Classes of exact solutions for several static and dynamic problems of non- uniform beams

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniformbeams is proposed. It is shown that the governing differential equations for several stability, freevibration and static problems of non-uniform beams can be written in the from of a unified self-conjugatedifferential equation of the second-order. There are two functions in the unified equation, unlike mostprevious researches dealing with this problem, one of the functions is selected as an arbitrary expressionin this paper, while the other one is expressed as a functional relation with the arbitrary function. Usingappropriate functional transformation, the self-conjugate equation is reduced to Bessel