The free vibration of functionally graded (FG) beams under thermal environments is fundamental to understanding forced vibration, flutter, and thermal buckling in high-temperature structures. However, current research primarily focuses on theoretical modeling and numerical solutions, with limited mechanistic insights into temperature-dependent frequency variations and multi-factor effects. This study presents an analytical investigation coupled with experimental validation to characterize the vibration behavior of FG beams under thermal environments. First, governing equations for thermal vibration of FG beams are derived under uniform, linear, and nonlinear temperature fields based on the power-law assumption, the rule of mixtures, Timoshenko beam theory, and Hamilton’s principle. Subsequently, analytical expressions for natural frequencies and mode shapes are obtained using the state-space method. Then, experimental validation is performed to verify the model’s accuracy. Finally, the combined effects of temperature field, power-law index, slenderness ratio, and boundary conditions on the natural frequencies are systematically analyzed.

To achieve effective vibration and noise reduction, it is essential to control both the noise sources and their transmission paths. However, modern architectural structures often encounter complex challenges arising from multiple airborne sources, structural vibrations, sound-structure coupling, and multi-path propagation. Traditional acoustic materials frequently fall short in addressing these issues comprehensively. In our previous simulation-based work, we developed a broadband composite noise reduction metamaterial tailored for railway station buildings, consisting of a spindle-shaped phononic crystal plate, Fabry-Perot (FP) sound absorption channels, and a micro-perforated panel. In this paper, we advanced the previously simulated design through a research and development process that includes simulation design, prototype fabrication, and experimental optimisation. The influence of the unit cell spacing, array configuration, alternating arrangement, and defect states of the phononic crystal plate on vibro-acoustic performance is examined, along with the effects of microperforated panel porosity, FP channel folding and periodicity, and double-layer perforated structure design on sound absorption performance. The relationship between the experimental results and the simulation analysis is discussed. The optimised structure achieves a noise control effect of 9 dB(A), providing an additional 1.6 dB(A) reduction compared with the baseline simulated design, along with a 19.8 % increase in the proportion of effective noise reduction frequency points and an expanded effective bandwidth. These findings demonstrate the feasibility and performance benefits of physical refinement of simulation-based metamaterial designs, offering a practical workflow for translating computational designs into validated functional prototypes.

Improving sound quality is essential for enhancing the competitiveness of household appliances. However, research on appliance noise has traditionally focused on sound pressure levels, with limited emphasis on acoustic design driven by psychoacoustic perception. This study investigates the sound quality analysis and noise control of gas water heaters. Sound quality measurements were conducted under five operating conditions (25%-100% load and instant heating mode), comparing two different models to identify differences in psychoacoustic parameters and their variation patterns. Subjective evaluations were then performed using paired comparison tests with 36 participants to examine the correlation between objective psychoacoustic metrics and subjective preference scores. A multiple linear regression model was established to predict user preferences. Subsequently, a noise reduction scheme was proposed for the model with relatively poor sound quality. Post-treatment sound quality was measured and analysed, and the regression model was used to predict the subjective evaluation results. The results show that the proposed composite noise reduction scheme notably improved sound quality, leading to significantly higher subjective preference scores. This work provides a useful reference for sound quality evaluation and noise control of household appliances based on psychoacoustic analysis.

Blade-vortex interaction (BVI) noise constitutes a primary source of aerodynamic noise radiated by helicopter main rotors during low-speed descent and approach operations. This study employs a validated coupled computational fluid dynamics/computational structural dynamics (CFD/ CSD) framework integrated with the Ffowcs Williams-Hawkings (FW-H) acoustic analogy to investigate the suppression mechanism of 3/rev Higher Harmonic Control (HHC) on BVI noise under a 6 degrees descent condition. Following validation against HART-II experimental data, parametric simulations are conducted to evaluate HHC efficacy across various control phases. Results demonstrate pronounced phase dependency: the optimal phase of 300 degrees yields a 2.8 dB reduction in peak sound pressure level through favourable acoustic directivity redistribution, whereas improperly configured phases of 180 degrees amplify noise by up to 2.1 dB. Mechanism analysis indicates that the harmonic pitch input alters blade aeroelastic behaviour by reshaping pitch oscillations, advancing torsional response, and increasing upward flapping. As a result, the blade-vortex vertical miss distance increases by an order of magnitude (0.005 m to 0.062 m), producing a 45% reduction in unsteady normal-force coefficient and a 3.2 dB local noise decrease. These findings provide quantitative guidance for phase-optimised HHC strategies aimed at practical BVI noise mitigation.

Acoustic black holes (ABHs) offer significant potential for lightweight vibration control; however, the role of material properties in governing their vibration reduction mechanisms remains insufficiently understood. This study investigates embedded ABH structures from a material-driven perspective through numerical modelling, parametric analysis, and experimental validation. The vibration characteristics of ABH plates with representative metallic and polymeric materials are systematically compared, and the effects of key material parameters-including elastic modulus, mass density, and loss factor-are quantitatively analyzed. The results reveal distinct material-dependent behaviors: metal-based ABHs exhibit narrow but high-amplitude attenuation bands concentrated at high frequencies, whereas polymer-based ABHs provide broader attenuation bands starting from lower frequencies but with reduced attenuation levels. It is further demonstrated that vibration reduction in ABH structures arises from the combined effects of local structural resonance, energy localization, and ABH-induced wave manipulation, rather than the ABH effect alone. The ratio of elastic modulus to density (E/rho) governs the onset frequency of effective attenuation bands, while independent variations in E and rho modulate vibration amplitude through changes in structural stiffness and inertia. Increasing material damping significantly enhances energy dissipation without altering characteristic frequencies. These findings provide new insights into the material-driven design of ABH structures and offer practical guidance for achieving broadband and efficient vibration reduction in lightweight engineering systems.

Aiming to address the vibration and noise reduction requirements of large-scale transportation, the latest research advancements in acoustic metamaterials are classified and reviewed based on practical engineering challenges in this paper. First, the noise characteristics of large-scale transportation, including aircraft, high-speed trains, and ships, are summarised, with the challenges posed by space and weight limitations in noise control being highlighted. The latest research developments in acoustic metamaterials are then reviewed, focusing on four major categories: solid locally resonant metamaterials, membrane-type acoustic metamaterials, Helmholtz resonance cavity structures, and space-coiling metamaterials. Considering the coupling mechanisms among different structures, composite structures are additionally included as a fifth category. Furthermore, adaptive and multifunctional acoustic metamaterials are introduced as emerging directions. Subsequently, the feasibility of these acoustic metamaterials for noise reduction in large-scale transportation is evaluated, and the practical applications of the five established categories are summarised. Finally, challenges and future research directions in the use of acoustic metamaterials for vibration and noise reduction in large-scale transportation are outlined.

Double walls are widely used as they provide a higher level of sound insulation without compromising on mass. However, due to the coupling resonance between the structure and the cavity, additional sound insulation valleys occur, which are not beneficial for noise control. This paper reveals the mechanism by which membrane-type acoustic metamaterials (MAMs) improve the sound insulation valley of double-wall structures, proposes an optimisation design method based on radial basis functions (RBF), and investigates the newly generated valley and the influence of geometric dimensions. First, sound insulation prediction models for both the double wall structure and MAMs were established. The formation mechanism of sound insulation valleys of the double wall structure, and the vibro-acoustic behaviours of MAMs and the sandwich construction containing the MAMs were analysed. Second, an optimisation design method using an RBF neural network model was proposed, optimising the sound insulation peak frequency of the MAMs to align with the specific valley frequency of the double wall structure. Third, the origins of newly induced sound insulation valleys caused by the incorporation of MAMs into the double-wall structure are analysed, and a comparative analysis is conducted on the sound insulation characteristics of finite-sized structures and their periodic infinite counterparts with different unit cell arrays. The results show that the use of MAMs as core layers can effectively improve the sound insulation valleys by 40.3 dB and 14.1 dB of the double wall. The addition of sound absorption materials to the cavity of the sandwich construction can further enhance the new sound insulation valleys by about 4-6 dB. The optimisation design method proposed in this paper is applicable to both finite-sized and infinite-sized structures.

A theoretical model of the normal sound insulation of a rectangular locally resonant (LR) plate with simply supported boundary conditions is established. The accuracy of the model is verified through comparison with finite element simulation results. Considering a 1-m 2 aluminum plate as the research object, a non-dominated genetic algorithm is introduced. The algorithm optimizes the lightweight sound insulation of an LR finite plate with a center frequency band of 20–800 Hz as the optimization objective of maximum average sound insulation and minimum mass. The optimization parameters are substrate thickness and local resonance parameters (including resonator target frequency ( f obj ), number of resonators, additional mass ratio, and resonator damping). Optimization results indicate that the average sound insulation fluctuates at approximately 2 dB due to changes in f obj . The results also provide an optimal solution to the algorithm. The optimal sound insulation value curve of LR plates corresponding to different surface densities of intermediate improved cases is fitted and compared with the sound insulation value of an equal-mass bare plate. Under lightweight optimization, the resonators are deemed capable of improving the local frequency band sound insulation. In contrast, the wideband average sound insulation can approximate but not surpass the insulation provided by the equal-mass bare plate. In practical applications, an LR plate that can improve the local frequency band sound insulation and ensure the overall lightweight sound insulation performance of the wide frequency band can be obtained. This can be achieved by analyzing the frequency spectrum of optimal points in the lightweight sound insulation optimization process. Relevant research can provide a basis for the evaluation and design of the low-frequency sound insulation of plates for transportation equipment, such as airplanes, high-speed trains, and cars.

The panel cavity structure is one of the key components of the aircraft (vehicle) body and is among the main noise transmission pathways. Based on the modal superposition and Galerkin method, this paper realizes the theoretical model of sound insulation of the clamped, double-panel structure. The non-dominated sorting genetic algorithm-II (NSGA-II) is used to realize the sound insulation of the clamped double-panel structure. Through optimization, the fitting function and law of structural surface density and the optimized normal weighted sound insulation Pareto fronts were obtained. The results show that among the optimization, for the Pareto front cases, their double-panel thickness ratio h1/h2 is relatively far away from 1, and the corresponding cavity thickness H is relatively large. The influence of boundary conditions and size effects of lightweight sound insulation optimization are also discussed. The research on the influence of boundary and size indicates that the difference in the optimal weighted sound insulation Pareto fronts corresponding to the same surface density is mostly within the 1 dB range. Both the boundary and thickness of the panel will affect the frequency STL, while the boundary conditions or structure size changed, even the total thickness of panels needs to be the same, and the structure can also have similar weighted sound transmission loss (Rw) when the thickness ratio of the double-panel structure is chosen properly. The difference of material effects is also discussed. This research provides a method for the sound insulation optimization of clamped double-panel structures concerning the boundary and size effect.

Thin plate is a typical key structure of various transportation vehicles such as airplanes and high-speed trains. The sound insulation performance of the plate, especially the low-frequency sound insulation performance, has attracted extensive attention. In this paper, first, taking the finite rectangular locally resonant plate as the research object, based on the plane wave expansion (PWE) method, the theoretical model of sound insulation under simply supported four-sided boundary conditions is established. Secondly, the correctness of the model is verified by calculating the normal incident sound insulation. Thirdly, the influence of the target frequency of oscillator, the number of local oscillators, the additional mass ratio, and the spring damping on the sound insulation performance of the locally resonant plate is analyzed. Finally, a single-value index of low-frequency weighted sound insulation is introduced to perform a single-value evaluation of the sound insulation in the 20–250 Hz frequency band. Relative studies provide a reference for the sound insulation design of the locally resonant plate.

Multi-layered design is an effective method to improve the damping performance of structures. The existing research focuses more on the multi-layered design of the structure from the macro-perspective, but lacks attention to the material itself from the micro-perspective. Thus, whether microscale multi-layered (MML) viscoelastic polymers have advantages in damping performance is not clear. Moreover, damping materials preparation and structural noise control is an interdisciplinary study. The noise and vibration control effect of MML viscoelastic polymers in actual composite structures needs to be further investigated. This paper conducts such a study on these issues. First, two different types of MML viscoelastic polymers, i.e., free damping (FD) and micro-constrained damping (MCD) composites, were prepared, and their material properties were characterized. Second, the frequency-dependent damping loss factors and elastic modulus of the different damping composites were identified. The influences of damping composite types and MML designs on material damping loss factor and elastic modulus were compared. Third, a prediction model of vibroacoustic behaviours of the honeycomb sandwich structure was established and validated to investigate the noise and vibration control effects of the MML damping composites on composite structures. The influences of the types, numbers of layers and application positions of the MML damping composites on the honeycomb sandwich structure were studied. The results indicated that MML design is helpful to improve the damping performance of viscoelastic polymers, but its influence on different damping composites is quite different. For noise control, MML-FD is more suitable for controlling airborne sound propagation, while MML-MCD is more suitable for controlling structural sound propagation.

This paper focuses on the low-frequency vibroacoustic characteristics of aluminium extrusion compounded with acoustic metamaterials. According to the actual geometry of floor aluminium extrusion of a high-speed train, a 1 m × 1 m and a 3 m × 3 m vibroacoustic models of the aluminium extrusion were established, respectively, based on the finite element method. Then a reasonable aluminium extrusion modelling and simulation size was discussed. Taking the first-order bending modal frequencies of different size aluminium extrusions and low weight as the objective functions, different beam-like resonators were optimised based on the multi-island genetic algorithm. Finally, the vibration control effect of the acoustic metamaterials on aluminium extrusions of different sizes, and the effects of different measures on vibroacoustic reduction of the aluminium extrusion were analysed. The results show that the acoustic metamaterials are more effective than the traditional measures on the controlling of single resonances.

In this paper, a method and model of sound insulation prediction for the side wall structure of a high-speed train based on back propagation neural network is proposed. Firstly, the components of high-speed train side walls are classified and analyzed. Based on the measured results and existing literature, the main factors affecting the sound insulation characteristics of side walls are listed to form a feature set. Then, correlation analysis and redundancy analysis were carried out for the above feature sets, and the optimal feature subset was determined based on the maximum correlation—minimum redundancy (M-RMR) criterion. Finally, the BP neural network model is established and trained with the sound insulation volume of side wall structure as the objective function. The results show that compared with the traditional FEM model, the BP neural network model significantly improves the computational efficiency and accuracy.

The interior noise prediction model is a valuable tool for estimating the interior noise level and obtaining important influencing parameters during the low-noise design stage of rail vehicles. Existing interior noise prediction models, however, have some flaws in their consideration of composite carbody structures. The SEA approach is used to establish a rail vehicle interior noise prediction model that takes into account the complete carbody composite structures, which include aluminium extrusion, porous sound-absorbing material, and layered interior structure. The aluminium extrusion is equivalent to an orthotropic plate subsystem, while porous sound-absorbing material and the layered interior structure are modelled as a lay-up noise control treatment on the plate subsystem. Analytical expressions are used to calculate the corresponding SEA parameters. The prediction model has been validated with test results and shows good accuracy from 200 to 800 Hz in 1/3 octave frequency bands, which offers a novel approach to rail vehicle interior noise prediction and a helpful tool for comparing the various noise control treatments.

Acoustic metamaterials (AMs) composed of periodic artificial structures have extraordinary sound wave manipulation capabilities compared with traditional acoustic materials, and they have attracted widespread research attention. The sound insulation performance of thin-walled structures commonly used in engineering applications with restricted space, for example, vehicles’ body structures, and the latest studies on the sound insulation of thin-walled metamaterial structures, are comprehensively discussed in this paper. First, the definition and math law of sound insulation are introduced, alongside the primary methods of sound insulation testing of specimens. Secondly, the main sound insulation acoustic metamaterial structures are summarized and classified, including membrane-type, plate-type, and smart-material-type sound insulation metamaterials, boundaries, and temperature effects, as well as the sound insulation research on composite structures combined with metamaterial structures. Finally, the research status, challenges, and trends of sound insulation metamaterial structures are summarized. It was found that combining the advantages of metamaterial and various composite panel structures with optimization methods considering lightweight and proper wide frequency band single evaluator has the potential to improve the sound insulation performance of composite metamaterials in the full frequency range. Relative review results provide a comprehensive reference for the sound insulation metamaterial design and application.

This paper presents a comprehensive test and systematic evaluation analysis of cabin noise in the Robinson R44 RAVEN u2161 helicopter. Initially, microphones were placed within the cabin to conduct systematic assessments of noise levels under various flight conditions, including takeoff, climbing, level flight, landing, hovering, etc. Subsequently, timeu2013frequency analysis was conducted on the test data utilizing traditional A-weighted sound pressure levels, which was followed by quantitative comparisons across different flight conditions. Then, detailed evaluation and discussion were conducted, taking into account the subjective perceptions and communication challenges of cabin crew members. This assessment incorporated the use of aviation noise indicators, speech interference levels, and metrics related to sound quality. Finally, potential noise reduction measures and their effects were preliminarily discussed. The results indicate that helicopter cabin noise exhibited variations across different flight states or positions within the same state, ranging from 87.6 dB(A) to 92.6 dB(A). Discrepancies between A-weighted sound pressure level and psychoacoustic parameters were observed, particularly during hovering states, which indicate that there is a necessity for the combination of multiple evaluation indicators. Notably, damping measure can serve as a pivotal factor in mitigating cabin noise.

The body of a high-speed train is a composite structure composed of different materials and structures. This makes the design of a noise-reduction scheme for a car body very complex. Therefore, it is important to clarify the key factors influencing sound insulation in the composite structure of a car body. This study uses machine learning to evaluate the key factors influencing the sound insulation performance of the composite floor of a high-speed train. First, a comprehensive feature database is constructed using sound insulation test results from a large number of samples obtained from laboratory acoustic measurements. Subsequently, a machine learning model for predicting the sound insulation of a composite floor is developed based on the random forest method. The model is used to analyze the sound insulation contributions of different materials and structures to the composite floor. Finally, the key factors influencing the sound insulation performance of composite floors are identified. The results indicate that, when all material characteristics are considered, the sound insulation and surface density of the aluminum profiles and the sound insulation of the interior panels are the three most important factors affecting the sound insulation of the composite floor. Their contributions are 8.5%, 7.3%, and 6.9%, respectively. If only the influence of the core material is considered, the sound insulation contribution of layer 1 exceeds 15% in most frequency bands, particularly at 250 and 500 Hz. The damping slurry contributed to 20% of the total sound insulation above 1000 Hz. The results of this study can provide a reference for the acoustic design of composite structures.

For railway carbody structures with irregular cross-sectional shapes and great longitudinal lengths, it is difficult to obtain their vibroacoustic characteristics using traditional computational methods. Moreover, traditional methods are time intensive and not conducive to the optimisation design of such complex and large structures. This study introduces an equivalent modelling approach for vibroacoustic analysis, i.e., sound transmission loss and sound radiation analysis, of railway aluminium extrusion. The aluminium extrusion is equivalent to a homogeneous orthotropic plate, and the equivalent mechanical properties of the plate are obtained via static analysis based on the small-deflection theory. The vibroacoustic characteristics are obtained using the hybrid method of finite element and statistical energy analysis. First, the equivalent modelling approach is validated using the results of a detailed prediction model and experimental test. Subsequently, the applicability of the equivalent approach is analysed by comparing it to the predicted results of the detailed model with different dimensions and boundary conditions. Ultimately, the minimum longitudinal length that needs to be considered for the analysis of railway aluminium extrusion is discussed using the equivalent approach and the computational efficiency is compared. The results reveal that the equivalent approach can effectively simulate the vibroacoustic performances of the aluminium extrusion in 1/3 octave bands centred below 1000 Hz and reduce the calculation time by 90% compared with the detailed prediction models of aluminium extrusion, which provided a foundation for vibroacoustic optimisation design of railway carbody structures.

Designing a sound-insulation scheme for a composite structure efficiently and accurately for noise control in equipment is essential. However, traditional simulation and experimental methods for obtaining an optimal solution are not only time-consuming but also difficult to implement. In this paper, a sound insulation optimisation design method based on machine learning is proposed. The method is applied to design a complex composite floor structure of a high-speed train. By testing numerous practical schemes in the acoustics laboratory to obtain a sample set, a machine learning model for predicting the sound insulation performance of a composite floor of a high-speed train is trained and verified. Subsequently, an efficient and accurate multi-parameter sound insulation optimisation design of the composite floor structure based on the machine learning model is implemented. First, the original data samples required for model training are analysed and sorted. Second, the target feature subset is selected through the main influencing factor analysis, correlation-redundancy analysis, and mRMR feature selection calculation. Then, based on the SVR method, the standardised feature data are used to train and verify the sound-insulation prediction model of the composite floor structure of a high-speed train. Finally, two embodi-ments are presented to verify the advantages of the model in the multi-parameter optimisation design of the sound-insulation model of the composite floor structure of a high-speed train. The results show that the optimal sound insulation is 51.69 dB when the thickness and surface density of the composite floor are given. Similarly, the minimum surface density is 89.42 kg/m2 when the thickness and sound insulation limit are given.

The design of sound-insulation schemes requires the development of new materials and structures while also paying attention to their laying order. If the sound-insulation performance of the whole structure can be improved by simply changing the laying order of materials or structures, it will bring great advantages to the implementation of the scheme and cost control. This paper studies this problem. First, taking a simple sandwich composite plate as an example, a sound-insulation prediction model for composite structures was established. The influence of different material laying schemes on the overall sound-insulation characteristics was calculated and analyzed. Then, sound-insulation tests were conducted on different samples in the acoustic laboratory. The accuracy of the simulation model was verified through a comparative analysis of experimental results. Finally, based on the sound-insulation influence law of the sandwich panel core layer materials obtained from simulation analysis, the sound-insulation optimization design of the composite floor of a high-speed train was carried out. The results show that when the sound absorption material is concentrated in the middle, and the sound-insulation material is sandwiched from both sides of the laying scheme, it represents a better effect on medium-frequency sound-insulation performance. When this method is applied to the sound-insulation optimization of a high-speed train carbody, the sound-insulation performance of the middle and low-frequency band of 125–315 Hz can be improved by 1–3 dB, and the overall weighted sound reduction index can be improved by 0.9 dB without changing the type, thickness or weight of the core layer materials.