Aiming at the problem of sparse measurement points due to test conditions in engineering, a smoothing method based on zero-padding in the wavenumber domain is proposed to increase data density. Firstly, the principle of data extension and smoothing is introduced. The core idea of this principle is to extend the discrete data series by zero-padding in the wavenumber domain. The conversion between the spatial and wavenumber domains is achieved using the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). Then, two sets of two-dimensional discrete random data are extended and smoothed, respectively, and the results verify the effectiveness and feasibility of the algorithm. The method can effectively increase the density of test data in engineering tests, achieve smoothing and extend the application to areas related to data processing.

Tire cavity noise is becoming more prominent as the speed of electric vehicles is getting higher. This study aims to use a built-in sound-absorbing material to reduce tire cavity noise. First, the radial force was extracted by rolling analysis, and the tire cavity noise was obtained. Then, in order to investigate how the placement of sound-absorbing material affects the noise reduction, sound-absorbing material was applied to the inner side of tire’s side and tread position respectively. Finally, studies were done on the impact of sound-absorbing material’s density, flow resistance, porosity, and thickness on tire noise reduction. The best way to reduce noise with a 215/55R17 tire was to apply sound-absorbing material at side position. The density, porosity, flow resistance and thickness of the sound-absorbing material were 55 kg/m³, 0.95, 5000 Pa·s/m² and 40 mm, respectively. The A-weighted sound pressure level decreased by 27.7 dB compared with that before the built-in sound-absorbing material. In response to the uncertainties on the reduction achieved by the sound-absorbing material, this study offers some recommendations for noise reduction of tire cavity. The studied effect is limited to the tire cavity, and the effect on the emitted sound energy has not been evaluated.

Part II of this study presents numerical simulations of reconstructing the excitation forces acting on the interior surface of an enclosure, based on the vibroacoustic information collected in the exterior region. Various types of excitation forces such as distributed, line, and point forces are considered. Moreover, fluid loading inside the enclosure is considered in the numerical simulations. Analytical proofs show that fluid loading has no impact on excitation forces, but has significant impacts on structural vibrations. This is especially true when the density of fluid medium inside an enclosure is high. Results demonstrate that when excitation forces are continuous, the accuracy in reconstruction may be very high. When excitation forces contain abrupt changes or discontinuities, for example, line and point force, the accuracy in reconstruction may be significantly reduced. This is because many expansion terms are required to properly describe the discontinuities of excitations. On the other hand, discretization grids are fixed a priori. When fixed discretization grids are used together with an increasing number of expansion terms, aliasing may occur that may completely distort the reconstructed excitation forces.

Noise control remains a critical challenge in mechanical engineering, particularly for low- and mid-frequency noise mitigation in industrial applications. This study proposes a composite structure combining micro-perforated panels (MPPs) and back-shaped cavities, targeting the 20–1000 Hz frequency range. An acoustic-electrical analogy model is developed to characterize the sound absorption mechanism. A carefully selected set of parameters is then utilized to fabricate a prototype, which undergoes rigorous experimental validation. Additionally, the finite element method is employed in conjunction with the control variable approach in tandem to systematically investigate the impact of eight structural parameters on the sound absorption performance of the composite structure. Following this, Particle Swarm Optimization (PSO) is employed to optimize the structural parameters. The results indicate that among the eight geometrical parameters, the perforation rate and the second layer’s cavity depth significantly affect the acoustic performance, while the remaining parameters exhibit minimal or negligible impact. The optimized composite structure demonstrates remarkable efficacy in mitigating low-frequency and mid-frequency noise, effectively broadening the acoustic bandwidth from 165 Hz to 740 Hz within these frequency ranges. The research conducted in this study provides valuable insights and serves as a reference for noise reduction in practical machinery equipment and indoor acoustic environments.

Vibration isolation systems are widely employed in automotive, marine, aerospace, and other engineering fields. Accurate input forces are of great significance for mechanical design, vibration prediction, and structure modification and optimization. One-stage vibration isolation system including engine, vibration isolators, and flexible supporting structure is modeled theoretically in this paper. Input excitation acting on the vibration isolation system is reconstructed using dynamic responses measured on engine and supporting structure under in-suit condition. The reconstructed forces reveal that dynamic responses on rigid body are likely to provide more accurate estimation results. Moreover, in order to improve the accuracy of excitation reconstructed by dynamic responses on flexible supporting structure, auto/cross-power spectral density function is utilized to reduce measurement noise.

Part I of this paper presents analytic solutions for reconstructing the excitation forces that act on the interior surfaces of a finite solid rectangular enclosure with the fluid loading effect taken into consideration, given vibroacoustic data in the exterior region. The reason for selecting a simple structure is to facilitate the reconstruction of excitation forces. To validate these analytic solutions, we apply the reciprocity principle and demonstrate that when the resultant excitation forces are used to excite the enclosure from the inside, the same vibroacoustic responses in the exterior region in exterior region can be obtained. To illustrate this point, we consider the case in which the top panel of a rectangular box is connected to the side walls through simply-supported boundary conditions, and the rest surfaces are rigid. The top surface of this box may be excited into vibrations by any type of excitation forces from the inside with the fluid loading effect taken into consideration. Note that for arbitrarily shaped structures under arbitrary boundary conditions, numerical solutions can be obtained. Therefore, it is possible to determine the excitation forces acting inside an enclosure based on the vibroacoustic information collected in the exterior. The knowledge of the excitation forces is critically important, because it can lead to optimal mitigation strategies to mitigate undesirable noise and vibrations.