ΜΜ14 | Advanced Structural Dynamics-Special Topics in Finite Element and Boundary Element Methods

Postgraduate Study Program | Computational and Experimental Engineering and Advanced Materials

Introduction to the dynamic behavior of structures – typical problems and applications. Dynamics of continuum media systems, equations of motion, analysis methods. Weak formulations and integral representations of partial differential equations and boundary value problems. Interpolation via shape functions, radial basis functions (RBF) and mean least square (MLS) approximations. The Boundary Element Method (BEM). Discretization of the equations of motion based on FEM and BEM. Mass matrices. Natural conservative discrete multiple degree of freedom systems. Free vibration, modal frequencies and mode shapes, the physical meaning and properties of mode shapes. Numerical eigenvalue-eigenvector calculation methods. The mode superposition method. Forced vibration and transient response calculation. Model reduction methods. Damping Matrices, the case of proportional damping. Discrete non-conservative MDOF systems with viscous damping. Formulation of equations of motion in state-space, damped free-vibration solution. Transient response simulation through direct time integration. Explicit and implicit time integration methods. Application problems and experimental procedures.