Mechanical Vibrations & Structural Dynamics

Free and forced vibrations, damping, harmonic excitation, resonance, critical speeds, and multi-DOF dynamics.

Theory Modules

Study the theory, review the governing formula, and test your knowledge with interactive questions.

Critical speed in rotating machinery is the shaft rotational speed at which the forcing frequency of rotation (spin s...

Damped systems are dynamical systems in which energy is dissipated (commonly via viscous damping) so that free vibrat...

Dampers (viscous damping elements) provide force proportional to relative velocity and dissipate mechanical energy in...

Forced vibration studies the steady-state and transient response of dynamical systems subjected to external time-depe...

Free vibration is the motion of a mechanical system after it is given an initial disturbance (displacement and/or vel...

Frequency response describes how a dynamic system (typically modeled as a linear time-invariant system) responds to s...

Introduction to Vibration: Vibration is oscillatory motion about an equilibrium position. In engineering this is ofte...

Modal analysis decomposes the dynamic response of a linear multi-degree-of-freedom (MDOF) system into a set of indepe...

Natural frequency is the frequency at which a mechanical system vibrates freely (no forcing) about an equilibrium pos...

Resonance is the condition in which a vibrating system is driven at a frequency close to one of its natural (undamped...

Rotating systems (rotors) are mechanical assemblies that spin about an axis and exhibit dynamics governed by mass, st...

Multi-degree-of-freedom (MDOF) vibration systems have multiple independent coordinates describing motion. Their dynam...

Undamped single-degree-of-freedom (SDOF) systems are linear mechanical systems with mass and stiffness but no energy...

Vibration isolation is the use of mounts, springs, dampers or combinations thereof to reduce the transmission of vibr...

Vibration studies motion about an equilibrium position when a system is displaced and released. For engineering struc...