This paper presents a queuing system model that incorporates multiple priorities, multiple abandonments, and heterogeneous servers. Waiting for service easily leads to impatient behaviors. The impact of two kinds of impatient behaviors, balking and reneging, on queueing system performance is examined. The problem is formulated as continuous-time Markov chains. It also introduces a special state called the non-sojourn state to record the number of customers who abandon the system. The state transition rate matrix is transformed into a block tridiagonal matrix by appropriately setting the state numbers. A novel indicator called interstate transition frequency is proposed, which aids in distinguishing state transitions during the system evaluation process. Based on the interstate transition frequency, a set of indicators is derived to offer additional analytical perspectives for the queuing system. Finally, the proposed model is applied to an automobile repair shop to validate its effectiveness in practical scenarios.

In this study, to solve the problems of shock environment and shock isolation, about which there is still a lack of reasonable description, an isokinetic shock distinguishing method (ISDM), which can quantitatively distinguish between shock and forced vibration state, is presented. And the shock isolation performance of an opposed disc springs (ODS) shock isolator with pretightening under boundary friction condition is investigated. The static and dynamic stiffness properties of the ODS shock isolator are discussed. Relying on ISDM, a shock dynamic model of the ODS shock isolator with pretightening under boundary friction condition is established. The average method is adopted to solve the model theoretically. The shock acceleration ratio (SAR), shock displacement ratio (SDR), and relative displacement ratio (RDR) of the model are calculated using the numerical method and verified by experiments. Both numerical and experimental results show that ISDM is effective. And the effects on isolation efficiency of the number of disc springs, additional supporting force, pretightening force, load, and the shock velocity constant of the ODS shock isolator are discussed, which provide guidelines for its further practical application.

Accurate shock loading is required for evaluating and analyzing the shock resistance of warship equipment. However, measured shock acceleration signals contain trend term errors, which cause serious low‐frequency distortion of the shock response spectrum (SRS). We propose a combination method of fast Fourier transform (FFT) and low‐frequency oscillator for correcting the underwater shock signals. Based on the equal displacement line fitted by the measured displacement response data, the Fourier transform spectrum of the shock acceleration signal is corrected for eliminating low‐frequency errors. The results of underwater explosion tests on a floating platform indicate that the average difference between the equal displacement line and SRS in the low‐frequency band (4∼20 Hz) can be reduced from 14.7% to 3.5%, and the mid‐high‐frequency band without the trend term is nearly unaffected. The corrected SRS can faithfully reflect the actual shock environment of the warship equipment at a specific installation location of the floating shock platform.

This article presents the fire Smith method, which integrates the plate model and the Smith method, to analyze the impact of fire temperature and extent on the buckling strength of frigates. This investigation focused on the frigate’s buckling strength and how it is affected by a fire, achieved by modifying both deck temperature and area. Leveraging the principle of oxygen consumption, a coefficient “D” was introduced to account for fire temperature and region variations. This enabled the characterization of buckling strength under varying temperature and regional conditions through 64 simulations conducted on a frigate model. The outcomes revealed that the disparity between simulation results and the fire Smith method remained below 10%, establishing a solid basis for engineering assessment. As the high-temperature area decreased and necessitated less oxygen, the ultimate strength initiated a decline. However, upon reaching a certain threshold temperature, the ultimate strength stabilized. Conversely, expansive high-temperature zones caused a decline in ultimate strength, coupled with an increased oxygen requirement. Under consistent oxygen consumption conditions, the rate of ultimate strength reduction intensified. Consequently, these divergent characteristics of ultimate strength in various high-temperature areas underscored that minimizing the expansive fire high-temperature zones can significantly enhance the ship’s fire resistance, safeguarding its structural integrity.