We consider a general Fibonacci harmonic lattice in which both the masses and the elastic constants are aperiodically arranged. Making use of a suitable decimation scheme, inspired in real-space renormalization group concepts, we obtain closed analytical expressions for the global transfer matrix and transmission coefficient for several resonant critical normal modes. The fractal structure of the frequency spectrum has a significant influence in the cumulative contribution of the different normal modes to the thermal transport. A sudden enhancement of the thermal coefficient around a set of special frequencies indicates the importance of resonance effects in the thermal conductivity of Fibonacci quasicrystals.
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