# Dynamics I and Dynamics II

Structural dynamics

## Contents

The lectures Structural Dynamics - Dynamics I and II aim at deepening the field of dynamics from technical mechanics. They form a double course over one or two semesters.

Focal points of Structural Dynamics - Dynamics I are modeling of multi-body systems, linearizing of equations of motion as well as analyzing vibrations with one degree of freedom:

• Modeling, degrees of freedom and kinematics,
• Principle of d' Alembert, Principle of Virtual Displacements for problems of dynamics,
• establishing equations of motions of multibody systems,
• linearizing equations of motions,
• law of unit displacements for problems of dynamics,
• linear systems with one degree of freedom,
• free vibrations, harmonically, periodically, and impulsively excited vibrations.

The intention of the lecture is thus firstly to develop an understanding of the most important criteria of modeling in dynamics. Secondly, skills are to be developed for setting up and mathematically describing simple discontinuous models of moving systems for a more or less complex engineering task. Nonlinear equations of motion are to be linearized as far as necessary. Thirdly, for the special case of a linear, oscillatory system with one degree of freedom and with viscous damping, the equation of motion should to be solved for the most common dynamic loads in the transient as well as in the stationary area.

The main focus of the part Structural Dynamics - Dynamics II is the mathematical treatment of models of undamped multibody systems with several degrees of freedom as well as the modeling and mathematical treatment of oscillating continua. The latter are treated analytically in simple cases and, more generally, by the Finite Element Method:

• eigenvalue analysis for multibody systems,
• free und excited undamped vibrations of multibody systems,
• modes of rigid movements,
• modal analysis,
• models of continua and their analytical solution,
• discretizing using Finite Elements,
• main focus: strain rod, bending beam, torsion bar.

The intention of the lecture is thus firstly to learn how to handle eigenvalues ​​and eigenvectors as well as the method of modal analysis in multi-body systems. This enables the transfer of analyzing oscillations with one degree of freedom to oscillations with multiple degrees of freedom. Secondly, the basics of vibrational analysis of the other important class of mechanical models, i.e. continua models, has also to be considered. This is done both by closed mathematical methods and approximately, numerically by using simple finite elements. The course covers also some additional content for opening perspectives for further lectures.

 Lecturer:Weekly amount: Semester frequency: Target group:Prerequisites: Jörg F. Wagner4 h lectures (in German)2 h additional exercises (optional)Every semesterMaster students of Aerospace Engineering as of 1st sem.Higher Mathematics 1 to 3,Technical Mechanics 1 to 3