Single-Course English 5 ECTS

Finite Element Methods for sound and vibrations

Overall Course Objectives

Loudspeakers and microphones are classical mechanical components that rely on the interaction between vibrations and acoustics. Modern applications (Industry 4.0) ranging from self-powering of IoT-devices by energy-harvesting of ambient acoustic energy, virtual sensing, medical equipment (biomechanics & life-sciences) to novel MEMS based microphones and speakers, all rely on engineers with a fundamental understanding of vibration analysis of complex structures and their coupling to the surroundings. In order to enable such skills, the goal of this course is to teach the students to use the Finite Element Method (FEM) to solve advanced, multiphysics vibration problems with specific consideration to problems that involve acoustic-mechanical interaction. This knowledge will be used to create complex finite element models for realistic assessment of the vibrations of micro scale components that involve acoustics at audible frequencies.

Learning Objectives

  • Apply the finite element method to formulate numerical models for vibration problems
  • Solve forced vibration problems using direct methods, modal superposition and advanced reduced order models (ROM) such as super-element methods (Craig-Bampton) and the second-order-Arnoldi-method (SOAM).
  • Evaluate and implement various material models including different damping models
  • Set up and evaluate power flow equations based on a finite element model
  • Compute spatial distributions of kinetic, potential and dissipated energy for vibrating structures
  • Formulate and implement absorbing boundary conditions for wave propagation problems
  • Compute the energy flow in a vibrating structure
  • Formulate finite element models for the interaction between a vibrating structure and an acoustic medium
  • Perform eigenvalue and forced vibration analysis for mechanical structures involving acoustic interaction
  • Construct complex finite element models for solving acoustic-mechanical interaction problems at micro scale.

Course Content

The course focuses on theoretical lectures combined with computer exercises using Matlab (and sometimes COMSOL) to solve structural vibration problems with and without acoustic coupling. Solution methods will cover modal superposition and direct methods as well as various reduced order model (ROM) techniques. Different material and damping models (proportional, structural) will be analyzed and absorbing boundary conditions will be implemented for the simulation of wave propagation. Power flow analysis and evaluation of kinetic, potential and dissipated energy in vibrating structures will be carried out. Interaction problems are formulated and computations in the form of eigenvalues and forced vibrations are performed. Complex finite element models for micro scale components are constructed.

Lectures and computer exercises serve basis for two reports.

Recommended prerequisites

41560/41237/31270/62643/41525/41812, Fundamental knowledge of mechanical vibrations is required. Knowledge of finite element theory and programming experience in matlab is an advantage.

Teaching Method

Lectures and computer exercises

See course in the course database.





13 weeks


DTU Lyngby Campus

Course code 41813
Course type Candidate
Semester start Week 5
Semester end Week 19
Days Wed 8-12

7.500,00 DKK