This study develops an analytical framework for flexural wave propagation in stress-driven nonlocal Euler–Bernoulli beams exposed to a temperature-dependent magnetic field. The stress-driven integral model, which avoids the inconsistencies of strain-driven differential formulations on bounded domains, reduces for an unbounded beam to a gradient-elastic law with a positive length scale and therefore predicts stiffening. The magnetic field, which may be inclined to the beam axis, the elastic modulus and the thermal expansion coefficient depend on temperature, and the thermal axial force caused by restrained expansion is included. The governing equation is derived from Hamilton’s principle and non-dimensionalised, and a dispersion relation for an unbounded beam yields the phase velocity, the group velocity and the temporal decay produced by a phenomenological magnetic damping term. The thermal axial force gives rise to a cut-off wave number below which the unbounded beam is unstable; this threshold is a property of the idealised model and not a finite-beam buckling load. The temperature dependence of the magnetic field matters mainly for long waves and near this threshold, and it is appreciable only for strong fields. The apparent growth of the cut-off with slenderness is shown to result from the normalisation with the beam length, and the admissible wave-number range of the Euler–Bernoulli model is established by comparison with the local Timoshenko beam. At high wave numbers the model exhibits a cubic relation between frequency and wave number, and a critical wave number below which the damped response is aperiodic is identified. Field strengths and damping parameters are treated as parametric values, so the results offer a non-dimensional basis for parametric studies of nanoscale beam wave dynamics, not predictions for a specific device.
This study uses a double sine series to extend the deflection and introduces an innovative Airy stress function—originally developed for rectangular plates—to analyze the non-linear behaviour of rectangular membranes. The method effectively captures the coupling between deflection and in-plane forces and accommodates generalized in-plane boundary conditions, overcoming key limitations of traditional analytical approaches. The energy variational method is used to derive a system of nonlinear algebraic equations which are solved iteratively, ensuring computational robustness and rapid convergence. Compared to finite difference and finite element methods, the proposed approach yields higher accuracy in the calculation of central deflection and both central and edge stresses. It not only advances membrane theory, but also provides an accurate and practical benchmark for applications in aerospace, architecture and materials science. The error in central deflection is conservatively estimated to be below 0.12
Friction stir welding (FSW) offers a promising solid-state approach for joining dissimilar materials in lightweight structures; however, aluminum–polymer systems present substantial thermophysical mismatches that lead to asymmetric heat transfer, complex interfacial behavior, and a narrow processing window that may induce polymer degradation. This study provides a comprehensive review of thermomechanical numerical simulation in dissimilar FSW, with particular emphasis on aluminum–polymer joints, complemented by a numerical thermal investigation of an AA6061–polycarbonate (PC) lap joint. Bibliometric analysis and systematic review of Scopus-indexed papers published between 2005 and 2026 were conducted to identify research evolution, thermomechanical fundamental, modeling strategies, state of the art, and critical research gaps. To complement the review, a coupled thermal finite-element model incorporating a DFLUX heat source and GAPCON interfacial conductance was developed and evaluated against in-situ infrared thermography. The model predicted a peak weld-center temperature of 248.13 °C, corresponding to a 0.05
A novel coupled multi-physical model is developed to investigate wave propagation in semiconductor elastic media under photothermal excitation, incorporating moisture diffusivity and photoacoustic effects under two-temperature theory. The governing equations describe the interaction between five fundamental field distributions: temperature, carrier density (plasma), elastic displacement, moisture concentration, and acoustic pressure. The photoacoustic wave equation is introduced to account for thermally induced acoustic pressure generation through volumetric thermal expansion, coupling thermal transients to stress wave propagation. The problem is formulated in two-dimensional space for an isotropic homogeneous semiconductor medium. Non-dimensional variables are introduced to simplify the analysis, and the normal mode analysis method is employed to convert the coupled system into ordinary differential equations. Analytical solutions are obtained using the boundary conditions. Numerical results and computational implementation are obtained using silicon material properties. The results demonstrate the coupled propagation of thermal, mechanical, electronic, moisture, and acoustic waves with finite propagation speeds. The thermoacoustic coupling is shown to be one-way: the pressure field is generated by the thermal transient but does not feed back into the thermal, elastic, carrier or moisture balances, so the model is a four-field reciprocally coupled system augmented by a driven acoustic field rather than a fully reciprocal five-field theory. The model provides a framework for characterizing semiconductor materials under combined photothermal, photoacoustic, and hygrothermal loading conditions relevant to microelectronic device reliability and nondestructive evaluation applications. All results are reported in non-dimensional variables; the conversion to physical units for silicon is given explicitly in Sect. 6.
A nonlinear thermoelastic model is developed based on previously established thermodynamically consistent models including a nonlinear thermoelastic model with a single thermal relaxation time [1] and a thermodynamically consistent dual-phase-lag (DPL) model for a rigid thermal conductor [2]. The present work combines both approaches into a unified framework, resulting in thermodynamically consistent nonlinear thermoelasticity within DPL theory. The proposed model provides a comprehensive framework for analyzing coupled phenomena at micro-scales and in rapid transient processes, including wave propagation problems where non-Fourier heat conduction effects are significant. Numerical results are presented for a concrete problem for Silicon to demonstrate the model’s applicability.
