Summary
In contrast to the past, when nonlinear phenomena arising in structures of practical interest were seen as almost pathological, today very often slender and highly flexible structures are used in engineering design to take advantage of the beneficial effects of nonlinear dynamics. Needless to say, a key point in correctly describing the dynamics of such structures is the appropriate writing of the relevant equations of motion. Although such equations can be written following different approaches, it is desirable that whatever derivation strategy is chosen, the equations are the same. Restricting attention to the nonlinear dynamics of deformable beams satisfying the Euler-Bernoulli assumptions, and with a generic initial configuration, the question that arises is: What conditions must the constitutive assumptions about generalized forces satisfy in order for the equations of motion obtained by the Newton approach to be identical to the Euler-Lagrange equations derived from an appropriate Lagrangian, whether natural or virtual? The goal of this work is to try to answer this basic question.
