Notes on anelastic effects and thermal noise in suspensions of test masses in interferometric gravitational-wave detectors

The thermal noise is expected to be one of the main limiting factors on the sensitivity of interferometric gravitational-wave detectors like LIGO and VIRGO. Thermal fluctuations of internal modes of the interferometer's test masses and of suspension modes will dominate the noise spectrum at the important frequency range between 50 and 200 Hz. It is assumed that losses in the test masses and suspensions will occur mainly due to internal friction in their materials, which is related to anelasticity effects in solids. The present notes comprise some basic results on the theory of anelasticity and thermal noise in pendulum suspensions. This collection is by no means complete and focus on aspects which are of interest for the author.