Nano-silica can stiffen cementitious composites, but its benefit depends on how well the nanoparticles are dispersed, and agglomeration is common in the alkaline pore solution of cement paste. This study presents an analytical framework for the free vibration of SiO2 nanoparticle-reinforced concrete beams resting on a Winkler–Pasternak elastic foundation, with nanoparticle agglomeration explicitly incorporated into the effective properties. Agglomeration is described by two parameters: the volume fraction of nanoparticle-rich inclusions, ξ, and the fraction of nanoparticles located within them, ζ. These parameters enter a two-stage homogenization scheme that combines a Voigt–Reuss estimate for each region with Paul’s model for the composite, and their admissible range is derived from the volume-fraction constraints. The resulting properties are embedded in a three-unknown higher-order shear deformation theory that satisfies the traction-free surface conditions without a shear correction factor. The governing equations are derived from Hamilton’s principle and solved analytically for simply supported, clamped–clamped and clamped–simply supported beams. The beam formulation agrees with published benchmarks for functionally graded beams to within 0.03% without a foundation and 0.6% on a Winkler–Pasternak foundation. For a fixed matrix and hydration state, increasing the SiO2 volume fraction from 0 to 0.20 raises the fundamental frequency by about 14% for all three boundary conditions. This gain comes almost entirely from stiffening, since the change in density contributes less than 1%. When half of the nano-silica is agglomerated and does not contribute to load transfer, this gain falls to about 8%, so roughly half of the dynamic benefit is lost. Over the investigated range of dimensionless foundation stiffness, the Pasternak parameter raises the frequency more than the Winkler parameter, and clamped–clamped beams give the highest frequencies, followed by clamped–simply supported and simply supported beams. The framework links dispersion quality, boundary restraint and foundation support to the dynamic response of nano-engineered concrete members.
To meet the requirements for a long buffering stroke and a stable load response within a limited installation space, this study investigates a guide-wheel-constrained plate-flow energy absorber (GPEA) that dissipates impact energy through repeated bending–straightening deformation of a steel plate. Quasi-static compression and drop-hammer impact tests were conducted. Under the investigated loading conditions, the experimental results showed that the No. 20 carbon-steel plate underwent stable and continuous bending–straightening deformation under the constraint of the guide wheels without fracture. After entering the stable deformation stage, the quasi-static load remained at approximately 9.3 kN, while the plateau force under impact loading was about 10 kN, with an effective crushing stroke of 145.5 mm. On this basis, a finite element model was established, and the predicted deformation mode and stable load response showed good agreement with the experimental results. Furthermore, an elastic–plastic bending model incorporating linear material hardening was developed to quantitatively describe the through-thickness stress–strain evolution, energy absorption, and mean force of the steel plate. For idealized frictionless single-cycle cases with plate thicknesses of 2 mm and 5 mm, the differences between the theoretical predictions and numerical results were 3.6% and 4.3%, respectively. The proposed theoretical model, derived from the elastic–plastic bending and straightening process, reveals the underlying mechanism of plastic deformation accumulation and continuous energy dissipation during repeated changes in plate curvature.
In plateau constant-pressure barracks, indoor pressure is maintained above outdoor pressure, placing window seals under a sustained pressure differential after installation pre-compression. This study develops a two-dimensional nonlinear contact model of a hollow D-shaped silicone rubber sealing strip, a pressure bead, and a mounting groove using the fluid pressure penetration method. A sequential pre-compression and pressure-differential loading procedure was applied to investigate the effects of fluid pressures of 5, 15 and 25 kPa and compression ratios (CRs) of 10%, 15%, 20% and 25% on contact behavior, while additional stress analyses were conducted at compression ratios of 10%, 20%, and 30%. Most investigated cases exhibit an asymmetric double-peak contact-pressure distribution, with a lower-pressure region between the two peaks, with lower pressure in the central region and higher peaks on both sides. Increasing fluid pressure redistributes the contact load toward the low-pressure side, whereas increasing compression strengthens interfacial constraint and reduces the sensitivity of the contact state to pressure variations. At a compression ratio of 25%, the contact-pressure curves under different fluid pressures show high consistency and stable peak positions. Within the investigated conditions, CR = 25% is recommended as a numerical reference for the representative straight section because of its favorable contact length and reduced peak-pressure sensitivity to a pressure differential. This recommendation concerns numerical contact characteristics and does not establish optimum airtightness or a minimum leakage rate.
The production of sustainable polymer-based composites from agricultural waste has gained great attention due to the growing demand for lighter and stronger materials. In this study, alkali-treated CLSF (30 wt.%) was used as reinforcement in vinyl ester composites containing 0, 5, 10 and 15 wt.% cashew nutshell biochar, fabricated by hand lay-up followed by compression molding. The effect of biochar content on the tensile strength, flexural strength, impact strength, Shore D hardness, erosion resistance and microstructure of the vinyl ester composites was systematically evaluated by mechanical testing, erosion testing, scanning electron microscopy (SEM) and X-Ray Diffraction (XRD). Biochar inclusion remarkably enhanced the properties of the composites when compared to the unfilled composite, depending on the optimum filler content. The composite containing 10 wt.% biochar showed the best flexural strength (31.88 MPa) and Shore D hardness (83.22), coupled with minimum erosion loss (0.021%), hence high stiffness and abrasion resistance. However, 5 wt.% biochar showed the best impact resistance, indicating effective energy absorption ability. SEM study showed enhanced filler distribution and fiber–matrix interface interaction for lower levels of biochar content, but higher amounts (15 wt.%) caused agglomeration of particles with the appearance of microvoids, resulting in reduced mechanical properties. X-ray diffraction showed that biochar addition leads to better structural ordering. In general, the obtained results clearly show that using 5–10 wt.% of cashew nutshell biochar increases multifunctional properties of coconut sheath fiber/vinyl ester composites.
This paper presents a combined theoretical and experimental methodology for analysing and validating mechanical error propagation in optical rotary encoders. A vector-based mathematical model is experimentally verified using a three-stage methodology comprising measurement of shaft centre motion, grating disc motion and encoder angular error. Independent measurements of the individual mechanical error sources are combined to predict the encoder angular error and compared with traceable angular comparator measurements. The proposed methodology achieved correlation coefficients up to 0.984 for two different grating disc mounting conditions, demonstrating good agreement between the predicted and measured angular error profiles. The results confirm that encoder angular error is governed by the combined contribution of multiple mechanical error sources and demonstrate that, once the dominant eccentricity component is minimised, optimisation of the circumferential optical readhead position provides an effective means of reducing the residual angular error. The proposed methodology provides a practical framework for analysing, predicting and optimising mechanical error sources during the design, assembly and calibration of high-accuracy optical rotary encoders.
