Dispersion and Attenuation Characteristics of Flexural Wave Propagation in Double Porosity Thermoelastic Kirchhoff Plates

Abstract

This study investigates the effects of double porosity structure and thermoelastic coupling on wave propagation in plate structures. A Kirchhoff thin‑plate model incorporating double porosity and thermoelasticity is developed for flexural wave analysis. By introducing two pore‑volume‑fraction fields and a temperature field, the governing equations are derived to account for the multi‑field coupling among thermal, elastic, and double porosity responses. Using harmonic wave solutions, a characteristic equation describing the frequency‑dependent dispersion of flexural waves is obtained, which takes the form of a tenth‑degree polynomial in the complex wavenumber, thereby elucidating the mechanisms of wave dispersion and attenuation. Theoretical analysis demonstrates that, compared with classical elastic plates and single‑phase thermoelastic plates, the multi‑field coupling in double porosity thermoelastic plates excites a greater number of wave modes. Five distinct modes are identified: the first is a macropore‑dominated pore wave; the second is a micropore‑dominated pore wave. Both pore‑wave modes exhibit cut‑off frequencies beyond which pronounced dispersion occurs. The third mode is a thermally coupled wave, whose dispersion and attenuation are comparable and intensify simultaneously with increasing frequency. The remaining two modes correspond to a coupled flexural traveling wave and a flexural standing wave. Although their variation trends generally align with those in classical thin plates, their phase speeds are lower than the classical predictions due to the combined effects of porosity and thermoelastic coupling. This work provides a theoretical basis for understanding wave propagation in porous thermoelastic plate‑like structures.