Technical University Munich – Summer Semester 2024
This pages presents a series of videos based on my SEA lecture hold during Summer Semester 2024 at TU-Munich
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Introduction and Motivation
Linear Systems
The linear systems session deals with single to multiple degree of freedom systems of lumped elements (springs, masses and dampers), there response to deterministic and random excitation and how energy is introduced in such systems. In order to deal with random excitation an introduction to random signal theory and spectral analysis is given. The main purpose of this chapter in my book and the lecture is to keep the treatment of SEA self-consistent.
Those who are familiar with linear lumped systems and random signal analysis can skip this main chapter.
Harmonic Oscillator
As this is the simplest case of dynamic resonators some of you might be used to it. However, it is an excellent playground for the presentation of resonances, characteristic dynamic quantities like impedance and dynamic stiffness and power balance. The most important part deals with the various damping processes that lead to the power dissipation 
of a system with energy 
using the damping loss factor 
.
2DOF and MDOF Systems
Short session about the next level – the coupled oscillator and multiple coupled oscillators.
The concept of lumped masses and springs is extended to multiple masses and directions. This is used to explain the global concept of the matrix form of discrete structural systems using mass and stiffness matrices.
Based on this modes and modal frequencies are presented as a resonance of a MDOF system.
Session 3: 2DOF and MDOF systems
Random Process
The session is about the signal analysis of random processes and time histories. This tools set is mandatory to describe excitation and response of systems to random signals and wave fields. Which itself is very important for SEA where the energy is stored in a reverberant and diffuse wave field.
Systems and System Response to Random Excitation
The excitation of dynamic systems with more than one input requires the description of the excitation by cross spectral density spectrum (CSD) of the excitation. For many inputs this becomes a large matrix of CSDs making the calculation unhandy. However, SEA subsystems are represented by reverberant and random wave fields – those fields definitely constitute a random excitation.
Waves in Fluids
The wave equation for acoustic waves is derived. Some solutions are presented in relationship to field quantities. The relationships of power, energy and intensity to the acoustic pressure will later be required to model a cavity by a reverberant sound field and thus as a SEA subsystem.