Buckling and vibration analyses of unidirectional composite helical coil springs under compression

As a standard member of machines, springs with pre-load either cylindrical or non-cylindrical shaped are frequently subjected to dynamic loads. Hence it is important to understand their static, dynamic, and buckling behaviours. Although many investigations of helical springs were performed in the last three decades, Few studies on the buckling and vibration behaviour of isotropic helical springs subjected to an axial load may be found in the available literature due to the complexity in the formulation of the problem. Besides this, there is no study about the analysis of composite helical springs subjected to an axial force. In this thesis, two important phenomena namely the buckling and vibrational analysis of the most commonly used composite helical compression springs subjected to an axial force are studied. The existing governing equations which consider the pre-axial load effect in the literature will be extended to composite helical springs. Stiffness method is used based on the first order shear deformation theory. The element stiffness matrix is obtained exactly based on the both the complementary functions and the transfer matrix methods. Numerical results are verified by the benchmark studies for isotropic helical springs subjected to an axial force. It is concluded that, since the true geometrical properties after deformation due to the axial static load are required in the formulation to understand the buckling/vibration behaviour of such pre-loaded springs, closed-form solutions for the vertical tip deflection of those helical springs having large pitch angles are derived using the Castigliano?s first theorem. Key Words: Vibration, Composite Springs, Helical Spring, Transfer Matrix, Buckling.