RELATIONSHIP BETWEEN FUNDAMENTAL NATURAL FREQUENCY AND MAXIMUM STATIC DEFLECTION FOR VARIOUS LINEAR VIBRATORY-SYSTEMS

It is shown that the fundamental natural frequency of a wide variety of discrete and continuous systems is inversely proportional to the gravitational acceleration divided by the maximum static deflection, raised to the 1/2 power. The value of the constant of proportionality is determined for multi-degree-of-freedom discrete systems, axially vibrating prismatic and tapered rods, prismatic and tapered slender beams, membranes, and thin plates of many planforms. Particular attention is paid to the effects of taper, axial preload, geometry and boundary conditions. The results of this investigation should be useful in predicting the approximate fundamental natural frequency from the static deflection, either calculated or determined experimentally. © 1993 Academic Press Limited.