Mechanical Vibrations


Stanford School of Engineering



Vibrations in machines and structures are typically undesirable as they produce stresses, energy losses and increased bearing loads. They contribute to structural wear and can lead to passenger discomfort in vehicles.

This course covers the vibrations of discrete systems and continuous structures and introduces the computational dynamics of linear engineering systems. Learn how to derive equations of motion and design vibration isolation systems. Gain an understanding of the concepts of natural frequencies and mode shapes and their significance. Complete system modeling tasks and formulate equations to measure and ultimately minimize vibrations.


AA 242A or equivalent (recommended but not required); basic knowledge of linear algebra and ODEs; no prior knowledge of structural dynamics is assumed.

Topics include

  • Dynamics of discrete and continuous systems
  • Damped and undamped vibrations of N-degree-of-freedom systems
  • Approximation of continuous systems by displacement methods
  • Solution methods for the Eigenvalue program
  • Direct-time integration methods