Response to Harmonic and Periodic Excitations - Vocabulary Flashcards

A set of vocabulary flashcards focusing on key terms and definitions from the notes on harmonic and periodic excitations.

Single-degree-of-freedom (SDF) system

A lumped-mass model described by m u¨ + c u˙ + k u = p(t) with one dynamic degree of freedom, used to study forced vibration and damping.

Steady-state response

The ongoing sinusoidal system response at the forcing frequency after transient components have decayed in a damped system.

Transient vibration

The initial free-vibration component of the response, determined by initial conditions, that decays over time due to damping.

Deformation response factor (Rd)

The ratio of the dynamic displacement amplitude to the static deformation, Rd = u0/(ust0), describing amplification relative to static deflection.

Resonant frequency

The forcing frequency at which the response amplitude is maximal; in an undamped system it equals the natural frequency wn, while in damped systems the exact peak shifts slightly.

Frequency-response curve

A plot of a response quantity (e.g., Rd, Rv, Ra) versus excitation frequency (often as a ratio w/wn), showing how response varies with forcing.

Vibration generator

A device with counter-rotating eccentric masses that creates a harmonic excitation p(t) = (me ω^2) sin ωt when attached to a structure.

Transmissibility (TR)

The ratio of transmitted response (force, displacement, or acceleration) to input excitation; depends on frequency ratio w/wn and damping and is given by a specific formula for force.

Equivalent viscous damping

A damping value Seq that makes a viscous-damped model reproduce the energy dissipation of other damping mechanisms; defined by energy balance (often at ω = ωn).

Fourier series representation

A representation of a periodic function p(t) as p(t) = a0 + ∑ aj cos(jω0t) + ∑ bj sin(jω0t), with coefficients computed from integrals and fundamental frequency ω0 = 2π/To.