Mechanical Vibrations

• Identify masses, stiffness, energy-dissipation and external forces in some standard mechanical systems.
• Use Newton’s second law, free body diagrams and the energy method to derive the equations of motion (scalar or matrix-vector form) for simple models of mechanical systems with a finite or infinite number of degrees of freedom.
• Determine the natural frequencies for mechanical systems with a finite or infinite number of degrees of freedom.
• Use analytical and numerical methods to solve equations of motion for mechanical systems.
• Understand and explain eigenfunctions, eigenvectors and eigenvalues.
• Identify resonance problems for both damped and undamped vibrating mechanical systems.
• Account for the limitations in the models and methods used, and predict the possible consequences of making simplified assumptions, especially linearization and limitation of the number of degrees of freedom.
• Use approximate methods to determine natural frequencies.
• Write technical reports with correct description of theoretical and experimental procedures, in a clear way, using technical terms, giving physical interpretations and evaluations of results.
• Use the computer software DAMA and MATLAB for solving vibration problems.
• To give the students a basic background for advanced studies in dynamics and vibrations.
• Read engineering literature on mechanical vibrations.

Equations of motion with initial conditions.

Vibrations of linear single and two degree-of-freedom systems, including free and forced vibrations for translation and rotation with damping and without damping.

Vibration isolators.

Pendulums and mass moment of inertia.

Vibrations of continuous systems: Equations of motion for strings, bars and beams. Boundary and initial conditions. Fourier series, orthogonality, eigenfunctions, eigenvectors and eigenvalues. Whirling shafts and Dunkerley’s formula. Rayleigh’s method and Rayleigh-Ritz method.

Finite Element Methods: Mass and Stiffness matrices and equations of motion for bars and beams expressed in Matrix form.

Introduction to non-linear vibration.

The software “DAMA” will be used as an animation tool, in order to enhance the students’ understanding of the motion and vibration of mechanical systems.

62675/62694

The teaching is both project-oriented and problem-based. There are both lectures and exercises. The mandatory project is bases upon experiments with a Frequency Analyzer as well as MATLAB and COMSOL simulations.

Faggruppe: Mekanisk teknologi
Valgfag