Vibrations of rods with general space curvature

Tsay, Huoy-Shyi; Kingsbury, Herbert B.

doi:10.1016/s0022-460x(88)81394-4

Cited by 15 publications

(5 citation statements)

References 2 publications

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“…The first two natural frequencies of a cantilevered straight pretwisted rod were calculated and showed nice agreement with experimental results. Also Tsay and Kingsbury (1988) (see also Kingsbury 1985) derived the equations of motion of a rod with arbitrary space curvature and pretwist. In the last two papers many of structural effects of pretwist were not included, like for example the tension-torsion coupling.…”

Section: Rotating Rodsmentioning

confidence: 99%

Structural and Dynamic Behavior of Pretwisted Rods and Beams

Rosen

1991

Applied Mechanics Reviews

120

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Because of being important structural elements in many engineering applications on one hand, and presenting inherent complicated coupling effects on the other hand, pretwisted rods have attracted the interest of many researchers. During the years, as a result of engineering breakthroughs, like the introduction of composite materials or operating at very high temperatures, the problems associated with pretwisted rods became more complicated. The present review will present the research during the last fifty years. It will be divided into three main subjects: static analysis, dynamic analysis and stability problems. The review will concentrate on the structural and dynamic aspects of pretwisted rods. Derivations of models and solution techniques will be addressed.

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Section: Rotating Rodsmentioning

confidence: 99%

Structural and Dynamic Behavior of Pretwisted Rods and Beams

Rosen

1991

Applied Mechanics Reviews

120

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“…Accordingly, for all the materials involved in the analyses, an additional viscous damping was introduced using the frequency-dependent Rayleigh formulation in which the damping matrix has two components linearly proportional to the mass and stiffness matrices. Specifically, according to the approach proposed by Tsay et al, 30 in all the analyses the damping at small strains has been evaluated by using two control frequencies (f 1 , f 2 ) assumed equal to the fundamental frequency f 0 of the dam (f 1 = f 0 ) and to the highest predominant frequency f p,max of the whole set of input motions adopted in the analyses (f 2 = f p,max ). The corresponding damping ratios ξ 1 = ξ 2 have been set equal to 1% in all the analyses.…”

Section: Numerical Modelling Of the San Pietro Dammentioning

confidence: 99%

“…Specifically, according to the approach proposed by Tsay et al., 30 in all the analyses the damping at small strains has been evaluated by using two control frequencies ( f 1 , f 2 ) assumed equal to the fundamental frequency f 0 of the dam ( f 1 = f 0 ) and to the highest predominant frequency f p,max of the whole set of input motions adopted in the analyses ( f 2 = f p,max ). The corresponding damping ratios ξ 1 = ξ 2 have been set equal to 1% in all the analyses.…”

Section: Numerical Modelling Of the San Pietro Dammentioning

confidence: 99%

Seismic intensity measures and predictive equations for the evaluation of earthquake—induced crest settlements of earth dams

Nardo,

Biondi,

Casablanca

et al. 2024

Earthq Engng Struct Dyn

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In this paper the results of 2D dynamic finite element analyses of a zoned earth dam are presented and discussed with the aim of detecting proper intensity measures able to describe the variation of the crest permanent settlement with the characteristics of the input ground motion. A large set of horizontal components of earthquake records has been selected and used as input motion considering both upstream and downstream directions. This allowed to explore the activation of plastic mechanisms in the dam embankment and the amplification of the horizontal accelerations. Starting from the analysis results, two original intensity measures, related to the amplitude, energy and frequency content of the input motion, have been detected and original empirical predictive formulas have also been derived to estimate the permanent crest settlement of the dam. The effectiveness of the proposed intensity measures and the reliability of the novel relationships between these intensity measures and earthquake‐induced permanent crest settlements have been checked against (i) numerical results of further dynamic analyses carried out for the same dam using additional sets of input motions, (ii) numerical results available in the literature for two other earth dams and (iii) field data relative to the crest settlements induced in four earth dams by two recent large earthquakes. The whole set of analysis results allowed defining an empirical equation that appears as a promising general predictive tool for the earthquake‐induced crest settlement of earth dams.

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“…The control performance will be affected if the coupling effects between motions in three directions are ignored. In addition, mathematical works in [31] show that even slight pace curvature introduces significant changes in the beam natural frequencies and especially on mode shapes, i.e. the coupling of the out-of-plane wave types, and extensional and flexural waves exhibits in the flexible beams [32].…”

Section: Introductionmentioning

confidence: 99%