This course concerns the study of deformable elastic structures. Based on simplified structural models, this is an introduction to the dynamics of elastic structures in the case of small perturbations. The objective is to give the student tools to design simple structures subjected to dynamic loads. This part starts from Hamilton principle for conservative structures to obtain equations of motion and boundary conditions for beams and plates. For unloaded undamped non-rotating structures, stationary dynamic solutions are eigenmodes: rigid body modes associated with zero eigenvalues and elastic modes associated with non-zero eigenfrequencies. Eigen shapes show important orthogonality properties. These properties are used to obtain uncoupled equation in a modal shape basis in case of dynamic loading. For time-periodic loads, resonance phenomena occur when the load’s frequency tends to the structure’s eigenfrequency.
