Vibrations and Dynamics Review

These flashcards cover key concepts related to vibrations, dynamics, and structural analysis.

Modal Analysis

The study of natural frequencies of a system under free or forced conditions without damping.

Harmonic Analysis

The study of steady state solutions to harmonic loads, often represented by sinusoidal equations.

Transient Analysis

Solutions to perturbations and time-varying loads.

Equation of Motion (EOM)

A mathematical expression that relates forces and motion of a system, often represented as Mx'' + Cx' + Kx = f(t).

Free Body Diagram (FBD)

A graphical representation used to visualize the forces acting on an object.

Natural Frequency (ωn)

The frequency at which a system oscillates when not subjected to any external force.

Damping Ratio (ζ)

A dimensionless measure comparing the amount of damping in a system to critical damping.

Critical Damping

The condition in which a system returns to equilibrium as quickly as possible without oscillating.

Undamped Vibration

Vibration of a system with no energy loss in the form of damping.

Complex Number

A number of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Phasor Solution

A method to represent sinusoidal functions as complex numbers to simplify calculations in engineering.

Quality Factor (Q)

A dimensionless parameter that characterizes the resonator's bandwidth relative to its center frequency.

Modal Analysis

A method used in structural engineering to determine the natural frequencies and mode shapes of a structure.

Damped Natural Frequency

The natural frequency of a damped system, often denoted as ωd.

Steady State Vibration

The state of a system when it has settled into consistent oscillation under constant forcing.

Load Factor (n)

A ratio that describes the relationship between the actual load and the designed load in dynamic analyses.

Flutter

A dynamic instability in elastic bodies caused by aerodynamic forces.