Dynamic stiffness for piecewise non-uniform Timoshenko column by power series - part I: Conservative axial force

The dynamic stiffness method uses the solutions of the governing equations as shape functions in a harmonic vibration analysis. One element can predic t many modes exactly in the classical sense. The disadvantages lie in the t ranscendental nature and in the need to solve a non-linear eigenproblem for the natural modes, which can be solved by the Wittrick-William algorithm a nd the Leung theorem. Another practical problem is to solve the governing e quations exactly for the shape functions, nonuniform members in particular. It is proposed to use power series for the purpose. Dynamic stiffness matr ices for non-uniform Timoshenko column are taken as examples. The shape fun ctions can be found easily by symbolic programming. Step beam structures ca n be treated without difficulty. The new contributions of the paper include a general formulation, an extended Leung's theorem and its application to parametric study. Copyright (C) 2001 John Wiley & Sons, Ltd.