Using sulfuric acid as the sulfating agent, two catalyst series were obtained from hydroxide and nitrate precursor with a sulfate loading identical to commercial sulfated hydroxide, i.e., 4.2 mass %. After calcination at 500, 600 and 700 °C, all nine samples had various contents of residual sulfates depending on the origin of the catalyst. Accordingly, their surface properties were different, which, together with various textural properties, govern the formation of the active phase and their catalytic activity in the n-hexane isomerization reaction. The dominant activity and yield of mainly mono-branched isomers were attained in reaction at 200 °C with a commercially sulfated zirconia catalyst calcined at 500 °C. Among the SZ catalyst series synthesized from hydroxide and nitrate, the second according to its activity profile was similar to that of the commercially sulfated one, while samples originating from hydroxide showed some activity only after calcination at 600 °C. This is due to the poorer textural properties of the hydroxide series, necessitating a higher calcination temperature in order to promote the simultaneous decomposition of S-containing species and their re-adsorption into the zirconia matrix following interaction and active phase formation. It seems that the tetragonal zirconia phase was not responsible for the catalytic activity but a synergistic effect of the textural properties of the samples and the sulfate loadings, which determine different acid strengths on the catalyst surface.
This paper presents a new approach to the problem of determining the frequencies and mode shapes of Euler-Bernoulli tapered cantilever beams with a tip mass and a spring at the free end. The approach is based on the replacement of the flexible beam by a rigid multibody system. Beams with constant thickness and exponentially and linearly tapered width, as well as double-tapered cantilever beams are considered. The influence of the tip mass, stiffness of the spring, and taper on the frequencies of the free transverse vibrations of tapered cantilever beams are examined. Numerical examples with results confirming the convergence and accuracy of the approach are given.
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