Abstract
Receptance methods have been used to set up general equations that govern the vibrational response of a finite array of N mono-coupled elements terminating at general boundaries. The equations have been modified to introduce ideal and the frequency dependent boundary conditions offered by semi-infinite periodic arrays attached at its ends. The general theory has been adapted to determine the natural frequencies of some finite 5-span beams on simple supports with their ends having various combinations of ideal and frequency dependent end conditions. Lowest group of natural frequencies of the finite beams having different disorders and different combinations of ideal, elastic and dissipative boundaries have been computed and discussed. The conditions under which the undamped combined systems can behave like spring-mass systems and spring-mass-damper systems have also been identified and explained.
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