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This chapter considers the torsional vibrations of uniform and nonuniform rods with circular cross‐section and rods with noncircular section. It derives the equations of motion for noncircular sections using both the Saint‐Venant and the Timoshenko‐Gere theories. The chapter presents the methods of determining the torsional rigidity of noncircular rods using the Prandtl stress function and the Prandtl membrane analogy. The angular displacement of a shaft in torsional vibration can be expressed in terms of normal modes using the expansion theorem. For a shaft or bar of noncircular cross‐section subjected to torsion, the cross‐sections do not simply rotate with respect to one another as in the case of a circular shaft, but they are deformed, too. The membrane analogy provides more than an experimental technique for the solution of torsion problem. It also serves as the basis for obtaining approximate analytical solutions for rods with narrow cross‐sections and open thin‐walled cross‐sections.
This chapter considers the torsional vibrations of uniform and nonuniform rods with circular cross‐section and rods with noncircular section. It derives the equations of motion for noncircular sections using both the Saint‐Venant and the Timoshenko‐Gere theories. The chapter presents the methods of determining the torsional rigidity of noncircular rods using the Prandtl stress function and the Prandtl membrane analogy. The angular displacement of a shaft in torsional vibration can be expressed in terms of normal modes using the expansion theorem. For a shaft or bar of noncircular cross‐section subjected to torsion, the cross‐sections do not simply rotate with respect to one another as in the case of a circular shaft, but they are deformed, too. The membrane analogy provides more than an experimental technique for the solution of torsion problem. It also serves as the basis for obtaining approximate analytical solutions for rods with narrow cross‐sections and open thin‐walled cross‐sections.
Torsional Vibration of Shafts
Rao, Singiresu S. (author)
Vibration of Continuous Systems ; 277-322
2019-03-06
46 pages
Article/Chapter (Book)
Electronic Resource
English
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