The lecture provides an in-depth perspective on the treatment of dynamical problems. Variational formulations of elastic systems at small (infinitesimal) and large (finite) deformations form the theoretical basis. The elementary numerical implementation is conducted in two steps: Space discretization using the method of finite elements and time discretization with finite difference methods.The following topics will be covered:

• Free (natural) and forced vibrations of one-degree-of-freedom models and multi-body-systems
• Variational formulations for discrete multi-degree-of-freedom oscillators, the Hamiltonian principle, Lagrange's equations of motion
• Eigen-frequencies and the concept of modal analysis
• Variational formulation of vibrations of continuous systems, analytical solutions for continuous oscillators
• Space discretization using the finite element method
• Discrete time-step integration schemes, explicit and implicit schemes, stability, accuracy and numerical damping