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# Stochastic Finite Element Method in Vibroacoustic Analysis

## Module MW2324

This Module is offered by Chair of Vibro-Acoustics of Vehicles and Machines (Prof. Marburg).

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Basic Information

MW2324 is a module over more years in German or English language at Master’s level which is offered every semester.

This Module is included in the following catalogues within the study programs in physics.

• Catalogue of non-physics elective courses
150 h 45 h 5 CP

### Content, Learning Outcome and Preconditions

#### Content

- Introduction to theory of vibroacoustics and structural vibration
- Introduction to uncertainty quantification methods
- Introduction to random variables and probability theory
- Sampling and non-sampling based FEM
- Karhunen–Loève and polynomial chaos expansions
- Intrusive and non-intrusive vibroacoustics FEM
- Collocation-based vibroacoustics FEM
- Random parameter identification in vibroacoustics FEM

#### Learning Outcome

After participating in this module, the students are able to:

- define instrusive and non-intrusive FEM formulations

- identify and explain the developments of Karhunen-Loève and polynomial chaos

- understand methods to quantify the uncertainties and practice the sampling and non-sampling FEM methods

- to identify and apply analytical and numerical FE methods for the structural dynamic description of vibro-acoustic problems

- develop vibro-acoustic models and to evaluate them in terms of parameter uncertainties

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 2 Stochastic finite element method in vibroacoustic analysis Sepahvand, K. Mon, 14:00–16:00, virtuell
Mon, 14:00–16:00, virtuell
eLearning
UE 1 Stochastic finite element method in vibroacoustic analysis Schmid, J.
Responsible/Coordination: Sepahvand, K.
Thu, 11:15–12:45, virtuell
Thu, 11:15–12:45, virtuell
eLearning

#### Learning and Teaching Methods

The lectures are taught using Tablet-PC and projector. The theory is illustrated by numerical examples. Students will get online access to lectures, exercises collection, and computational examples and projects. Most of the exercises have to be calculated by students as homework before they are discussed in the tutorials. The homework will be graded as a part of the final grade of the course. Computer-based simulation projects will be performed step by step, interactively.

#### Media

Lectures: Tablet-PC, Presentation
Tutorials: Analytical and numerical examples, Matlab and ANSYS-based simulation examples

#### Literature

- Lecture notes, work sheets
- "Advanced Computational Vibroacoustics: Reduced-Order Models and Uncertainty Quantification" by Roger Ohayon and Christian Soize, 2014.

### Module Exam

#### Description of exams and course work

On the one hand the module will be assessed in the form of a written exam (90 min) or a oral test (20 min) (the decision is made at the beginning of the semester and is based on the number of participants in this course) in which students demonstrate they have understood the formulations and methods of stochastic finite element method (sFEM) and uncertainty quantification, and know how to define and distinguish them. Allowed as an auxiliary tool is a non-programmable calculator. (50%)

On the other hand a project work in the form of homework (programming exercice) are used to report the extent to which participants are able to develop vibro-acoustic models using ANSYS and Matlab and to apply stochastic FEM on their own. Besides the ability of modeling, the acquired knowledge of sFEM formulations will be asked in the homework. (50% )

#### Exam Repetition

There is a possibility to take the exam in the following semester.

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