Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Abstract

Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1-4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.

Transverse Motions of Bernoulli-euler Beam Resting on Elastic Foundation and under Two Concentrated Moving Loads

“…Yesilce and Catal [8] estimated normalized usual frequencies of the pile using carry-over matrix and incorporating rotatory inertia. Hosing et al [9] carried out investigation on the solution to natural flexural excitation of a continuous structural element on discrete elastic support.…”

Quality-Factor Enhancing Locations for Substrate Mounted Resonators

“…[11][12][13][14] Multi-span beams carrying multiple spring mass systems have also been investigated. 15,16 Non-uniform beams carrying an arbitrary number of spring mass systems have also investigated 17 as well. However, the inverse problem of estimating a design parameter, such as a stiffness or a mass, so that the combined system meets certain requirements has received less attention.…”

Transverse Vibration of Clamped-Pinned-Free Beam with Mass at Free End

“…The clamped-pinned-free without mass [6] and the clamped-free with mass at free end without pin [7] have been studied. In more recent years, researchers have investigated the free vibration of multi-span beams with flexible constraints [8], axial vibrations of multi-span beams with concentrated masses [9], multi-span beams with moving masses [10], and multi-span beams carrying spring-mass systems [11,12].…”