A Generalized Minimum Principle and Its Application to the Vibration of a Wedge With Rotatory Inertia and ShearSource: Journal of Applied Mechanics:;1963:;volume( 030 ):;issue: 002::page 176Author:H. C. Lee
DOI: 10.1115/1.3636508Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The minimum principle and step-by-step iteration method are generalized for coupled simultaneous differential equations in order to obtain an approximate solution for the flexural vibration frequencies of a wedge with rotatory inertia and shear effects. This procedure avoids the difficulty of solving the nonself-adjoint equation which results when the simultaneous equations for bending slope and displacement are combined into a single differential equation. The upper and lower bounds of the first two eigenvalues are established and a comparison is made with the classical Kirchhoff solution where the rotatory inertia and shear are neglected.
keyword(s): Inertia (Mechanics) , Shear (Mechanics) , Vibration , Wedges , Equations , Differential equations , Oscillating frequencies , Displacement AND Eigenvalues ,
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| contributor author | H. C. Lee | |
| date accessioned | 2017-05-08T23:08:41Z | |
| date available | 2017-05-08T23:08:41Z | |
| date copyright | June, 1963 | |
| date issued | 1963 | |
| identifier issn | 0021-8936 | |
| identifier other | JAMCAV-25708#176_1.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/93267 | |
| description abstract | The minimum principle and step-by-step iteration method are generalized for coupled simultaneous differential equations in order to obtain an approximate solution for the flexural vibration frequencies of a wedge with rotatory inertia and shear effects. This procedure avoids the difficulty of solving the nonself-adjoint equation which results when the simultaneous equations for bending slope and displacement are combined into a single differential equation. The upper and lower bounds of the first two eigenvalues are established and a comparison is made with the classical Kirchhoff solution where the rotatory inertia and shear are neglected. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | A Generalized Minimum Principle and Its Application to the Vibration of a Wedge With Rotatory Inertia and Shear | |
| type | Journal Paper | |
| journal volume | 30 | |
| journal issue | 2 | |
| journal title | Journal of Applied Mechanics | |
| identifier doi | 10.1115/1.3636508 | |
| journal fristpage | 176 | |
| journal lastpage | 180 | |
| identifier eissn | 1528-9036 | |
| keywords | Inertia (Mechanics) | |
| keywords | Shear (Mechanics) | |
| keywords | Vibration | |
| keywords | Wedges | |
| keywords | Equations | |
| keywords | Differential equations | |
| keywords | Oscillating frequencies | |
| keywords | Displacement AND Eigenvalues | |
| tree | Journal of Applied Mechanics:;1963:;volume( 030 ):;issue: 002 | |
| contenttype | Fulltext |