Fractional and memory effects on wave reflection in pre-stressed microstructured solids with dual porosity

Abstract

The present work investigates the influence of fractional-order derivative and memory-dependent derivative on the behavior of various waves reflected at the free surface of a size-dependent, pre-stressed, microstructured thermoelastic solid with a dual porosity framework. A generalized Moore–Gibson–Thomson (MGT) model, incorporating higher-order terms and memory effects, is adopted to describe the complex heat transfer behavior within the material. A nonlocal framework based on Eringen’s theory is utilized to derive the basic relations of the considered medium. An examination of the non-dimensionalized governing equations is conducted employing the normal mode technique to provide accurate solutions. The research demonstrates the presence of six separate wave modes that travel at varying speeds within the medium. The energy and amplitude ratios of reflected waves are determined by applying suitable boundary conditions. The influence of varying incidence angles on the reflected wave energy distribution is investigated numerically and visualized using MATLAB software. The study reveals that the energy ratios of the reflected waves are sensitive to the fractional-order parameter, kernel functions, initial stress, and nonlocality parameter. The analysis suggests a conservative reflection process, indicating minimal energy loss during reflection. Key findings and their implications for relevant scenarios are presented in the conclusion. Comparisons with existing models for certain cases demonstrate good agreement, supporting the validity of the present model.