Nonlinear Vibration Solution for an Inclined Timoshenko Beam Under the Action of a Moving Force with Constant/Nonconstant Velocity

Mamandi, Ahmad; Kargarnovin, M. H.; Farsi, Salman

doi:10.1007/s10958-014-1996-7

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…The present expression of general solutions given by (18) and (19) is equivalent to the expression for three frequency ranges, 0 < < , = , and > , by van Rensburg and van der Merwe [28].…”

Section: Mathematical Model Of a Timoshenko Beam The Governing Equatmentioning

confidence: 93%

“…where The general solution at = can be readily obtained from either (18) or (19), by allowing to approach , as follows: (47)…”

Section: Natural Frequencies and Mode Shapesmentioning

confidence: 99%

“…To obtain the first two terms in (46) from either (18) or (19), L'Hospital's rule is applied. Applying the simply supported boundary conditions given by (21) to (46) yields the following eigenvalue problem:…”

Section: Natural Frequencies and Mode Shapesmentioning

confidence: 99%

“…To examine the transverse vibrations of a 1D beam structure, the Timoshenko beam model has been widely adopted to take into account the effects of shear deformation and rotatory inertia on the dynamic responses. In transverse vibration analysis, various solution techniques have been described in the literature including MAM or eigenfunction expansion methods [1,2], mode summation methods or assumed mode methods [3][4][5], semianalytical methods [6][7][8][9][10][11], integral transform methods (Laplace-Carson transform and Fourier transform) [12][13][14], transfer matrix method [15], Lagrange multiplier methods [16,17], Galerkin methods [18,19], finite element methods [20,21], finite difference method [22], time-domain spectral element method [23], and frequency-domain spectral element method [24].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Kim

Park

Lee

2017

Shock and Vibration

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The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

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“…The present expression of general solutions given by (18) and (19) is equivalent to the expression for three frequency ranges, 0 < < , = , and > , by van Rensburg and van der Merwe [28].…”

Section: Mathematical Model Of a Timoshenko Beam The Governing Equatmentioning

confidence: 93%

“…where The general solution at = can be readily obtained from either (18) or (19), by allowing to approach , as follows: (47)…”

Section: Natural Frequencies and Mode Shapesmentioning

confidence: 99%