Optimal frequency design of tower structures via an approximation concept

The purpose of this paper is to develop a new numerical method via an approximation concept for finding the optimal bending stiffness distribution of a one-dimensional distributed-parameter structure (i.e, beam) under a fundamental natural frequency constraint. The distributed-parameter structure is modeled by an FEM system and the bending stiffness distribution is approximated by a piecewise-linear function. A cubic displacement function is utilized in the FEM system. Then the displacement function is determined so that the optimality condition described at every point would be satisfied only at the element ends. It is shown that the optimal bending stiffnesses can be obtained from a set of simultaneous linear equations which is rearranged from a set of governing equations of the lowest eigenvibration. No iteration is required in determining the optimal displacement functions and bending stiffnesses. A numerical example of a tower structure is presented in order to demonstrate the validity, efficiency and accuracy of this method.