Mode jumping in the buckling of struts and plates: a comparative study

A detailed investigation of the phenomenon of mode jumping in compressed struts on stiffening foundations and elastic plates of varying lengths is performed, with emphasis on the effects of altering boundary conditions. The variety of possible modal interactions is presented in a concise form using the parameter space of Arnol'd tongues, borrowed from non-linear dynamical systems theory. For the strut system, a full range of end conditions from simply supported to clamped is examined. For the plate, simply supported and clamped flexural conditions along both long (unloaded) and short (loaded) edges are considered, together with in-plane conditions ranging from free to pull in, to fully restrained. For each system, simply supported end conditions are found to provide protection against early mode jumping in a so-called “safety envelope”, but this is eroded as the end conditions are systematically altered from simply supported to clamped. For the plate system, mode jumping is induced at an earlier stage in the loading process by restricting the long (unloaded) edges against in-plane movement, but is delayed by clamping the same edges against rotation.     

Observation of the aggregation behavior of silica sols using laser speckle contrast measurements

We report on a new optical method to observe the onset of aggregation in alcoholic tetraethoxysilane (TEOS) sols using laser speckle contrast measurements. The contrast in a speckle image produced by coherent light provides information about the internal contrast of the medium being studied. For silica sols, changing the amount of acid or base catalyst was the most important factor in determining the aggregation behavior of the sol. We investigated this effect by varying the TEOS/base ratio by a factor of 6. This shifted the onset of aggregation as determined by speckle contrast from 46% of the gel time for the lowest amount of base to 74% for the highest. Conversely, varying TEOS/acid ratio by a factor of 3, shifted the onset of aggregation from 74% of the gel time for the lowest amount of acid to 64% for the highest. Measurements of this type provide information that can be used to test models of sol aggregation and gel formation.     

A binuclear rhodium(I) complex with two tetraphosphine ligands at 100 K

Bis(μ‐3,11‐diethyl‐6,8‐di­phenyl‐3,6,8,11‐tetraphosphatri­dec­ane‐κ⁴P³,P⁶:P⁸,P¹¹)­dirhodium(I) bis­(tetra­fluoro­borate), [Rh₂(C₂₅H₄₀P₄)₂](BF₄)₂, is a bimetallic complex containing two binucleating tetra‐tertiary phosphine ligands. The distance between the metal centers is 5.4555 (11) Å, with no metal–metal bond. The Rh—P bond distances range from 2.2483 (14) to 2.3295 (14) Å. The geometry about the Rh^I atoms is tetrahedrally distorted square planar and the dihedral angle between the two coordination planes is 66.28 (5)°.