Spektralvibrationen

Spektralvibrationen describe vibrational phenomena analyzed primarily through their spectral content. In physics and engineering, it denotes representing a vibrational signal as a spectrum of frequencies rather than as a time-domain waveform. This approach helps identify resonant modes, harmonic content, and damping characteristics of a system.

The mathematical basis rests on transforming a time-domain signal into the frequency domain. A signal v(t) has a spectrum V(f) obtained by a Fourier transform, V(f) = ∫ v(t) e^{-i2πft} dt. The magnitude |V(f)| shows energy distribution across frequencies, and the power spectral density provides a measure of how power is allocated over frequency. Peaks in the spectrum indicate eigenfrequencies or resonances, while peak widths relate to damping.

Measurement and analysis employ sensors such as accelerometers, laser Doppler vibrometers, or microphones, depending on the system. Spectral analysis uses fast Fourier transform, Welch’s method, and related estimators. For non-stationary signals, time–frequency tools like the short-time Fourier transform or wavelet transforms are used to track spectral changes over time.

Applications of spektralvibrationen span structural health monitoring, machinery fault detection, vibration isolation design, and acoustic analysis of musical instruments. The spectral view supports nondestructive testing by revealing hidden resonances and informing material or structural properties through their vibrational signatures.

Key considerations include managing noise, spectral leakage, and windowing effects. Resolution depends on record length and sampling rate, and interpretation often benefits from complementary techniques in modal analysis to link spectral features to physical modes.