Axial Static Load Dependence Free Vibration Analysis of Helical Springs Based on the Theory of Spatially Curved Bars

Abstract

This work addresses an accurate and detailed axial static load dependence linearly elastic free vibration analysis of cylindrical helical springs based on the theory of spatially curved bars and the transfer matrix method. For a continuous system, governing equations comprise coupled vibration modes namely transverse vibrations in two orthogonal planes, torsional and axial vibrations. The axial and shear deformation effects together with the rotatory inertia effects are all considered based on the first order shear deformation theory and their effects on the frequencies are investigated. The effects of the initial stress resultants on the frequencies are also studied. After buckling, forward-shifting phenomenon of higher frequencies is noticeably demonstrated. It is also revealed that a free/forced vibration analysis with an axial static load should not be performed individually without checking buckling loads.

Buckling Analysis of Rectangular Beams Having Ceramic Liners at Its Top and Bottom Surfaces with the help of the Exact Transfer Matrix

“…Therefore in the design of columns, determination of the critical buckling loads becomes an inevitable stage. method [26][27][28], the homotopy perturbation method [28][29][30][31][32][33], Adomian decomposition method [28,34], the transfer matrix method [35][36][37][38][39], the stiffness matrix method [39], the fictitious load method [40], the modified vibration modes [41] and much more [42][43][44][45][46]. In the solution of more complex problems, some of the solution methods mentioned above may also be used in a combined manner.…”