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Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations and subject to axial loads. The elastic layer connecting the beams are modelled as a three-parameter nonlinear Winkler–Pasternak layer with the Winkler layer having linear and nonlinear components and Pasternak layer having only a linear component. Variational principles are derived for the forced and freely vibrating double beam system using a semi-inverse approach. Hamilton’s principle for the system is given and the Rayleigh quotients are derived for the vibration frequency of the freely vibrating system and for the buckling load. Natural and geometric variationally consistent boundary conditions are derived which leads to a set of coupled boundary conditions due to the presence of Pasternak layer connecting the beams.

The present experimental study assesses the mechanical properties of glass/carbon/glass hybrid composite laminates after being exposed to moisture in a deep freezer and elevated temperatures for extended periods. The top and bottom layers of the hybrid laminates are reinforced with glass fibre, and the middle layer is reinforced with carbon fibre using the epoxy matrix as a binder polymer material. The hybrid laminates were manufactured using the resin transfer moulding method, and their compressive and tensile properties were determined using a tensile testing machine. The storage modulus, loss modulus, and damping factors of all groups of laminates were identified using a dynamic mechanical analysis as a function of temperature and vibration frequency. The experimental results on compressive and tensile properties revealed slight variations when the hybrid laminates were kept at low temperatures in a deep freezer for extended periods. This might occur due to the increasing molecular crosslinking of the polymer network. As the testing temperature increased, compressive, tensile, storage modules, loss modulus, and damping factors decreased. This might occur due to the increasing mobility of the binder material. Particularly, the highest stiffness parameters were obtained at −80 °C/GCG (glass/carbon/glass) laminates due to the presence of a beta transition in the glassy region. The relationships between the glass transitions and the targeted frequencies were characterized. The values of the glass transition shift towards higher temperatures as the frequency increases. This might occur due to a reduction in the gaps between the crosslinking of the epoxy network when the frequency increases. The accuracy of the storage modulus results was compared with the empirical models. The model based on the Arrhenius law provided the closest correlation. Meanwhile, another model was observed that was not accurate enough to predict when gamma and beta relaxations occur in a glassy state. [ABSTRACT FROM AUTHOR]

This study uses the optimal (custom) design to focus on the supermasscolloider wet milling process for synthesizing calcium carbonate nanoparticles from the Achatina Fulica using the optimal (custom) design. The snail shell particle size of 150 μm from dry milling was wet milled to get smaller particle sizes. The response surface design method was used to investigate the effect of independent parameters such as consistency (amount of microparticle loading in calcium carbonate suspension) and the number of runs on the particle size of calcium carbonate produced using a supermasscolloider. Results show that the microparticle loading in calcium carbonate suspension and the number of runs significantly affected the synthesized particles. The increase in microparticle loading reduced the effectiveness of the supermasscolloider blade, resulting in the production of particle sizes ranging from 21- to 40 nm. A higher number of runs with a smaller loading of microparticles in calcium carbonate suspension offered a fine particle size of 21.30 nm. The experimental data quartic polynomial models gave a coefficient of determination (R2) of 0.92. The optimum milling runs of 750 and 1% consistency microparticle loading produced a calcium carbonate nanoparticle size of 21 nm. This technique has shown that calcium carbonate nanoparticles can be produced at low cost, at less period, with low agglomeration from Achatina Fulica shell using supermasscolloider. [ABSTRACT FROM AUTHOR]