Flapwise bending vibration of rotating plates. (English) Zbl 1024.74028
Summary: We derive linear equations of motion for the flapwise bending vibration analysis of rotating plates. The equations of motion are transformed into dimensionless forms in which three dimensionless parameters are identified. The effects of the dimensionless parameters on the characteristics of the flapwise bending vibration of rotating plates are investigated. The accuracy of the present method is verified through comparing its numerical results to those obtained by a method existing method in the literature. Eigenvalue loci crossing and eigenvalue loci veering phenomena are observed and discussed. Additionally, we examine the variations of mode shapes associated with these phenomena.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K20 | Plates |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
Keywords:
flapwise bending vibration; rotating plates; stiffening effect; eigenvalue loci veering; dimensionless parameters; mode shape variation; linear equations of motion; eigenvalue loci crossingReferences:
| [1] | The free transverse vibration of airscrew blades. British A.R.C. Reports and Memoranda No. 766, 1921. |
| [2] | Schilhansl, Journal of Applied Mechanics and Transactions of American Society of Mechanical Engineers 25 pp 28– (1958) |
| [3] | Leissa, Applied Mechanics Reviews 34 pp 629– (1981) |
| [4] | Rao, The Shock and Vibration Digest 19 pp 3– (1987) |
| [5] | Dokainish, International Journal for Numerical Methods in Engineering 3 pp 233– (1971) |
| [6] | Ramamurti, Journal of Sound and Vibration 97 pp 429– (1984) |
| [7] | Kane, Journal of Guidance, Control, and Dynamics 10 pp 139– (1987) |
| [8] | Yoo, Journal of Sound and Vibration 181 pp 261– (1995) |
| [9] | Yoo, Journal of Sound and Vibration 212 pp 807– (1998) |
| [10] | Vibration of plates. NASA SP-160, 1969. |
| [11] | Dynamics: Theory and Application. McGraw-Hill: New York, 1985. |
| [12] | An Introduction to Differential Geometry. Princeton University Press: Princeton, 1964. |
| [13] | Leissa, Journal of Applied Mathematics and Physics 25 pp 99– (1974) |
| [14] | Kuttler, Journal of Sound and Vibration 75 pp 585– (1986) |
| [15] | Perkins, Journal of Sound and Vibration 106 pp 451– (1986) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
