LAUSR

Many engineering structures can be modeled with a system of rigid bodies connected with elastic am segments, hence, free vibration analysis of these models of structure are of crucial importance. Many papers deal with vibration analysis of the system composed of a single rigid body and two elastic beam segments [1-3] as well as of the system of cantilever beam with a rigid body attached to its free end [4-6]. In [7] two dimensional structures composed of two-part elastic beam-rigid body elements are analyzed by using transfer matrix and direct approach. Vibration of hybrid elastic beam carrying several elastic-supported rigid bodies is analyzed in [8]. All above references consider that the mass centers of the rigid bodies are located on the neutral axis of elastic beams. This paper presents the extension of the existing results of free vibration of structures of rigid bodies connected with elastic beam segments, but unlike existing results, in this paper mass centers of rigid bodies are not located on the neutral axes of elastic beam segments. Also, all elastic beam segments are in the same plane and during oscillations, rigid bodies perform planar motion. For determination of natural frequencies of the system, modification of the conventional continuous-mass transfer matrix method (CTMM) [9] has been performed. Performed modification of CTMM gives the coefficients of lowerorder determinant as compared to the determinant obtained in [9], which has importance in numerical analysis of the systems with a large number of elastic beam segments and rigid bodies. Theoretical apporach of this paper is based on paper [10]. In this paper, the case when the left side of structure is clamped and the right side of structure is simply supported, is applied. But the beam is cantilevered and obtained results can be applied easily on any type of constraints on these places.