumed to be uniform and Euler-Bernoulli beam theory assumptions are considered. Moreover, two types of damping mechanisms; namely viscous and structural dampings, are considered for the arm material properties. The arm base motion is controlled utilizing a linear actuator, while a piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual beam vibrations. The equations of motion for the system are obtained using Hamilton's principle, which are based on the original infinite dimensional distributed system. Utilizing the Lyapunov method, the control force acting on the linear actuator and control voltage for the PZT actuator are designed such that the base is regulated to a desired set-point and the exponential stability of the system is attained. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, controller convergence at finite time, suppression of residual oscillations and simplicity of the control implementation. The feasibility of the controller is validated through both numerical simulations and experimental testing.
98 citations