Natural frequencies of vibration of cantilever sandwich beams

Abstract

Theoretical and experimental studies were made in obtaining the natural frequencies of cantilever sandwich beams subjected to only gravity forces. The method of minimizing the total energy of the system was used for determining the frequencies. A vibration system made by Unholtz-Dickie was utilized to set the beam in vibration. Resonance occurred when the frequency of the shaker coincided with the natural frequency of the beam. The resonance frequencies were measured by transducers mounted at various locations on the beam. A total of sixteen beams of various lengths, thickness and core density were tested. It was found that the natural frequency of a cantilever sandwich beam depends largely upon the thickness, length, core density and stiffness of the beam. In addition, the natural frequency has a nonlinear variation with the mode and for any particular mode, the value of the frequency increases as the length of the beam decreases. Design factors were developed based upon the ratios of the theoretical frequencies of homogeneous beams having the same thicknesses and stiffnesses of that of sandwich beams and of the frequencies experimentally determined for similar sandwich beams.