Novel resonator geometry for easily manufactured tunable locally resonant metamaterial

Mechanical waves and sound waves have complex propagation characteristics that are manipulated by periodic structures such as elastic metamaterials and phononic crystals for the purposes of wave guiding, vibration isolation and sound absorption. System parameters are tuned to induce auxetic physical properties such as negative effective mass density and negative Poisson's ratio. Locally resonant metamaterial (LRM) uses Fano-type interference to manipulate elastic wave propagation from the host structure by formation of a band gap due to local resonance. Not restricted by the Bragg interference limit, such sub-wavelength structures are particularly effective in attenuation of the low frequency oscillations. Tunability of the lower and upper bounds of the band gap through simple geometrical and material variations has made the LRMs a strong candidate for the noise and vibration control of automotive and industrial applications. In this study, we demonstrate a tunable LRM design that can be fabricated by injection moulding and vacuum casting. The mould for the fabrication of the resonator features a cylindrical hollow section. Pins of different diameter can be inserted into the mould to vary the material distribution in the cavity, thereby changing the resonance. A numerical model using COMSOL Multiphysics has been developed to investigate the dispersion mechanism. A parametric study of the pin diameter with respect to target band gap frequency demonstrates the capability of broadband vibration attenuation while keeping the overall size of the resonator small and constant. These results are promising for practical implementation of LRMs

Topography optimization of an enclosure panel for low-frequency noise and vibration reduction using the equivalent radiated power approach

An enclosure panel is widely used in industrial applications. The panel under a dynamic loading excites the surrounding air medium and noise is radiated into the acoustic space. The radiated sound can be suppressed by having changes in the structure. The noise reduction performance can be further improved by a design optimization. In this study, a topography optimization is conducted to design an enclosure panel. Topography optimization results in a bead pattern, which helps maintain the thickness at a constant level throughout the structure. The final optimized structure can be manufactured using a stamping process. Compared with other optimization methods, topography optimization requires minimal manufacturing effort and cost, with no additional increase in mass. Moreover, this type of optimization is effective for noise reduction problems because no holes are created in the structure. In this study, the objective function selected to minimize the low-frequency noise is the equivalent radiated power. The topography optimization of the enclosure panel has been conducted using the commercial software Altair OptiStruct, with loads and constraints considered. In order to verify the optimization result, in-situ experiment was performed with panels produced by the stamping process

Vibroacoustic characteristics of a damped box-type structure

In industrial applications, rigid-walled cavities that are enclosed by flexible panels can be commonly encountered. Owing to the coupling of the velocity of the panel with the air pressure in the enclosure, noise and vibration in- and out of- the system is amplified. Such problems are frequently alleviated by passive vibration control, where damping treatments are effective in mid and high frequencies. It has been shown that when such treatments are applied nonproportionally, not only the vibration of the panel, but also the radiated sound pressure from the panel can be reduced, while limiting the mass increase. In this study, the governing relation for this phenomenon is expressed by using the uncoupled modal parameters of the panel and cavity. Complex modes that arise from nonproportionally damped systems are shown to be closely linked to optimal damping characteristics. We further show that the coupling strength between the cavity modes and panel modes are dependent on the spatial distribution of the damping. A damping layer topology optimization problem is formulated to demonstrate the interconnectedness of the modal parameters with optimal damping layer layout

On the formation of complex modes in non-proportionally damped systems

In the classical studies of non-proportionally damped systems, the resulting complex modal parameters are obtained by solving the generalized eigenvalue problem. In the present study, we propose a unique method to obtain complex modes for discrete and continuous systems. Based on a wave analogy, the difference between a complex mode and a real normal mode is represented by the summation of patterns that propagate from the boundaries. Owing to the spatial non-proportionality of the damping, these patterns undergo changes at a damping intersection. The governing equation for this phenomenon is expressed by Snell's law. We show that, in a similar manner to the refractive index for the medium in which light waves travel, a damping field index can be conceived for individual damping regions, such that they may be scaled against the damping field index of the undamped region, which is assumed to be unity. However, unlike the refractive index, we show that the damping field index is dependent on the spatial distribution of damping. The procedure for obtaining the complex modes is illustrated based on a plate structure with simply supported boundary conditions. The practical applications of the proposed approach and its limitations are discussed based on numerical examples

Experimental modal analysis of rolled multi layer cylindrical shell

Cylindrical shells are frequently encountered in industry, flight structures, pipeline systems and marine crafts. In these applications cylindrical shells are commonly subjected to harmonic excitations induced by pumps, turbines, compressors etc. Structures exposed to such loads can have structural failure due to sustained effect originated from the vibration by the dynamic load, and structural resonances. For suppression of noise and vibration in the system many design techniques have been employed, and the concept of laminated or multi layer shell has been utilized in several work. In such configuration layers with or without additional damping material stacked on top of each other to achieve the optimum vibration behavior. In rolled multi layer cylindrical shells this phenomenon is realized by rolling a thin plate around a cylindrical shell. Analyzing the coupled system in frequency domain, it is observed that the contact relation between adjacent layers change the system eigenvalues and eigenvectors, as well as resulting in overall reduction in noise and vibration compared to simple shell. In this research experimental modal analysis has been done, and case studies have been presented for different thickness configurations of rolled multi layer shell structure

Effect of damping distribution on coupling in panel–cavity systems: Conditions for optimality through a modal approach

© 2020 In this study, we examine an acoustic–structure interaction problem for nonproportionally damped systems. Coupled responses for a structure and acoustic enclosure are derived using a modified modal coupling formulation. Uncoupled modal patterns are used to assess the coupling effectiveness. Comparison with a proportional damping case reveals characteristics that associate complex modes with damping optimality. Such an interrelation is investigated through topology optimization of a damping layer to minimize the acoustic pressure in the cavity. The findings of this numerical study indicate a spatial relation between the imaginary part of the coupling coefficient and the optimal damping layout. Further investigation of complex modal patterns with wave interpretation shows that the optimal damping characteristics of the panel can be expressed by a spatially varying nonproportional damping index. Case studies involving various nonproportional damping configurations are presented to confirm the significant correlation with respect to observed phenomena

Vibro-acoustic noise analysis of a washing machine

This study is a comprehensive effort in analyzing the vibro-acoustic characteristics of a top loaded washing machine, and focuses on the identification of the main noise source. For this purpose, the vibro-acoustic behaviors of components in washing machine are investigated systematically. Modal analysis of the main components in the system (cabinet, tub, and motor) are performed for identification of vibration modes that are related to noise radiation. The cogging torque that is associated with the brushless DC motor is identified with the order analysis. The critical frequency bands are determined with respect to components, and preliminary investigation for the noise source identification is concluded. For a quantitative ranking of contributions from several components to output noise during operation of the washing machine, Operational Transfer Path Analysis method is used. The vibration and acoustic response are measured in a relation to stepwise control of the operation speed of the BLDC motor. Transmissibility functions with respect to transfer paths are calculated, and cross-talk cancellation is applied using principal component analysis. The evaluated synthesized response matched well with the measured noise output through all measurement steps

A framework of flexible locally resonant metamaterials for attachment to curved structures

Locally resonant metamaterials (LRMs) have been extensively investigated for their superior attenuation performance in the band gap frequencies despite not resulting in a large mass increase, comparatively. However, for their application on actual industrial structures, there exist limitations, the most important of which is the flexibility of the LRM structure. Several studies have succeeded in attaching LRMs to curved surfaces, but if the curvature changes, the unit structure must be redesigned. In this paper, a flexible LRM design independent of curvature is proposed, and numerical simulations illustrate the implementation of the band gap in a beam. Proof of concept of the flexible LRM has been shown through modal experiments on various curved surfaces. Excellent attenuation characteristics of the flexible LRM are demonstrated viaa comparison with a constrained layer damping treatment, which are typically considered in noise, vibration and harshness (NVH) area. As the proposed flexible LRM can be attached to various curvatures without restriction or redesign, it differentiates itself as a practical alternative to other LRM designs and expected to be explored in diverse applications