𝔖 Bobbio Scriptorium
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THE VIBRATIONS OF A “STIFF ” GRAVITY PENDULUM WITH A PARTICLE BOB

✍ Scribed by S. Naguleswaran

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
424 KB
Volume
191
Category
Article
ISSN
0022-460X

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✦ Synopsis

A gravity pendulum is modelled as a vertical uniform Euler-Bernoulli beam with a particle bob. To study the effect of the type of support, ideally clamped, pinned, sliding or free boundary conditions are addressed. The vibrations of the four types of pendulums in ''hanging'' and in ''inverted'' positions are considered. The first three dimensionless non-zero natural frequencies V1, V2 and V3 for various combinations of the gravity parameter g and the end mass parameter d are presented. Asymptotic solutions when g and/or d is large are discussed. Critical combinations of the gravity parameter and the end mass parameter for which a natural frequency of an ''inverted'' pendulum is zero (i.e., buckling conditions) are presented.

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