## On the buckling of an elastic rotating beam

Research output: Contribution to journal › Journal article – Annual report year: 1997 › Research › peer-review

### Standard

**On the buckling of an elastic rotating beam.** / Furta, Stanislaw D.; Kliem, Wolfhard; Pommer, Christian.

Research output: Contribution to journal › Journal article – Annual report year: 1997 › Research › peer-review

### Harvard

*European Journal of Mechanics A - Solids*, vol. 16, no. 2, pp. 307-324.

### APA

*European Journal of Mechanics A - Solids*,

*16*(2), 307-324.

### CBE

### MLA

*European Journal of Mechanics A - Solids*. 1997, 16(2). 307-324.

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### Author

### Bibtex

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### RIS

TY - JOUR

T1 - On the buckling of an elastic rotating beam

AU - Furta, Stanislaw D.

AU - Kliem, Wolfhard

AU - Pommer, Christian

PY - 1997

Y1 - 1997

N2 - A nonlinear model is developed, which describes the buckling phenomena of an elastic beam clamped to the interior of a rotating wheel. We use a power series method to obtain an approximate expression of the buckling equation and compare this with previous results in the literature. The linearized problem is integrated and this results in a second order differential equation of the Fuchs type, which allows an asymptotic expansion of the buckling equation. By means of Lyapunov and Chetaev functions, a rigorous proof is given that the loss of stability of the trivial equilibrium shape occurs for any length of the beam provided the angular velocity of the rotating wheel is sufficiently large. Finally we discuss the nonlinear problem and describe the qualitative behaviour of branches in a bifurcation diagram.

AB - A nonlinear model is developed, which describes the buckling phenomena of an elastic beam clamped to the interior of a rotating wheel. We use a power series method to obtain an approximate expression of the buckling equation and compare this with previous results in the literature. The linearized problem is integrated and this results in a second order differential equation of the Fuchs type, which allows an asymptotic expansion of the buckling equation. By means of Lyapunov and Chetaev functions, a rigorous proof is given that the loss of stability of the trivial equilibrium shape occurs for any length of the beam provided the angular velocity of the rotating wheel is sufficiently large. Finally we discuss the nonlinear problem and describe the qualitative behaviour of branches in a bifurcation diagram.

M3 - Journal article

VL - 16

SP - 307

EP - 324

JO - European Journal of Mechanics A - Solids

JF - European Journal of Mechanics A - Solids

SN - 0997-7538

IS - 2

ER -