## Semester overview

This page contains information on the courses offered in the winter and summer semester.

The dates and rooms of the courses are available at the information portal teaching.

Structural Mechanics

Introduction to tensor analysis

Advanced basics of three-dimensional elasticity theory

• Displacement, distortion and stress state, general and principal axis transformations, laws of elasticity, ortho- and isotropic, dilatation and deviation distributions, deformation energy density, forms of representation, general spatial equilibrium conditions (global, local)
• Basic equations (elimination of the stresses or displacements: Navier's V-differential equation, Beltrami-Mitschel's differential equation, Airy's stress functions), simple rotationally symmetric applications (2D problems), references to FEM, exercises (2D axial symmetry), plane, rotationally symmetric applications (1D), plane problems (plain stress, plane strain), transformations, applications

classical structural theories

• bar and surface structures, lightweight construction
Lightweight Structures and Structural Mechanics

Special features of thin-walled (open and closed) profile bars:

• Transverse force shear, shear center, shear field beam, torsion with cross-sectional curvature, stability ( ..., tilting)

Stability:

• kinking of bars
• buckling of plates
• Outlook with regard to reinforced plates and pipes

Sandwich structures:

• Structure, materials, core designs, deformation calculation, insight into the special features (stability, enhanced sandwich theory)

Fibre composite construction methods:

• Fiber and matrix selection, transformations, classical laminate theory (CLT), special features, insight into strength design

Exercises:

• Analytical exercises, finite element calculations and evaluation including interpretation regarding the lecture material (sandwich structures, stability problems, ...) with commercial software (ABAQUS)
Vibrations of Vehicles and Structures

Repetition and additions to the 1 DOF oscillator

• Free damped oscillations, logarithmic decrement, terms
• Forced oscillations in the frequency range:
• harmonic excitation, uniform (complex) representation of force/spring, unbalance and base point excitation
• Magnification and phase functions, general periodic excitation (Fourier series), general transient excitation (Fourier integral)
• Forced oscillations in the time domain
• Shock response functions, Duhamel integral

Introduction to Multiple Degrees of Freedom Systems

Elementary vehicle vibrations

• Introduction, substitute models, basics at 1 DOF - Model under unevenness excitation:
Natural vibrations, damping, magnification functions, Wheel load fluctuations, hydraulic and rubber damping
• Description of stochastic oscillations:
Key figures, spectral power densities
sinusoidal and general periodic (wave) roadway excitation, stochastic roadway description, path and time angular frequency; discussion of relevant excitation sources
• Evaluation criteria:
Wheel load fluctuations, driving safety, road stress, suspension travel (seat and wheel), human perception, simple vehicles; tyre and seat characteristics

2 - 3 DOF - Quarter model under single point excitation

• Influences of body suspension and damping, wheel mass and suspension; vibration engineering design: Conflict diagram; pitch and roll movements
Introduction to the Finite Element Method

Due to the availability of inexpensive computing power, modern, computer-aided calculation methods are increasingly used in the calculation and design departments. Especially the finite element method has gained acceptance because of its formalizability. Starting from the fundamentals of continuum mechanics, the finite element method is developed and the calculation of deformations, stresses and vibration eigenmodes is presented.

Non-linear Structural and Continuum Mechanics

[Translate to Englisch:] Introduction, terms, motivationEinführung, Begriffe, Motivation

Repetitions for tensor algebra and analysis

Nonlinear deformation kinematics

• Lagrange and Eulerian approach; deformation, displacement, velocity gradient, polar decomposition; Green-Lagrange, Almansi, Hencky distortion tensors;deformation, rotation, distortion velocity tensors, ...

Measures of stress and kinetic quantities

• Cauchy, first and second Piola-Kirchoff stress tensors,...

Balance equations

• general field formulation, mass, momentum, angular momentum, mechanical energy balance

Material Laws

• general propositions, objectivity, symmetries, hyperelasticity: Ogden, Mooney-Rivlin, Neo-Hooke, Saint-Venant Kirchhoff, ...)

FE examples for the calculation of rubber with large deformations

Literature:

• Holzapfel: Nonlinear Solid Mechanics, ISBN 471-82319-8
• Belytschko, Wang, Moran: Nonlinear Finite Elements for Continua and Structures, ISBN 471-98774-3
• Wriggers: Nichtlineare Finite-Element-Methoden, ISBN 354067747X
Sound and Vibration Measurement , Part B

Part A: Sound Measurement - is is presented by Dr Thomas Geyer.

Part B: Vibration Measurement

• Introduction to the principle measurement chain, excitation sources, sensors, representation in the frequency domain, examples of spectra, logarithmic representation, aliasing, leakage, window functions, settings for the measurement sequence and special features of the frequency analyzer, characteristic functions of signal analysis, theoretical modal analysis, orthogonality relation, transfer matrix, modal analysis of measured frequency responses, SDOF and MDOF methods, criteria for checking modal quantities (e.g. MAC), structural modification, multi-point excitation according to phase separation methods, model updating, transfer matrix methods, assessment criteria of vibration effects on man and machine / damage diagnosis
• Accompanying experiments: among others, experimental determination of damping, experimental modal analysis, model updating, order analysis
Laboratory Motor Vehicles

The Chair of Structural Mechanics offers the following experiments within the Laboratory Motor Vehicles:

• Introduction to fibre composites
• Here the basics of the production of fibre composite components are taught using simple components as examples.
Some questions concerning the design of fibre composite components are discussed and an overview of different reinforcing fibres and matrix materials as well as other lightweight constructions (sandwich structures) is given.
• Experimental modal test
• The students perform an experimental modal test on two examples (steel plate, vehicle body). The modal analysis is a possibility to determine the modal parameters (natural frequencies, damping, vibration modes) of components by stimulating the respective structure to vibrate in a defined way and recording this vibration response. The excitation is done for the steel plate by a modal hammer and for the vehicle body by an electrodynamic shaker. Initially, an insight into the theoretical basics of signal and modal analysis is given. Subsequently, an experimental modal analysis is performed and evaluated, whereby the experimental results are compared and discussed with the calculated (FEM) results.