Analytical and Experimental Natural Frequencies of Transverse Vibration of Sandwich Beams Interconnected by Winkler Elastic Foundation

Abstract

The free transverse vibration of an elastically connected axially loaded double beam system for different materials and geometry were measured experimentally and analyzed theoretically. The theory predicts that natural frequencies of the system are composed of two infinite sets, describing in-phase and out-of-phase vibrations. It is observed, for the case of identical beams, that the in-phase frequencies are independent of the elastic foundation stiffness and its frequencies are identical to a single beam with the same boundary conditions. To compare and verify the accuracy and reliability of theoretical models, experimental measurements of natural frequencies of free vibration of axially tensioned, double beams interconnected by a silicone rubber foundation with fixed-fixed supported conditions are conducted. The first four synchronous natural frequencies were measured, and they were found to increase with increasing tension. The experiments showed that the synchronous natural frequencies of axially tensioned double beam system with fixed-fixed end conditions are in excellent agreement with those for a tensioned single beam with the same end conditions. The asynchronous mode frequencies are not observed, and believed to be due to the existence of damping properties in the elastic foundation, which suppressed the out-of-phase (asynchronous) mode frequencies.