Free Vibration of Unidirectional Composite Cylindrical Helical Springs with Rectangular Cross section

Abstract:

The naturally curved and twisted beam theory was applied to the beams for anisotropic materials, and an analytical expression for the warping function of Saint Venant’s torsion of unidirectional composite bars with rectangular cross section was obtained. Then, the differential equations of motion for unidirectional composite cylindrical helical springs with noncircular cross sections, which consist of 14 first order partial differential equations, were further derived. In the formulation, the warping effect upon natural frequencies and vibration mode shapes was first studied in addition to considering the rotary inertia, the shear and axial deformation effects. Improved Riccati transfer matrix method was introduced to solve the free vibration differential equations of the springs which presented a strong rigidity. Calculation results show that, for unidirectional composite cylindrical helical springs with rectangular cross section, the warping deformation has a significant influence on the free vibration characteristics of such springs, which should be considered in the free vibration analysis. Finally, the effects of various parameters on the natural frequencies of the springs were investigated.