Complex Engineering Research Articles

Tactical flight optimizer: a novel optimization technique tested on mathematical, mechanical, and structural optimization problems

Abstract The current study presents a novel gradient-free metaheuristic search algorithm named Tactical Flight Optimizer (TFO), tailored to meet the growing need for high-performance optimization techniques in solving complex engineering and mathematical problems. The main contribution of this study is the development of a method that simulates tactical air combat formations, offering a sophisticated alternative to conventional search algorithms. In the proposed method, the location of each agent is updated based on a resultant vector derived from three updating vectors. The updating vectors incorporate total information stored by the agents in each iteration. Consequently, the navigation process is guided by a more logical mechanism rather than a simple random process. The search performance of the TFO is initially benchmarked by solving a set of constrained mathematical functions. Subsequently, it is evaluated by addressing a suite of constrained mechanical and structural problems, containing both discrete and continuous decision variables. The obtained results are compared with five other well-stablished metaheuristic techniques. Acquired numerical results indicate that the TFO algorithm can provide promising results in solving both mathematical and engineering problems in terms of computational cost, accuracy, and stability.

Development of robust constitutive synthetic promoter using genetic resources of plant pararetroviruses

With the advancement of plant synthetic biology, complex genetic engineering circuits are being developed, which require more diverse genetic regulatory elements (promoters) to operate. Constitutive promoters are widely used for such gene engineering projects, but the list of strong, constitutive plant promoters with strength surpassing the widely used promoter, the CaMV35S, is limited. In this work, we attempted to increase the constitutive promoter library by developing efficient synthetic promoters suitable for high-level gene expression. To do that, we selected three strong pararetroviral-based promoters from Mirabilis mosaic virus (MMV), Figwort mosaic virus (FMV), and Horseradish latent virus (HRLV) and rationally designed and combined their promoter elements. We then tested the newly developed promoters in Nicotiana benthamiana and found a highly active tri-hybrid promoter, MuasFuasH17 (MFH17). We further used these promoter elements in generating random mutant promoters by DNA shuffling techniques in an attempt to change/improve the MFH17 promoter. We further evaluated the activity of the MFH17 promoter in Oryza sativa seedlings and studied the effect of as-1 elements present in it. Finally, we tested the efficacy and tissue specificity of the MFH17 promoter in planta by developing transgenic Nicotiana tabacum and Arabidopsis thaliana plants and found it highly constitutive and efficient in driving the gene throughout the plant tissues. Overall, we conclude that this tripartite synthetic promoter MFH17 is a strong, highly constitutive, and dual-species (dicot and monocot) expressing promoter, which can be a valuable addition to the constitutive plant promoter library for plant synthetic biology.

Dynamic stiffness formulation for the vibration response of functionally graded nanoplates considering the neutral surface position with microstructural defects

In the present paper, the dynamic stiffness matrix of a functionally graded nanoplate (FG-nP) has been developed and used to carry out a vibration analysis. The nonlocal elasticity theory in conjunction with classical plate theory (CPT) has been used to drive the governing equations of motion using Hamilton’s principle. The nonlocal elasticity theory incorporates the length scale parameter, which can withhold the small-scale effect that is necessary for model FG-nP. The pioneer Wittrick–Williams algorithm is employed to evaluate the dynamic stiffness matrix. The property of the FG-nP has been calculated using the power law. The authenticity and efficacy of the present formulation have been ascertained using various validation studies. The accurate prediction of the effect of porosity inclusions on different volume fraction indexes, boundary conditions, and higher vibration modes has been reported. The influence of the nonlocal parameter, boundary conditions, various gradation techniques, and geometric parameters on vibration behavior has been extensively explored. The results show the versatility of the proposed approach in addressing small scaled complex engineering structures. This research significantly contributes to the understanding and analysis of functionally graded nanoplates, providing valuable insights for applications in aerospace, structural systems, sensors, actuators, and energy harvesting devices.

Study on the vibration characteristics and influence range of buried dam pipeline

To alleviate water resource shortages and tensions and meet the water diversion needs of different river basins, buried (cross-dam) pipelines have become an essential component of water diversion projects. They are installed in levee projects in key river basins such as the Yellow River, Jingjiang River, and Beijiang River. Due to the complex engineering structure and multiple sources of vibration excitation, if vibrations propagate along the pipeline axis towards the surrounding levee, they could have an adverse impact on the stability and safe operation of the levee. To accurately identify the vibration and transmission characteristics of the buried pipeline dikes, determine its primary vibration sources, and clarify the propagation laws of pipeline vibrations within the levee, this study, based on prototype observation data and utilizing signal fusion processing technology, investigates the inherent vibration characteristics of the buried pipeline dikes from the perspectives of excitation, transmission, and response. At the same time, by introducing the “finite element-infinite element” theory, a coupled finite element-infinite element model is established for the pipeline, levee, anchor piers, support piers, foundation, and infinite half-space. This model is then used to analyze the site response induced by flow-induced vibration in buried pipeline levee structures. The results show that the primary vibration frequencies of the buried pipeline dike structure are the unit rotation frequency of 74.4 Hz and the blade vibration frequency of 24.8 Hz. These vibration sources originate from the pump unit and propagate outward along the pipeline axis. Using the transmission range of the vibration source as the basis for determining the vibration impact range, it was established that the horizontal vibration impact of the buried pipeline extends 10 m on either side of the pipeline axis, while the vertical vibration impact extends 7.5 m below the dike crest.

Assessment of Peak Particle Velocity of Blast Vibration using Hybrid Soft Computing Approaches

Abstract Blasting vibration is a major adverse effect in rock blasting excavation, and accurately predicting its peak particle velocity (PPV) is vital for ensuring engineering safety and risk management. This study proposes an innovative IHO-VMD-CatBoost model that integrates variational mode decomposition (VMD) and the CatBoost algorithm, with hyperparameters globally optimized using the improved hippocampus optimization algorithm (IHO). Compared to existing models, the proposed method improves feature extraction from vibration signals and significantly enhances prediction accuracy, especially in complex geological conditions. Using measured data from open-pit mine blasting, the model extracts key features such as maximum section charge, total charge, and horizontal distance, achieving superior performance compared to 13 traditional models. It reports a root mean square error of 0.28 cm/s, a mean absolute error of 0.17 cm/s, an index of agreement of 0.993, and a variance accounted for value of 97.28%, demonstrating superior prediction accuracy, a high degree of fit with observed data, and overall robustness in PPV prediction. Additionally, analyses based on the SHapley Additive Explanations framework provide insights into the complex nonlinear relationships between factors like horizontal distance and maximum section charge, improving the model's interpretability. The model demonstrates robustness, stability, and applicability in various tests, confirming its reliability in complex engineering scenarios, and offering a valuable solution for safe mining and optimized blasting design.

A novel multi-sensor data fusion enabled health indicator construction and remaining useful life prediction of aero-engine

Remaining useful life (RUL) prediction is vital to formulate a suitable maintenance strategy in manufacturing systems health management. Multisensor data fusion of complex engineering systems has attracted substantial attention due to the fact that a single sensor can only collect partial information. Health indicator (HI) construction plays a crucial role in multisensor data fusion and machinery prognostic, mainly because it attempts to quantify a history and ongoing degradation process by fusing the advantages of multiple sensors. However, large numbers of coefficients are involved for most of the existing HIs. Additionally, simplifications during modeling may inhibit the wide application of the constructed HI. To address these two challenges, a new multisensor data fusion method is proposed in this paper by constructing a HI for the characterization of the degradation process. Firstly, the sensors that collect invalid data or conflicting data are removed through a correlation coefficient operation. Then, principal component analysis (PCA) is adopted to reduce the number of coefficient before constructing the HI. Furthermore, the objective function is constructed under the comprehensive consideration of the three factors of the HI, that is, monotonicity, trendability, and fitting errors. The effectiveness of the proposed method is verified using the C-MAPSS dataset. Multiple comparison results show that the HI possesses excellent performance in both degradation characterization and remaining useful life prediction.

The Analysis of Applications of Microcomputers in Information Engineering: From Automatic Control Electromechanical Systems to LSI Circuit Design

This paper explores the significant developments in computer technology within the field of information engineering, with a particular focus on the applications of microcomputers. The research delves into two key areas: automatic control electromechanical systems and large-scale integrated circuits (LSI). In recent years, the integration of microcomputers in these systems has transformed the way data is processed, improving system efficiency and precision. The literature review identifies advancements in microcomputer-based control systems, which enhance real-time responsiveness and system stability, alongside innovations in circuit design that contribute to higher integration density and reduced power consumption. Case studies further highlight practical applications in industrial automation and GPS receiver design, demonstrating how microcomputers optimize both functionality and energy efficiency. By synthesizing these findings, this paper underscores the critical role of microcomputers in advancing modern information engineering and offers recommendations for future research, especially in areas where artificial intelligence and edge computing are integrated into next-generation systems. This study contributes to the understanding of how microcomputers enhance technological efficiency and drive innovation in complex engineering environments

Alternative Assessment for Enhancing Complex Problem-Solving Skills in Mechanical System Design Course

Traditional assessment methods in engineering education, such as exam-based evaluations, often fail to adequately measure complex problem-solving skills and practical application of knowledge, necessitating the exploration of innovative assessment approaches. This paper introduces the Constructive-Teamwork-Experiential-Presentation (CTEP), an alternative assessment approach applied in the Mechanical System Design course (ENT348) for undergraduate mechanical engineering students. The CTEP model is tailored to enhance complex problem-solving (CPS) abilities and engage students in complex engineering activities (CEA). It aligns with the 2020 standards of the Engineering Accreditation Council (EAC) and the Malaysian Qualifications Framework (MQF) 2.0, specifically addressing Programme Outcomes (PO) 3 (Design) and PO10 (Communication). Over four academic terms, this model incorporated interactive design tasks, collaborative teamwork, simulation exercises, and student presentations. The findings indicate notable improvements in achieving PO3 and PO10, with average attainment rates rising to 80% and 78%, respectively. Beyond academic achievements, the model also supported the development of essential skills such as creativity, collaboration, and effective communication. Challenges related to time management and limited resources were mitigated through guided supervision and institutional backing. Future studies aim to evaluate the potential of extending the CTEP model to other engineering disciplines.

Cooperative Systems Increasing the Chance of Success of Innovative Projects: A Case from the Brazilian Aerospace Sector

ABSTRACT This paper addresses the use of cooperative systems in the management of innovative projects and their contribution to increasing the chances of success in the case study of the KC-390 Program, a significant project in the Brazilian aeronautical industry. Based on the administrative theory of cooperative systems, the study focuses on collaboration and trust in innovative projects, using the Technology Readiness Level as a guide for decisions. Complex products and systems require customized approaches due to their complexity and high engineering costs. Innovation in these projects depends on collaboration and trust between the developer and the requester. The methodology used includes applied and qualitative research, exploring bibliographic, documentary, and field research data. The KC-390 case study highlights the partnership between the Brazilian Air Force Command and Empresa Brasileira de Aeronaves (Embraer), evidencing how this relationship has been fundamental for technological development. The paper also explores the dual certification process of the KC-390, where the implementation of a collaborative process in the Conformity Demonstration Planning phase brought innovation to military certification. This innovation broke with the traditional paradigm of certification of aeronautical products in the country and was possible, mainly, due to the relationship of trust between the certifying authority and the integrating company.

Odontogenic exosomes simulating the developmental microenvironment promote complete regeneration of pulp-dentin complex in vivo.

Establishing an optimized regenerative microenvironment for pulp-dentin complex engineering has become increasingly critical. Recently, exosomes have emerged as favorable biomimetic nanotherapeutic tools to simulate the developmental microenvironment and facilitate tissue regeneration. This study aimed to elucidate the multifaceted roles of exosomes from human dental pulp stem cells (DPSCs) that initiated odontogenic differentiation while sustaining mesenchymal stem cell (MSC) characteristics in odontogenesis, angiogenesis, and neurogenesis during pulp-dentin complex regeneration. Differential centrifugation was performed to isolate exosomes from normal DPSCs (DPSC-Exos) and DPSCs that initially triggered odontogenic differentiation (DPSC-Od-Exos). The impact of these exosomes on the biological behavior of DPSCs and human umbilical vein endothelial cells (HUVECs) was examined in vitro through CCK-8 assay and Transwell migration assay, as well as assays dedicated to assessing odontogenic, angiogenic, and neurogenic capabilities. In vivo, Matrigel plugs and human tooth root fragments incorporating either DPSC-Exos or DPSC-Od-Exos were subcutaneously transplanted into mouse models. Subsequent histological, immunohistochemical, and immunofluorescent analyses were conducted to determine the regenerative outcomes. DPSC-Exos and DPSC-Od-Exos revealed no remarkable difference in their characteristics. In vitro analyses indicated that DPSC-Od-Exos significantly facilitated the proliferation, migration, and multilineage differentiation of DPSCs compared with DPSC-Exos. Furthermore, DPSC-Od-Exos elicited a more pronounced effect on the tubular structure formation of HUVECs. Consistently, Matrigel plug assays confirmed that DPSC-Od-Exos exhibited superior performance in promoting endothelial differentiation of DPSCs and stimulating angiogenesis in HUVECs. Notably, DPSC-Od-Exos contributed to complete pulp-dentin complex regeneration in human tooth root fragments, characterized by enriched neurovascular structures and a continuous layer of odontoblast-like cells, which extended cytoplasmic projections into the newly formed dentinal tubules. By simulating the developmental microenvironment, multifunctional DPSC-Od-Exos demonstrated promising potential for reconstructing dentin-like tissue, vascular networks, and neural architectures, thereby enhancing our understanding of the therapeutic implications of DPSC-Od-Exos in regenerative endodontic treatment.

An analytical method for broadband acoustic analysis of 2D cavities containing or bounded by porous materials

Real-life vibro-acoustic systems often involve porous treatments, resulting in complex-valued and frequency-dependent models that are challenging to solve. Traditional prediction techniques like the finite element (FE) method requires huge computational cost, especially in the mid to high frequency ranges. This paper develops a novel spectral dynamic stiffness (SDS) formulation, using very few number of degrees of freedom but describing the broadband acoustic behaviour of acoustic cavities with porous materials highly accurately. The method employs frequency-dependent shape function that satisfies exactly the (damped) Helmholtz equation to describe the (equivalent) acoustic pressure field, and also features an innovative approach to use the fast-convergent Modified Fourier series to describe any arbitrary acoustic BCs. Finally, the SDS matrices for cavities containing or bounded by porous materials are formulated in an analytical manner. It is demonstrated that the method exhibits a much higher computational efficiency over the FE package COMSOL, at least 6 times faster than the COMSOL with a similar level of accuracy, and benchmark solutions are provided. This promising method can provide a powerful tool for systems with porous materials that have frequency-dependent characteristics, paving the way for efficient and accurate acoustic analysis in complex engineering applications.

Research on the basic theory and application of enhanced recovery in tight sandstone gas reservoirs.

Tight sandstone gas reservoirs are characterized by high water saturation, significant seepage resistance, low single-well productivity, rapid decline, and low gas recovery. Enhancing the recovery rate of tight sandstone gas reservoirs is a complex engineering challenge that necessitates thorough, refined, and systematic research into its fundamental theories. This study employs a comprehensive approach integrating mercury injection, nuclear magnetic resonance, micro-model visualization, and simulation experiments of displacement and inter-layer seepage flow, alongside foundational seepage theories, to systematically explore the characteristics of tight sandstone gas reservoirs, seepage patterns, and methods for improving gas recovery. Our findings reveal: (1) Detailed characterization of the microscopic pore characteristics in tight sandstone reservoirs helps disclose the status and mechanisms of gas-water occurrence and the principal mechanisms of water production under gas-water co-sealing conditions, such as gas expansion, energy of water-sealed gas, movable water volume, and displacement pressure gradient; (2) Testing single-phase and gas-water two-phase seepage characteristics under bound water saturation identifies permeability and water saturation as critical parameters influencing gas seepage characteristics; (3) Inter-layer gas-water interaction flow experiments demonstrate the interference in multi-layer commingled production and introduce the concept of an interference index, a predictive model for well productivity and dynamic performance in the Sulige tight sandstone gas reservoir; (4) A model correlating reservoir recovery rates with drive indices has been developed, highlighting that increasing production pressure differential and reducing seepage resistance are the primary strategies for enhancing recovery rates in tight sandstone gas reservoirs, supplemented by six technological countermeasures including water-blocking, water control, and densifying well networks. The research outcomes provide effective guidance for practical measures to enhance recovery in tight sandstone gas reservoirs.

Formation specifics of engineering geological conditions in Belarus under the influence of erosion processes

The article presents the results of a comprehensive study of the development conditions and features of water erosion manifestation in various natural and economic settings as an important condition of the formation of engineering geological features of the territory. The authors have established that the development, forms of manifestation and intensity of water erosion processes in the territory of Belarus, with all the diversity of natural and economic situations, are controlled by the energy potential of the relief, the basin structure of the territory and human economic activity. Engineering geological conditions were typified for the development of water erosion processes. The most complex engineering geological situations are observed within the marginal glacial uplands, which have a high energy potential of the topography, a two-rock type of ground massif, and a complex basin structure; as well as in areas of active economic development.

Improved aquila optimizer for swarm-based solutions to complex engineering problems

The traditional optimization approaches suffer from certain problems like getting stuck in local optima, low speed, susceptibility to local optima, and searching unknown search spaces, thus requiring reliance on single-based solutions. Herein, an Improved Aquila Optimizer (IAO) is proposed, which is a unique meta-heuristic optimization method motivated by the hunting behavior of Aquila. An improved version of Aquila optimizer seeks to increase effectiveness and productivity. IAO emulates the hunting behaviors of Aquila, elucidating each step of the hunting process. The IAO algorithm contains innovative elements to boost its optimization capabilities. It combines a combination of low flight with a leisurely descent for exploitation, high-altitude vertical dives, contour flying with brief gliding attacks for exploration, and controlled swooping maneuvers for effective prey capture. To assess the effectiveness of IAO, Herein, numerous experiments were carried out. Firstly, IAO was compared using 23 classical optimization functions. The achieved results demonstrate that the proposed model outperforms various champion algorithms. Secondly, the proposed algorithm is applied to five real-world engineering problems. The achieved results prove effectiveness in diverse application domains. The key findings of the research work highlight IAO’s resilience and adaptability in solving challenging optimization issues and its importance as a strong optimization tool for real-world engineering applications. Convergence curves compare the speed of proposed algorithms with selected algorithms for 1000 iterations. Time complexity analysis shows that the best time is 0.00015225 which is better as compared to other algorithms also Wilcoxon ranksum test is carried out to calculate the p-value is less than 0.05 rejecting the null hypothesis. The research emphasizes the potential of IAO as a tool for tackling real-world optimization challenges by explaining its efficacy and competitiveness compared to other optimization procedures via comprehensive testing and analysis.

Technical service system in the agro-industrial complex

The article considers the issues of modern technical service and its organizational system in the system of engineering and technical support of the agro-industrial complex. The efficiency of agricultural production is mainly influenced by the level of organization in the technical service industry.

Aerodynamic Challenges and Innovations in Wing Designs for Supersonic Flight: A Comprehensive Review

Supersonic flight has been of interest for decades due to the advantages it offers in speed and efficiency of transport, which are advantageous to both commercial and military aircraft. This paper covers a comprehensive review of various wing configurations for supersonic flight. We explore the aerodynamic and structural challenges associated with the various wing types. Supersonic flight offers significant benefits, but also poses complex engineering challenges including concerns with drag, stability, and sonic booms. This review examines the performance of straight, low-sweep, swept-back, delta, forward-swept, and oblique wings and highlights their respective advantages and limitations across different regimes. Straight and low-sweep wings excel at subsonic speeds, but struggle with high drag at supersonic velocities, while swept-back wings and delta wings offer superior performance at high speeds but come with trade-offs in lift and low-speed efficiency. Forward-swept wings provide potential for noise reduction and overall favorable supersonic flight characteristics, but face challenges like aeroelastic instability. Oblique wings, though promising in reducing drag and sonic booms, have significant structural challenges at high Mach numbers. Ongoing research in materials science and aerodynamic modeling continues to advance supersonic aircraft design. These studies and development efforts are paving the way for next-generation supersonic aircraft. Keywords: Aerospace and Aeronautical Engineering; Computation and Theory; Supersonic Flight; Wing Design; Aerodynamics and Sonic Booms

Research on Fault Diagnosis Method for Marine Diesel Engines Based on Multi-Scale Attention Mechanism Transformer

In modern intelligent shipping, ensuring the stable and reliable technical condition of marine diesel engines is critical for safe and efficient vessel operations. Conventional fault diagnosis approaches and many existing Transformer-based methods often focus on single-scale features, potentially overlooking subtle fault indicators and reducing diagnostic accuracy under complex working conditions. To address these limitations, this paper proposes a Multi-Scale Attention Transformer (MSAT) model that integrates both high- and low-resolution attention mechanisms. This multi-scale strategy enhances the extraction of detailed and coarse-grained features, improving the model’s capacity to detect and characterize complex diesel engine faults. Additionally, an optimized Nadam optimizer is employed to refine convergence speed and accuracy, surpassing the Adam-based baseline by 0.71%. Rigorous testing on a publicly available diesel engine fault dataset demonstrates that the MSAT model achieves a diagnostic accuracy of 99.86% at a 60 dB signal-to-noise ratio (SNR), outperforming established models such as GRU and LSTM by more than 1%. Even under severe noise interference (0 dB SNR), the model maintains a high accuracy of 96.86%, highlighting its robustness and suitability for real-time monitoring in challenging marine environments. By quantitatively validating these improvements in diagnostic accuracy and noise resistance, this work offers a novel and effective solution for predictive maintenance and operational condition assessment of marine diesel engines, contributing to the reliability and safety of intelligent shipping systems.

Deep knowledge transfer powered ultrasonic guided wave damage monitoring under incomplete database scenarios: Theories, applications and challenges

Abstract Ultrasonic guided waves can travel long distances within the detected structures, which is of great significance for monitoring large complex engineering systems. However, the multimodal and dispersive properties of the specific research object making this promising whole structure monitoring difficult to interpret the signal mathematically and physically. With the development and maturity of deep learning and big data mining technologies, many scholars have noticed artificial intelligence algorithms such as deep learning can provide a new tool in ultrasonic guided wave signal processing, avoiding the mechanism analysis difficulties in the application of ultrasonic guided wave. But the integrity of structural state data sets has become a new pain point in engineering applications under this new approach, and how to apply the knowledge obtained from the existing data set to different but related fields through knowledge transfer in such cases begin to attract the attention of scholars and engineers. Although several systematic and valuable review articles on data-driven ultrasonic guided wave monitoring methods have been published, they only summarized relevant studies from the perspective of data-driven algorithms, ignoring the knowledge transfer process in practical application scenarios, and the intelligent ultrasonic guided wave monitoring methods based on knowledge transfer of incomplete sets are still lacking a comprehensive review. This paper focuses on the ultrasonic guided wave transfer monitoring technology when the training sample is missing, explores the feature correlation between samples in different domains, improves the transfer ability of the structural monitoring model under different conditions, and analyzes the ultrasonic guided wave intelligent monitoring methods for structural state under different sample missing conditions from three aspects: semi-supervised monitoring, multi-task transfer and cross-structure transfer. It is also expected to provide a new method and approach to solve the condition monitoring problems in other complex scenarios.

A Multi-Strategy Improved Honey Badger Algorithm for Engineering Design Problems

A multi-strategy improved honey badger algorithm (MIHBA) is proposed to address the problem that the honey badger algorithm may fall into local optimum and premature convergence when dealing with complex optimization problems. By introducing Halton sequences to initialize the population, the diversity of the population is enhanced, and premature convergence is effectively avoided. The dynamic density factor of water waves is added to improve the search efficiency of the algorithm in the solution space. Lens opposition learning based on the principle of lens imaging is also introduced to enhance the ability of the algorithm to get rid of local optimums. MIHBA achieves the best ranking in 23 test functions and 4 engineering design problems. The improvement of this paper improves the convergence speed and accuracy of the algorithm, enhances the adaptability and solving ability of the algorithm to complex functions, and provides new ideas for solving complex engineering design problems.

A tunable conical helical spring acoustic metamaterial for complex and harsh environments

Abstract Traditional local resonance (LR) structures can control low-frequency elastic waves, but they still face significant challenges in complex and harsh engineering applications. Due to the complexity of boundary conditions and vibration modes in harsh environments, a high degree of flexibility in vibration isolation structures is required. Fortunately, helical acoustic metamaterials offer such advantages. This paper proposes a tunable conical helical spring (TCHS: a combination of multiple unequal pitches and radii) acoustic metamaterial, which can effectively control elastic waves and vibrations in complex and harsh environments. The mechanisms underlying the generation of bending vibration band gaps were analyzed using the finite element method (FEM). This analysis included examining the transmission spectra, eigenmodes, and displacement vector fields of the LR structure. By adjusting geometric parameters such as the pitch and radius of the conical helical spring, low-frequency band gaps between 34–43 Hz and 45–122 Hz were successfully achieved. Most importantly, the vibration characteristics of the phononic crystal plate were studied under various boundary conditions (bilateral fixed, unilateral fixed, and free constraints) as well as loading conditions (point load and edge load). The results demonstrate that the decay positions observed in the transmission spectra under different conditions were highly consistent with the energy band positions. Therefore, the structure offers potential applications in the field of vibration and noise control in complex and harsh environments.