The vibration of porous Al–Al₂O₃ micro-cantilever sandwich beams in fluids was studied utilizing the modified couple stress theory and the scale distribution theory (MCST and SDT). Four types of porosity distributions were defined; the uniform distribution of pores was defined as U-type, while O-type, V-type and X-type represented non-uniform distributions of pores. The material properties of different porous sandwich beams were calculated. The properties of the micro-cantilever sandwich beams were adjusted to account for scale effects according to MCST. With the fluid driving force taken into consideration, the amplitude-frequency response, and resonant frequencies of the FGM sandwich beams in three different fluids were calculated using the Euler–Bernoulli beam theory. The computational studies showed that the presence of gradient factor p and the pores in the micro-cantilever sandwich beams affect the temperature field distribution and amplitude-frequency response in fluids. Increasing gradient factor p leads to a more obvious thermal concentration of the one-dimensional temperature field and migrates the resonance peaks to lower frequencies. In contrast to the uniform distribution type, the non-uniformly distributed pores also cause a decrease in the resonance frequency.

As application conditions become increasingly demanding and usage becomes more aggressive, the performance of traditional insulated gate bipolar transistor (IGBT) and fast recovery diode (FRD) systems can no longer meet the required specifications. In these systems, FRDs are required to carry load current and allow current to return from the load to the IGBTs. Consequently, the reverse recovery performance of the FRDs significantly restricts the overall efficiency of the system. Therefore, how to predict the reverse recovery characteristics of the FRDs with greater precision has attracted considerable attention. In this context, this paper presents an in-depth investigation of the high-level injection carrier distribution and reverse recovery characteristics of punchthrough P-I-N (PT-PIN) FRD with a buffer layer. Specifically, the research explores the physical properties of the materials, doping concentrations, and the geometric structure of the devices. Furthermore, it takes into account the complex interactions among carrier recombination, diffusion, and drift, leading to the development of a model that delineates the spatial distribution of carriers and their influence on current conduction. Building upon the traditional step-wise analysis method, subsequently, the temporal aspects of the FRDs reverse recovery process were further segmented. Utilizing the derived carrier distribution model, a reverse recovery analytical model was constructed. The model was validated using a 1200 V, 100 A IGBT with 1200 V, 60 A FRD configured in a reverse parallel arrangement, which demonstrated a 5% improvement in prediction accuracy of V_R compared with previous models that employed the lumped charge method. Finally, a range of experiments with varying R_G, V_CC and I_F confirmed the broad applicability of this analytical model.