A note on frequencies of a beam with a heavy tip mass

Swaminadham, M and Michael, Antony (1979) A note on frequencies of a beam with a heavy tip mass. Journal of Sound and Vibration, 66. pp. 144-147. ISSN 0022-460X

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Abstract

The frequency equation for a cantilever beam with a heavy mass at its free end is derived, taking into account shear and rotary inertia effects. Boundary conditions are altered to account for the discontinuities of the second and third derivatives of the displacement functions at the point of attachment of the extra mass, and the frequency equation is derived from the differential equation of uniform beam motion. Computer calculations for the first five modes for various mass and moment of inertia ratios show that the presence of a concentrated end mass lowers all the natural frequencies, with the fundamental affected most strongly. Rotary inertia is found to have a greater effect than translational inertia, and both of these second order effects are more important in a tightly clamped beam than in a loosely clamped or hinged beam

Item Type:	Article
Uncontrolled Keywords:	Cantilever beams;Dynamic structural analysis;Frequency response;Resonant vibration;Structural vibration;Boundary value problems;Differential equations;Equations of motion;Microcomputers;Moments of inertia;Resonant frequencies;Rigid structures;Roots of equations;Turbomachine blades;Vibration mode
Subjects:	ENGINEERING > Structural Mechanics
Depositing User:	Ms. Alphones Mary
Date Deposited:	29 Jun 2006
Last Modified:	18 Aug 2015 07:38
URI:	http://nal-ir.nal.res.in/id/eprint/1506

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