Effect of Axial Force on the Free Vibration of Reddy-Bickford Multi-span Beam Carrying Multiple Spring-mass Systems

摘要

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.