Effect of Axial Force on the Free Vibration of Reddy—Bickford Multi-span 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 to know the natural frequencies of the coupled beam—mass system for a proper design of the structural elements. There is plenty of 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, but less is available regarding Reddy—Bickford multi-span beam carrying multiple spring—mass systems with/without axial force effect. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of Reddy—Bickford beams. The model allows the influence of the shear effect and spring—mass systems on the dynamic behavior of the beams to be analyzed by using Reddy—Bickford beam theory. The effects of the attached spring—mass systems on the free vibration characteristics of one to four span beams are studied. The calculated natural frequencies of Reddy—Bickford and Timoshenko multi-span beams using a secant method for nontrivial solution of the different values of axial force are given. The mode shapes of Reddy—Bickford multi-span beams are also presented.