THE VIBRATIONS OF A STIFF GRAVITY PENDULUM WITH A PARTICLE BOB

A gravity pendulum is modelled as a vertical uniform Euler-Bernoulli b eam with a particle bob. To study the effect of the type of support, i deally clamped, pinned, sliding or free boundary conditions are addres sed. The vibrations of the four types of pendulums in ''hanging'' and in ''inverted'' positions are considered. The first three dimensionles s non-zero natural frequencies Omega(1), Omega(2) and Omega(3) for var ious combinations of the gravity parameter gamma and the end mass para meter delta are presented. Asymptotic solutions when gamma and/or delt a is large are discussed. Critical combinations of the gravity paramet er and the end mass parameter for which a natural frequency of an ''in verted'' pendulum is zero (i.e., buckling conditions) are presented. ( C) 1996 Academic Press Limited