On the determination of natural frequencies of a cantilever beam in free bending vibration: a rigid multibody approach

A rigid multibody method for free vibration analysis of beams with variable axial parameters

“…Essentially, the method in this paper is based on similar ideas to those presented in Šalinić and Nikolić (2013a, 2013b). However, the applicability of the method described in Šalinić and Nikolić (2013a, 2013b) is restricted to transverse vibrations of homogeneous beams, whereas the method presented in this paper allows analysis of torsional vibrations and axial vibrations, as well as vibrations of beams undergoing transverse–transverse–torsional–axial motions.…”

“…Essentially, the method in this paper is based on similar ideas to those presented in Šalinić and Nikolić (2013a, 2013b). However, the applicability of the method described in Šalinić and Nikolić (2013a, 2013b) is restricted to transverse vibrations of homogeneous beams, whereas the method presented in this paper allows analysis of torsional vibrations and axial vibrations, as well as vibrations of beams undergoing transverse–transverse–torsional–axial motions. Also, the method from Šalinić and Nikolić (2013a, 2013b) uses massless beams which lead to a singular mass matrix, so a special computational procedure is necessary to reduce the system of ordinary differential equations to a system of differential and algebraic equations and then form the corresponding eigenvalue problem.…”