Vibrationsrespons

Vibrationsrespons, or vibration response, refers to the motion or displacement of a structure or component in reaction to an external or internal vibration input. It is a central concept in mechanical engineering, structural dynamics, acoustics, and seismology, used to assess how systems respond to forces, shocks, or excitations over time.

In many engineering contexts, systems are modeled as linear time-invariant with a lumped mass, damping, and stiffness: m x'' + c x' + k x = F(t). The natural frequency is ω_n = sqrt(k/m), and the damping ratio is ζ = c/(2 sqrt(mk)). The steady-state response to a harmonic force F(t) = F0 cos(ω t) yields an amplitude X and phase lag φ given by X = (F0/m) / sqrt((ω_n^2 − ω^2)^2 + (2 ζ ω_n ω)^2) and φ = arctan((2 ζ ω_n ω)/(ω_n^2 − ω^2)). The corresponding frequency response function H(jω) describes how displacement, velocity, or acceleration output relates to the input over frequency.

Resonance occurs when the excitation frequency is near ω_n, particularly for small damping, leading to large amplitudes unless damping or isolation mitigates the response. The impulse response of a second-order system reflects how the system reacts to a sudden force, while the step response shows steady-state displacement under a constant force.

Measurement and analysis involve sensors such as accelerometers to capture motion, followed by time- or frequency-domain analysis (e.g., Fourier transforms, power spectral density) to characterize the vibrational behavior. Applications range from evaluating product comfort and fatigue life to ensuring structural safety in buildings, vehicles, and aerospace components. Design approaches to control vibrations include increasing damping, adding isolation, or tuning natural frequencies to avoid harmful excitation.