VIBRATIONS OF CANTILEVER BEAMS WITH VARIOUS INITIAL CONDITIONS

The motion of a cantilever beam is studied after it has been deflected into an initial shape and released from rest. This is determined by superimposing the displacements of the free vibration modes. While the analytical procedure used may be found in many textbooks, numerical results and a physical understanding of the vibratory motion are seriously lacking. Four examples are taken from which the initial deflection resembles, but is different from, the fundamental mode shape of free vibration. For two of the examples, plots of the resulting, aperiodic motions are made for various points taken along the beam. Displaced shapes of the beam at subsequent times are also shown. Another example begins with an initial shape resembling the second mode. From the plotted results the question of "What is a vibration?" arises, and is discussed. © 1991.