The present paper is concerned with vibrations of linear elastic structures, the supports of which are performing prescribed large rigid-body motions, while imposed external forces are acting at the same time. The vibrations thus produced are assumed to remain in the small or moderately large strain regime. As an illustrative example for this type of problems, we mention the flexible wing of an aircraft in flight. In the latter case, the rigid-body motion is defined through the motion of the comparatively stiff fuselage to which the vibrating wing is attached. The goal of the present paper is to derive a time-dependent distribution of actuating stresses produced by additional eigenstrains, such that the vibrations produced by the imposed forces and the rigid-body motion can be cancelled out exactly. In order to fix ideas about the latter inverse problem, we start with the introductory example of a support-excited linear elastic system with two degrees-of-freedom and three active elements. Afterwards we present an exact solution in the framework of three-dimensional elastodynamics. We show that the distribution of the actuating stresses must be equal to a statically admissible quasi-static stress distribution that is in temporal equilibrium with the imposed forces and the inertia forces due to the rigid-body motion. Our solution thus explicitly reflects the non-uniqueness of the inverse problem under consideration. We finally present results for a rotating Bernoulli-Euler beam with moderately large displacements.
|Number of pages||12|
|Publication status||Published - 2003|
|Event||Proceedings of the Tenth International Congress on Sound and Vibration - Stockholm, Sweden|
Duration: 7 Jul 2003 → 10 Jul 2003
|Conference||Proceedings of the Tenth International Congress on Sound and Vibration|
|Period||07.07.2003 → 10.07.2003|