Stability and resonance conditions of elementary fractional transfer functions

Elementary fractional transfer functions are studied in this paper. Some basic properties of elementary transfer functions of the first kind are recalled. Then, two main results are presented regarding elementary fractional transfer functions of the second kind, written in a canonical form and characterized by a commensurate order, a pseudo-damping factor, and a natural frequency. First, stability conditions are established in terms of the pseudo-damping factor and the commensurate order, as a corollary to Matignon’s stability theorem. They extend the previous result into conditions that are simpler to check. Then, resonance conditions are established numerically in terms of the commensurate order and the pseudo-damping factor and give interesting information on the frequency behavior of fractional systems. It is shown that elementary transfer functions of the second kind might have up to two resonant frequencies. Moreover, three abaci are given allowing to determine the pseudo-damping factor and the commensurate order for, respectively, a desired normalized gain at each resonance, a desired phase at each resonance, and a desired normalized first or second resonant frequency.     

X-ray Micro Computed Tomography investigation of accelerated thermal degradation of epoxy resin/glass microsphere syntactic foam

The heat resistance and the structural integrity of syntactic foam materials are vital for their high performance. Syntactic foam made of hollow glass microspheres and Diglycidyl Ether of Bisphenol A (DGEBA) based epoxy resin cured with Isophorone Diamine (IPD) hardener was subjected to oxidative thermal stress cycles. The degraded syntactic foam sample was examined using an X-ray Micro Computed Tomography (XμCT) to evaluate its internal damage between each state in a combined effect of cycling and increased temperature. Glass microsphere fracture, void enlargement and resin microcracks were observed as a result of the thermal stress using 3D XμCT images. The reconstructed slice representation showed the microcracks and microsphere damage distribution inside the sample. The damaged glass spheres percentage is shown to increase sharply with the progress of the thermal cycle. There was no change in the local density of the syntactic foam as a result of the thermal cycle. An XμCT system proves to be a successful non-destructive technique for examining syntactic foam for defects and structural damages in the micron scale.