ABSTRACT
In this chapter, we develop a rapidly convergent method for solving fourth-order self-conjugate problems. As a basic mathematical model we take the equation of transverse vibrations of a thin inhomogeneous rod subjected to arbitrary boundary conditions. Just as for second-order equations, we establish a differential relation between the eigenvalue and the length of the interval. High efficiency of the algorithm is demonstrated by examples. The problem of parametric synthesis is solved for conical beams whose flexural rigidity may have variation of order up to from one edge to the other, while its linear density variation may be of an order up to .
