Study on the Sensitivity of Decaying Wave Propagating Through a Medium with No Surface Traction

Abstract— This study presents a comprehensive analysis of the sensitivity of decaying Rayleigh waves propagating through semiconductor elastic solids within the framework of generalized thermoelasticity. The medium is modeled as a half-space semiconductor rotating at a constant angular frequency, and the effects of key thermoelastic and rotational parameters on wave propagation are investigated. A fractional-order three-phase lag (3PL) heat conduction model is employed, incorporating higher-order time derivatives to capture coupled thermoelastic behavior. The secular equation for Rayleigh waves is derived analytically, and normalized local sensitivity analysis (NLSA) is applied to quantify the influence of input parameters including rotation \(\left( \Omega \right)\), fractional order \(\left( \alpha \right)\), and phase lags on wave properties. Silicon is used as a representative material, with all computations carried out in MATLAB. Results show that increases in Ω and α lead to higher phase velocity and penetration depth, while reducing attenuation and specific heat loss. Sensitivity rankings reveal that Ω and α are the most influential parameters, while \({{\tau }_{v}}\) and \({{\tau }_{T}}\) have negligible effects, making them suitable for factor fixing. This is the first study to couple fractional-order 3PL thermoelasticity with rotational effects in semiconductors while employing NLSA for parameter ranking, revealing up to 22% attenuation reduction at high rotation rates consistent with SAW gyroscope experiments. This work provides novel insight by integrating fractional-order 3PL thermoelastic modeling with NLSA in a rotating semiconductor context, offering valuable guidance for the design of surface-wave-based sensing and optoelectronic devices.