Chapter 4 - Curved Beams

Abstract

This chapter discusses the vibration of thin and thick composite curved beams through the use of two theories. In the first theory, thin beams are studied where the effects of shear deformation and rotary inertia are neglected. This theory will be referred to as thin beam theory or classical beam theory (CBT). In the second theory, shear deformation and rotary inertia effects are considered. This theory will be referred to as thick beam theory or shear deformation beam theory (SDBT). The equations derived for moderately thick beams are different from those derived for thin beams. Shear deformation and rotary inertia should be included in the derivation of a thick beam theory. An accurate formulation is made for the stress resultants of thick beams. Boundary conditions can also be obtained from the last terms of the variational equation. By introducing the stiffness and kinematical relationships into the equations of motion, they have been expressed in terms of displacements. If the assumed displacement functions have sufficient continuity, then the equations of compatibility are identically satisfied.