dampinganalyse

Dampinganalyse is the study of energy dissipation in vibrating systems and how damping shapes the decay of oscillations and the frequency response under dynamic loading. It is used in mechanical, civil, aerospace, acoustical, and electrical engineering to quantify how quickly motions decay, how resonance peaks are attenuated, and how damping interacts with system stiffness and mass.

In the common lumped-parameter framework, a damped structure is described by the equation M x'' + C x' + K x = f(t), where M is the mass matrix, C the damping matrix, K the stiffness matrix, x the displacement vector, and f(t) an external force. The undamped natural frequencies ω_n and eigenmodes change in the presence of damping, with the damped natural frequency ω_d = ω_n sqrt(1 − ζ^2) for each mode and the damping ratio ζ indicating the relative rate of energy loss. For single-degree-of-freedom systems, c = 2 m ω_n ζ and ζ = c/(2 sqrt(k m)).

Methods for damping analysis include time-domain approaches (free decay and impulse tests to extract the logarithmic decrement δ and ζ ≈ δ/(2π) for lightly damped systems) and frequency-domain approaches (frequency response functions, FRFs, from which damping is inferred from peak bandwidth or phase characteristics). In multi-degree-of-freedom problems, modal damping ζ_i is defined for each mode, and proportional (Rayleigh) damping C ≈ α M + β K is a common simplifying assumption, yielding ζ_i = (α/2ω_i) + (β ω_i/2).

Applications encompass structural design for safety and comfort, vibration control, noise reduction, and performance optimization in vehicles, buildings, machinery, and consumer electronics. Limitations include frequency-dependent and nonlinear damping effects, measurement noise, and non-proportional damping complicating modal interpretations.