A kinematic integral variable approach to dynamics of beams with a periodic-like structure

In the paper a new averaged model for the dynamic response of a periodic-like straight beam with a variable cross-section is proposed. The beam under consideration is assumed to interact with Winkler's subsoil having periodic-like properties. Assumptions of the Bernoulli-Euler beam theory as well as the influence of axial forces on deflection of the beam are taken into account. The approach adapted in the paper is based on concepts of the tolerance averaging approach by Woźniak (1999). In this way it is possible to formulate the averaged equations of the structured beams, which describe the length-scale effect.