R. Nawaz

In this study, the vibrational behavior of Rayleigh and shear beams placed over the Hetényi and Pasternak foundations is investigated, with special attention paid to the effects of axial stresses (both tensile and compressive). The uniqueness of the work comes from the thorough consideration of how axial forces, shear deformation, rotational inertia, and foundation factors affect the eigenfrequencies and eigenmodes that control beam vibrations. Eigenfrequencies and eigenmodes are determined through computational analyses with the Galerkin finite element method (GFEM) employing quadratic and cubic polynomials. Comparisons between finite element results and analytical outcomes, both in generalized and specialized contexts, serve to demonstrate the correctness and effectiveness of the approximate solution. The study shows that the Hetényi foundation's influence on eigenfrequency depends on foundation stiffness and relative beam magnitudes, and that shear deformation affects eigenfrequencies more than rotary inertia does. Higher frequencies are largely unaffected by compressive and tensile stresses, but the fundamental frequency is rigorously influenced. Further demonstrating its accuracy, the finite element approach shows great agreement in forecasting eigenmodes and eigenfrequencies. A variety of real‐world situations involving elastically confined beams resting on elastic foundations and being subjected to axial forces are the focus of the study. Axial forces commonly result from external loads, thermal expansion, or structural interactions in real‐world settings. Therefore, it is crucial to understand how they affect beam vibration when designing structures that can endure expected stresses and vibrations while maintaining safety and performance criteria.

Peristalsis of non-Newtonian nanofluid via a non-uniform conduit has several applications in physiology and industry. This study proposes a mathematical model as well as exploration of the impacts of entropy generation for peristalsis of magneto nanofluid with temperature-dependent thermal conductivity via an expanding asymmetric channel. Buongiorno’s model for study of nanofluid flow has been adopted. Rheological aspects are accounted using the Carreau–Yasuda model due to its experimentally validated significance. Impacts of applied electric and magnetic fields have been taken into account. Thermophoresis, ohmic heating, viscous heating and Brownian motion effects are incorporated in the model. Numerical method is used via NDSolve in Mathematica after implementing the lubrication approach and Debye–Huckel linearization. The effects of embedded parameters on the flow, heat transfer, entropy generation and Bejan number are studied using graphical depictions. Outcomes indicate that a rise in electroosmotic parameter enhances heat transfer rate, whereas it reduces entropy generation and mass transfer rate at the boundary. Therefore, this study can provide basics to study nanofluidic systems which has applications in drug delivery. Increasing trends for temperature, heat transfer rate and entropy generation, while declining trends in the concentration of the particles are noted for higher joule heating.