In-Plane Vibrations of a Thin Rotating Disk
A model for the in-plane oscillations of a thin rotating disk has been derived using a nonlinear strain measure to calculate the disk energy. This accounts for the stiffening of the disk due to the radial expansion resulting from its rotation. The corresponding nondimensionalized natural frequencies...
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Veröffentlicht in: | Journal of vibration and acoustics 2003-01, Vol.125 (1), p.68-72 |
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creator | Deshpande, Moreshwar Mote, C. D |
description | A model for the in-plane oscillations of a thin rotating disk has been derived using a nonlinear strain measure to calculate the disk energy. This accounts for the stiffening of the disk due to the radial expansion resulting from its rotation. The corresponding nondimensionalized natural frequencies are seen to depend only on the nondimensionalized rotation speed and have been calculated. The radially expanded disk configuration is linearly stable over the range of rotation speeds studied here. The sine and cosine modes for all nodal diameters couple to each other at all non-zero rotation speeds and the strength of this coupling increases with rotation speed. This coupling causes the reported frequencies of the stationary disk to split. The zero, one and two nodal diameter in-plane modes do not have a critical speed corresponding to the vanishing of the backward travelling wave frequency. The use of a linear strain measure in earlier work incorrectly predicts instability of the rotating equilibrium and the existence of critical speeds in these modes. |
doi_str_mv | 10.1115/1.1522419 |
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D</creatorcontrib><title>In-Plane Vibrations of a Thin Rotating Disk</title><title>Journal of vibration and acoustics</title><addtitle>J. Vib. Acoust</addtitle><description>A model for the in-plane oscillations of a thin rotating disk has been derived using a nonlinear strain measure to calculate the disk energy. This accounts for the stiffening of the disk due to the radial expansion resulting from its rotation. The corresponding nondimensionalized natural frequencies are seen to depend only on the nondimensionalized rotation speed and have been calculated. The radially expanded disk configuration is linearly stable over the range of rotation speeds studied here. The sine and cosine modes for all nodal diameters couple to each other at all non-zero rotation speeds and the strength of this coupling increases with rotation speed. This coupling causes the reported frequencies of the stationary disk to split. The zero, one and two nodal diameter in-plane modes do not have a critical speed corresponding to the vanishing of the backward travelling wave frequency. The use of a linear strain measure in earlier work incorrectly predicts instability of the rotating equilibrium and the existence of critical speeds in these modes.</description><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Physics</subject><subject>Solid mechanics</subject><subject>Structural and continuum mechanics</subject><subject>Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)</subject><subject>Vibrations and mechanical waves</subject><issn>1048-9002</issn><issn>1528-8927</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><recordid>eNpFkM1LAzEQxYMoWKsHz172oiCyNZ-b5Cj1q1BQpHoNs2lWU7fZmuwe_O9NacHTPIbfe8w8hM4JnhBCxC2ZEEEpJ_oAjbJSpdJUHmaNuSo1xvQYnaS0wpgwJsQI3cxC-dpCcMWHryP0vgup6JoCisWXD8Vb1-dd-Czuffo-RUcNtMmd7ecYvT8-LKbP5fzlaTa9m5fAsOrLmlPOsK5A8KWTWnFV6RoUtRKAq6YGovFyqRklSipdc8erWgtBsbWgOHNsjK52uZvY_Qwu9Wbtk3Xt9sxuSIZmm6IVy-D1DrSxSym6xmyiX0P8NQSbbR2GmH0dmb3ch0Ky0DYRgvXp38AFq4iUmbvYcZDWzqy6IYb8q-ESK0nYH43ZZKU</recordid><startdate>20030101</startdate><enddate>20030101</enddate><creator>Deshpande, Moreshwar</creator><creator>Mote, C. 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D</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><jtitle>Journal of vibration and acoustics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Deshpande, Moreshwar</au><au>Mote, C. D</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>In-Plane Vibrations of a Thin Rotating Disk</atitle><jtitle>Journal of vibration and acoustics</jtitle><stitle>J. Vib. Acoust</stitle><date>2003-01-01</date><risdate>2003</risdate><volume>125</volume><issue>1</issue><spage>68</spage><epage>72</epage><pages>68-72</pages><issn>1048-9002</issn><eissn>1528-8927</eissn><abstract>A model for the in-plane oscillations of a thin rotating disk has been derived using a nonlinear strain measure to calculate the disk energy. This accounts for the stiffening of the disk due to the radial expansion resulting from its rotation. The corresponding nondimensionalized natural frequencies are seen to depend only on the nondimensionalized rotation speed and have been calculated. The radially expanded disk configuration is linearly stable over the range of rotation speeds studied here. The sine and cosine modes for all nodal diameters couple to each other at all non-zero rotation speeds and the strength of this coupling increases with rotation speed. This coupling causes the reported frequencies of the stationary disk to split. The zero, one and two nodal diameter in-plane modes do not have a critical speed corresponding to the vanishing of the backward travelling wave frequency. The use of a linear strain measure in earlier work incorrectly predicts instability of the rotating equilibrium and the existence of critical speeds in these modes.</abstract><cop>New York, NY</cop><pub>ASME</pub><doi>10.1115/1.1522419</doi><tpages>5</tpages></addata></record> |
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source | ASME Transactions Journals (Current) |
subjects | Exact sciences and technology Fundamental areas of phenomenology (including applications) Physics Solid mechanics Structural and continuum mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Vibrations and mechanical waves |
title | In-Plane Vibrations of a Thin Rotating Disk |
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