Conservation laws for nonhomogeneous Bernoulli-Euler beams (Q1328741)

We construct conservation laws for the statics and dynamics of nonhomogeneous Bernoulli-Euler beams. To derive these conservation laws, we use the neutral action (NA) method. Classically, Noether's first theorem is available for construction of conservation laws for Lagrangian systems, such as a Bernoulli-Euler beam. However, since the NA method is applicable to dissipative as well as to Lagrangian systems, and since it encompasses Noether's method within the realm of Lagrangian systems, we choose to employ the NA method to achieve our purpose. A comparison of these two methodologies, with an example illustrating the relative efficiency of the NA method over Noether's approach, will also be presented.