An approach to modeling vibrations of systems composed of beams, rigid bodies, and point masses

Abstract

An approach for vibration analysis of three-dimensional motion beam systems is formulated. The proposed method employs analytical solutions that are used to formulate a unified, three-dimensional dynamic representation the elements of beam systems, including beams, rigid bodies, and point masses. Interconnections between system’s components and their connections to the inertial frame are formulated as motion constraints. The interconnections can be rigid or flexible and can be located at arbitrary locations on the system components. The unified representations of different types of system elements and of different interconnection allows vibration analysis of complex beam systems. A procedure is developed for computation of natural frequencies and mode shapes by employing a sequence of orthogonal transformations. A three-dimensional structure that includes flexibly and rigidly connected beams and rigid bodies with different types of connections, is used to demonstrate the capabilities of the proposed method. The accuracy of the approach is verified by restricting the structure to planar motion with rigid connections and comparing the results to results of obtained in previous studies. The example structure is used to demonstrate the ability of the proposed approach to conduct vibrational analysis study of three-dimensional structures with different boundary conditions. Moreover, it also demonstrates suitability of the approach for studying sensitivity of vibrations characteristics, such as modal frequencies, with respect to system parameters, e.g. interconnections stiffness.