In the module "Structural Dynamics", students gain in-depth knowledge of the dynamic behavior of structures under dynamic loading. The focus is on the procedures for determining the stress under periodic and transient loading with small structural damping.
##### General data about the module
 Study program M.Sc. Aerospace Engineering Module number 1089 Trimester Fall trimester (3rd Master trimester) ECTS 5 Work load 150h total, thereof           48h presence time           102h self-study Typ/TWS 2 TWS lecture 2 TWS excercise
##### Qualification goals
1. The students know the essential procedures for solving the classical vibration equations for structures with small damping and an arbitrary number of degrees of freedom.
2. The students know the terms "natural frequency", "natural mode", "modal mass", "modal stiffness" and "modal damping". They know how to classify problems in the "frequency domain" and "time domain".
3. The students know the difference between an analytical and a numerical solution of the vibration equation and can use the corresponding methods.
4. They are able to create a suitable mathematical substitute model for a given physical problem and to solve it using suitable methods.
5. The students are able to use suitable approximation methods for simple tasks in order to quickly make initial statements regarding the dynamic behavior of structures.

##### Content

The module is divided into the following sections:

• Forced oscillations of mass-spring systems with one DOF
• analytical solutions
• numerical solutions of the equation of motion
• Forced oscillations of systems with many degrees of freedom
• Natural frequencies, natural modes
• Systematic formulation of the equation of motion
• Generation of the stiffness matrix
• Mass matrix
• Reduction of degrees of freedom
• Orthogonality of eigenvectors, decoupling of equations of motion
• Damped oscillations, damping models
• Numerical integration of the equations of motion, Newmark-ß method
• Representation of oscillations in the state space
• General information about the dynamic analysis of structures
• Approximation methods
• Bending vibrations
• Torsional vibrations
• Coupled bending-torsional vibrations
• Ritz method
• Galerkin method
• Experimental modal analysis