The present work is an extension of a tool vastly used by the authors to solve static boundary problems in one, two, and even three dimensions. It consists in a so-called generalized solution with special trigonometric Fourier functions to solve the equations of motion of beams. An important theorem that guarantees that the classic answer is attained through an alternative way is demonstrated. In other words, it is a variational methodology to solve differential equations in engineering. An example solved numerically completes the present proposal.