10 - Instabilities associated with rotating beams

Abstract

When slender structural members, such as beams are forced to rotate in specific ways, some portions of the structure may be put under compression. This situation may induce buckling. However, there are also situations involving rotation that induce static instability in which only tensile forces are involved. This chapter examines both situations. The first situation deals with axial instability of rotating rods that is oriented perpendicular to the axis of rotation and hence referred to as “radial” rods; (a rod is defined as a special case of a beam that only undergoes stretching caused by an axial force). The second situation looks at the buckling instability of radial beams. For small strain, only a linear model for axial deformation of rotating rods can be derived. This linear model exhibits instability when the angular speed reaches a certain critical value. Unless this linear model is valid for large strain, it is impossible to determine whether this instability occurs in reality. This is because the strain ceases to be small well short of the critical speed as the angular speed increases. To understand this situation, the analysis of axial deformation of rotating rods is presented using two strain energy functions to model nonlinear elastic behavior.