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.
In the present work, the nonlinear responses of functionally graded beams experiencing large-amplitude vibrations under simultaneous aerodynamic excitation and rapid thermal loading are analyzed. Both thermal and mechanical material characteristics are considered to change continuously along the beam thickness. The temperature distribution is determined by solving the one-dimensional heat conduction equation in the thickness direction. The aerodynamic pressure effects are represented using the modified form of the third-order piston theory. Furthermore, the material properties are defined as functions of both the temperature field and the coordinate across the thickness, where the gradation is described by Voigt’s homogenization scheme, and the temperature dependency is introduced through the higher-order Touloukian model. To account for thickness-direction tension, the displacement field is defined using a quasi-3D theory incorporating a thickness-stretching parameter and a third-order shape function as proposed by Reddy. The strain components are then derived, including the von Kármán geometric nonlinearity. Using Hamilton’s variational principle, the motion equations are derived and expressed within a matrix formulation based on the VDQ approach, followed by spatial discretization. The temporal discretization is carried out through the implicit Newmark time-integration algorithm, enabling numerical computation of the structural response. A detailed parametric investigation is then performed to examine how primary design and environmental variables—such as flow velocity, geometric slenderness, imposed temperature field, and the material gradation index—influence the nondimensional transverse displacement of the beam.
Non-linear mechanics of elastic Bernoulli-Euler curved beams is investigated within 4-D spacetime geometric framework. Large displacements of such structures are addressed by novel rate elasticity methodology, avoiding finite deformation approaches and linearization of nonlinear kinematic relations common in literature. The variational rate virtual power principle (RVPP) is formulated and ensuing notion of effective stress rate leveraged. A rate form of nonlinear elasticity for planar curved beams is consequently established, and application of the RVPP yields the consistent elastic stiffness operator governing the structural evolution problem. Straightforward and computationally efficient incremental procedure is implemented in the brand new automatic program named REBUV. An enhanced version of the Riks-Crisfield arc-length method is developed by exploiting the derived expression of the stiffness operator and is successfully applied to the investigated highly nonlinear benchmark problems. Comparison with analytical finite deformation approaches and established computational methods is carried out, supporting effectiveness of the presented approach. This paper provides significant extension to curved beams of a methodology proved capable of solving problems and limitations affecting conventional analytical and computational approaches.
An internal thermo-elasticity is introduced in the continualized model for mass-in-mass metamaterial in the continualized equation for attached masses. This thermo-elasticity alters the strain wave behavior more significantly than that introduced previously in the continualized equation for the masses of the main chain. The main result is that the band gap is not described by the dispersion analysis. Immediate disappearance of the band gap at non-zero internal thermo-elasticity is not observed in numerical simulations of the boundary harmonic excitation of the waves. It is obtained an approximated dispersion equation for small internal thermo-elasticity which accounts for gradual disappearance of the band gap. Another result concerns arising of two-mode wave due to internal thermo-elasticity for excitation frequencies above the band gap. It is shown, that this analytical solution is realized in numerical boundary excitation of the strain waves.
