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The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest [1] [2] [3] early in the 20th century. [ 4 ] [ 5 ] The model takes into account shear deformation and rotational bending effects, making it suitable for describing the behaviour of thick beams, sandwich composite beams , or beams subject to high ...
Macaulay's method has been generalized for Euler-Bernoulli beams with axial compression, [3] to Timoshenko beams, [4] to elastic foundations, [5] and to problems in which the bending and shear stiffness changes discontinuously in a beam.
For thin beams (beam length to thickness ratios of the order 20 or more) these effects are of minor importance. For thick beams, however, these effects can be significant. More advanced beam theories such as the Timoshenko beam theory (developed by the Russian-born scientist Stephen Timoshenko) have been developed to account for these effects.
The discontinuity of the mass trajectory is also well visible in the Timoshenko beam. [citation needed] High shear stiffness emphasizes the phenomenon. [citation needed] Vibrations of the Timoshenko beam: red lines - beam axes in time, black line - mass trajectory (w 0 - static deflection).
1922: Timoshenko corrects the Euler–Bernoulli beam equation; 1936: Hardy Cross' publication of the moment distribution method, an important innovation in the design of continuous frames. 1941: Alexander Hrennikoff solved the discretization of plane elasticity problems using a lattice framework; 1942: R. Courant divided a domain into finite ...
The Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory was developed in 1888 by Love [ 2 ] using assumptions proposed by Kirchhoff. It is assumed that a mid-surface plane can be used to represent the three-dimensional plate in two-dimensional form.
The interrelation between Timoshenko-Ehrenfest beam and Euler-Bernoulli beam theory was investigated in the book by Wang, Reddy and Lee. [22] He died in 1972 and his ashes are buried in Alta Mesa Memorial Park, Palo Alto, California. Eduard Ivanovich Grigolyuk (1923—2005) wrote several papers devoted to S.P. Timoshenko’s life and work.
Rotordynamics (or rotor dynamics) is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage.