To address critical challenges in coal seam gas drainage—specifically low permeability and the inherent limitations of single-frequency ultrasonic fracturing, such as rapid energy attenuation and restricted effective range—this study investigates the potential of a novel dual-frequency approach. Using a custom-designed dual-frequency ultrasonic fracturing system, we investigated the impact of frequency coupling on meso-structural damage, macroscopic mechanical behavior, and energy evolution in coal. Uniaxial compression tests synchronized with acoustic emission (AE) monitoring were employed to analyze fracture network propagation, AE characteristics, strength degradation, and elastic energy dissipation under varying frequency coupling fields. Results demonstrate that the frequency coupling effect of dual-frequency ultrasound significantly surpasses single-frequency stimulation. Fracturing efficiency is intrinsically dependent on the frequency ratio (η), with optimal coupling performance observed within the range of η in (1.5, 2.0). Within this optimal interval, the total surface fracture length increased by 23.45% (from 67.8 mm in the control group to 83.7 mm in the dual-frequency group), driving a morphological transition from singular cracks to complex fractal network structures. Mechanical testing revealed a sharp deterioration in compressive strength as η increased, culminating in a maximum strength reduction of 87.2%. Furthermore, energy evolution analysis identified an “energy pre-dissipation” mechanism. Following dual-frequency treatment, the total input energy required for failure decreased by 82.99% (from 0.00876 MJ·m^-3 to 0.00149 MJ·m^-3), while the peak elastic strain energy dropped by 84.44% (from 0.00707 MJ·m^-3 to 0.00110 MJ·m^-3). This confirms that dual-frequency fractured coal undergoes brittle instability with minimal mechanical work input. Finally, a non-linear damage constitutive model incorporating frequency coupling effects was developed based on the Weibull distribution. Innovatively, this model integrates a fracture fractal dimension parameter to quantify initial damage and AE cumulative ring counts to characterize evolutionary damage. The model achieves high predictive accuracy, with a maximum error of only 6.06% compared to experimental data, effectively capturing the mechanical response of dual-frequency fractured coal.

Silica aerogels are critical for thermal protection in extreme environments; however, their mechanical response mechanisms under high temperatures remain elusive. This study employs large-scale molecular dynamics simulations to systematically investigate the mechanical behavior of silica aerogels (0.43–0.71 g/cm³) across a temperature range of 298–1800 K. The results reveal a fundamental competition between thermal softening and sintering-induced strengthening. Under tensile loading, the thermal softening effect dominates, leading to a significant fracture strength reduction of up to 49.6% at 1800 K, while simultaneously enhancing ductility, extending fracture strain to 80%. Conversely, under compressive loading, the sintering effect induced by temperatures above 900 K outweighs softening, resulting in a ~20% increase in the elastic modulus for high-density samples at 1300 K. Microstructural analysis attributes this enhancement to the preferential collapse of large pores and densification into an atomic-scale micropore range (0.5–1.0 nm). This work elucidates how the interplay between softening and sintering dictates material failure or strengthening, providing a microscopic theoretical basis for designing thermal shock-resistant materials for new energy batteries.

The dual challenge of ensuring operational safety and enhancing the efficiency of coalbed methane (CBM) extraction is paramount in deep mining. While cyclic disturbances from mining activities are known to affect coal seam integrity and gas seepage, the underlying damage-permeability coupling mechanism remains poorly quantified, lacking a universal predictive model that transcends specific loading conditions. Here, we systematically investigate the mechanical degradation and permeability evolution of gas-containing coal under a range of cyclic loading frequencies, amplitudes, axial stresses, and gas pressures using an advanced dynamic-static triaxial testing system. A pivotal discovery was made: regardless of the external loading path, the evolution of coal permeability is fundamentally governed by a single, unified internal state variable, the cumulative damage factor (D), quantified via energy dissipation. Based on this, we establish for the first time a universal quantitative model that directly links the damage factor (D) to the permeability ratio, unifying the effects of disparate mechanical disturbances on seepage behavior. This work not in a more precise theoretical framework for forecasting gas outburst hazards but, crucially, provides critical scientific guidance and a quantitative tool for emerging energy technologies like Enhanced CBM (ECBM) recovery via controlled mechanical stimulation.