Dynamic instability behaviour of tapered bars with flaws supported on an elastic foundation

Datta, P. K.; Nagraj, C.S.

doi:10.1016/0022-460x(89)90488-4

Cited by 15 publications

(7 citation statements)

References 5 publications

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“…In other words, as the static load increases, instabilities are obtained at a lower excitation frequency. This behavior is similar to the effects seen in the parametric instability regions for first regions of instability [5,7]. In the present case, the width of the instability regions suggests that these second regions of instability cannot be neglected.…”

Section: Resultssupporting

confidence: 86%

“…In this context, it should be pointed out that equations (6a) and (6b) are the boundaries of regions of instability. The shape of the stable and unstable boundaries for the first regions of parametric stabilities is well documented in the literature [3,[5][6][7]. However, this is the first work to derive the stability boundaries for second regions of instability by the finite element method in a quantitative approach.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 90%

“…And the other equation to bound the stability region is, Equations (6a) and (6b) can include the periodic terms if the eigenvalues are obtained in terms of the disturbing frequency, W. They define the boundaries of the region and should be compared with the boundaries of the first regions of dynamic stability, with period 2T [5][6][7], for which the assumed solution was shown in equation (4). Corresponding to the solution of period 2T (the first regions of dynamic instability), the stability boundaries are obtained as,…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…At this stage it is important to consider the simplified case which is implicitly included in equations (6) and (7). In case of free vibration, a = 0 and b = 0.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

See 3 more Smart Citations

Study of Second Regions of Dynamic Instability of a Uniform Beam

Ganguly

Datta

2004

International Journal of Mechanical Engineering Education

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Dynamic instability of a beam is solved for second regions of instability. The governing equations are of the Mathieu—Hill type, where the parametric regions are sought. While the solution to the first region of a beam has been widely reported, there is none available in the literature for the second region. In this work, the regions are determined by the finite element method. Bolotin determined the solution analytically, but it is more of a qualitative solution of the problem. In this work, a quantitative solution is sought from the finite element method. The width of the regions are significant. The effects of the static load factor and the dynamic load factor are obtained.

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Section: Resultssupporting

confidence: 86%

Section: Mathematical Formulation Of the Problemmentioning

confidence: 90%

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…At this stage it is important to consider the simplified case which is implicitly included in equations (6) and (7). In case of free vibration, a = 0 and b = 0.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

See 2 more Smart Citations

Study of Second Regions of Dynamic Instability of a Uniform Beam

Ganguly

Datta

2004

International Journal of Mechanical Engineering Education

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show abstract

“…The location, size and amount of damage were used to characterize the damaged zone. Based on the damage model by Parekh and Carlson [20], the dynamic instability of a tapered Euler-Bernoulli bar with localized damage and supported on an elastic foundation was analyzed by Datta and Nagraj [21] by a finite element approach. The effects of axial loads, foundation stiffness, location and extent of damage on the dynamic instability behavior were studied.…”

Section: Introductionmentioning

confidence: 99%