Temperature and frequency dependence of anelasticity in a nickel oscillator

The frequency dependence of the real and imaginary parts of a nickel oscillator’s transfer function is described over 3 decades in frequency by the use of simple expressions. These expressions incorporate only the resonance frequency ω0, the quality factor Q, and a characteristic exponent β determined by a single measurement of creep. They are based on the ansatz φ(ω)=Q−1(ω/ω0)−β, where φ is the imaginary part of the spring constant. Over a 100 K range of temperature T, the exponent β≂0.18 was constant even though Q(T) changed by a factor of 8. These expressions are potentially useful for accurately describing a mechanical oscillator whose transfer function must be modeled at frequencies far below ω0. Examples include accelerometers based on a flexure element and suspensions for interferometric gravitational wave detectors.