Solution of free vibration equation of elastically supported Timoshenko columns with a tip mass by differential transform method

In this study free vibration analysis of a Timoshenko column with a tip mass having rotary inertia is carried out by both exact solution and differential transform method (DTM). The support of the system is modeled by an elastic spring against rotation. Fixity factor is used to define the relative stiffness of the elastic connection and the column. The governing equation of the column is solved by the separation of variables method including the rotatory inertia to get the exact solution. The same problem is also solved by DTM algorithm and the results are compared with the ones of exact solution. The comparison tables are presented in numerical analysis to show that a very good agreement is observed for DTM.

► We investigate analytical and DTM solutions of free vibration of a Timoshenko column.
► We examine the variations in free vibration natural frequencies of the column.
► We observe good agreement in the results of DTM with the results of analytical method.