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.

Experimental investigation of a small-scale bridge model under a moving mass

Abstract: The dynamic response of a small-scale bridge model under a moving mass is investigated. The analysis is based on the continuous Euler–Bernoulli beam theory. By expanding the unknown structural response in a series of the beam eigenfunctions, the given problem is reduced to the solution of a set of second order linear differential equations with time varying coefficients. The analytical solution is validated through a series of experiments. A small-scale model is designed to satisfy both static and dynamic similitude with a selected prototype bridge structure, and a set of necessary similitude conditions for the given problem is provided. Attention is paid, in particular, to satisfaction of the mass similitude requirement, often constituting one of the main difficulties in the design of small-scale dynamic models. It is shown that experimental results are in good agreement with theoretical predictions, thus validating the analytical procedure.

Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams

Abstract: A modified continuum model of the nanoscale beams is presented by incorporating surface elasticity in this paper. The classical beam theory is adopted to model the bulk, while the bulk stresses along the surfaces of the bulk substrate are required to satisfy the surface balance equations of the continuum surface elasticity. On the basis of this modified beam theory the governing equation of the nanobeam is derived where the effect of the geometry nonlinearity is also considered. The Galerkin method is used to give a reduced-order model of the problem. Beams made from two materials: aluminum and silicon are chosen as examples. The numerical results show that the mechanical buckling and free vibration phenomena of nanobeams are size-dependence. The effects of the surface energies on the critical axial force of buckling, post-buckling and linear free vibration frequency are discussed. Finally, the amplitude frequency response is given numerically through the incremental harmonic balanced method.

Vibration of a Cracked Cantilever Beam

Abstract: A continuous cracked bar vibration model is developed for the lateral vibration ofa a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions for the cracked beam as an one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations of an aluminum cantilever beam with a single-edge crack are presented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental results fall very close to the values predicted by the continuous crack formulation. Moreover, the continuous cracked beam theory agrees better with the experimental results than the lumped crack flexibility theory.