# SD2175 Numerical Methods for Acoustics and Vibration 9.0 credits

#### Numeriska metoder för akustik och vibrationer

The course covers the theoretical background and some practical experience on acoustic and vibration finite element and boundary element analysis. Modelling of damping in response predictions.

### Offering and execution

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## Course information

### Content and learning outcomes

#### Course contents *

Introduction to numerical methods in engineering. Mathematical models versus numerical models. Finite difference method. Galerkins method and method of weighted residuals. Simple elements. Stiffness method. Element formulations. Coordinate transformations. Isoparametry. Numerical interpolation. Convergence properties for dynamic problems. Hierarchical elements. Direct and iterative solvers. Eigenvalue analysis. Modal superposition. Integral equations. Examples of acoustic radiation and scattering using BEM. Simple fluid-structure interaction. Response analysis of a coupled problem. Modelling of damping and its effect on the response.

#### Intended learning outcomes *

After completing this course, students should be able to:

• Explain the key concepts behind numerical methods for acoustics and vibrations, such as finite element and finite difference methods, and discuss them in terms of simplifications, accuracy, performance and validation.
• Apply numerical theory to acoustics and vibrations problems by implementing it in numerical programs, and perform numerical calculations using computational software such as Matlab and Comsol Multiphysics.
• Reflect on numerical implementations, choose appropriate modelling approaches and troubleshoot problems that arise.
• Evaluate and critically judge numerical results in order to suggest improvements from both physical and numerical modelling perspectives.
• Present the outcome of their work in group discussions, formal oral presentations and written reports.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Basic courses in mathematics and mechanics.

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

Kurskompendium: Numeriska metoder inom akustik och vibrationer.

### Examination and completion

A, B, C, D, E, FX, F

#### Examination *

• INLA - 4x Assignment & Written report, 6.0 credits, Grading scale: P, F
• PROA - Project & Oral and Written Report, 3.0 credits, Grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

#### Other requirements for final grade *

Examination, written test (TEN1; 4 university credits), Assignments (INL1; 3 university credits), Computer task, oral defence (INL1, 2 university credits).

#### Opportunity to complete the requirements via supplementary examination

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#### Opportunity to raise an approved grade via renewed examination

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### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SD2175

#### Offered by

SCI/Aeronautical and Vehicle Engineering

#### Main field of study *

No information inserted

#### Education cycle *

Second cycle

SD2165 Acoustical Measurements
SD2150 Experimental Structure Dynamics
SD2155 Flow Acoustics
SD2160 Sound and Vibration, Project Course
SD2170 Energy Methods
SD2180 Non-Linear Acoustics
SD2185 Ultrasonics
SD2190 Vehicle Acoustics and Vibration

#### Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.