Elsevier

Thin-Walled Structures

Volume 167, October 2021, 108200
Thin-Walled Structures

Full length article
Cut-out resonators for tuned vibration suppression of plates

https://doi.org/10.1016/j.tws.2021.108200Get rights and content

Highlights

  • Moment-coupled built-in resonators proposed.

  • Computational and experimental studies demonstrate working mechanisms.

  • Vibration attenuation of plates is functional regardless of plate boundaries.

  • Absorption mechanism does not require periodic resonator placement.

Abstract

This research investigates a concept for cut-out resonators that exploit a small area of active mass of a host plate structure for sake of tuned, low frequency vibration attenuation. Integrated computational and experimental studies reveal that embedding the resonators at locations offering high bending moment gradient and arranging the central resonator beam along a nodal line of bending moment best excite the first resonator eigenmode for targeted vibration suppression. These results are independent of plate boundary conditions and do not require periodic resonators to achieve notable vibration suppression outcomes. These design concepts may guide the development of resonators for vibration absorption of plates with arbitrary boundary conditions.

Introduction

The pursuit for low frequency vibration attenuation of plates has flourished in automotive, aerospace, or civil engineering applications. The mechanisms of tuned mass damping and bandgaps are commonly used to mitigate undesired vibrations of plates. The classic tuned mass damper (TMD) is essentially a mass connected to the host structure by a parallel combination of spring and damper [1]. Vibration energy is mitigated by reactive inertial force from the TMD against the exciting force, leading to a passive elimination of vibration over a tuned frequency range. Researchers have investigated methods to improve the effectiveness [2], [3], [4], [5], [6] and robustness [5], [6] of TMDs. For example, the studies on single TMDs applied to one degree-of-freedom (1-DOF) host structures indicate that interfacing the TMD damper element with a ground is more effective than when the TMD damper interfaces directly with the host structure [2], [7]. The addition of elastic springs in parallel to grounded dampers provides TMDs still greater effectiveness by offering a complex impedance path to the ground by which to attenuate host structure vibration [3], [8]. Increasing the number of TMDs may improve the vibration absorption capabilities [4], [5], [9], [10]. Li and Ni [6] report that the optimal non-uniform distribution of TMDs delivers greater vibration attenuation than uniform distributions of optimized TMDs. Zuo [5] finds that serially interfaced TMDs are more effective and robust than parallel connected TMDs. Moreover, Igusa and Xu [10] point out the operating frequency range of a TMD is proportional to the square root of mass ratio. Extending from 1-DOF host structures to continuous structures, studies discuss how TMDs suppress the vibrations of plates [11], [12]. Cheung and Wong [11] suggest that an optimal TMD for a targeted mode of plate vibration has a high mass ratio. Although the effectiveness and robustness may be improved by modifying the arrangements of mass, spring, and damper elements, a large ratio of TMD mass to structure mass is required to obtain substantial vibration suppression [9].

For a periodic array of 1-DOF TMDs on a plate, bandgaps for wave propagation are developed by introducing the concept of negative effective mass [13], [14], [15]. Standing and traveling waves at the frequencies within bandgap are inhibited from propagating through the periodic structures. Sugino et al. [16] report that the normalized bandgap bandwidth is 1+μ1, where μ is the mass ratio between the TMDs and host structure. Researchers also explore 2-DOF TMDs [17], [18] and multiple DOF (MDOF) resonators in periodic arrays to extend the functionality of wave attenuating bandgaps. Here, the MDOF resonators may be pillars [19], [20], [21], rubber inclusions [22], inter-connected beams [23], [24], [25], and membrane/plate type resonators [26], [27]. For the MDOF resonators applied to plates, bandgaps are induced by destructive interference between Bragg scattered waves. Compared with 1-DOF TMDs, the number of bandgaps that MDOF resonators may produce lead to multiple bandgaps tailored by the arrangement of the resonators [28], [29]. Yet, the bandgaps of MDOF resonators are often effective in mid to high frequency range, while many plate vibration challenges are in the low frequency range.

To overcome the limitation of relying on large added mass ratios to achieve large attenuation of low frequency elastic waves and mechanical vibrations, researchers have designed tuned inerter dampers [30], [31], [32], piezoelectric patches [33], [34] and lightweight resonators [35], [36], [37]. Using tuned inerter dampers, vibration isolation can be achieved by a small amount of added mass compared to classical TMDs. For piezoelectric patches, Toftekær et al. [33] proposed patches with piezoelectric shunt damping for plate vibration suppression using only 5% mass ratio and 4% surface area coverage of the host plate, but this design requires an external connection to a shunt circuit. Sun et al. [35] presented periodic grid frames filled with rubber membranes to attenuate plate vibration at low frequencies. For this periodic structure, the mass ratio may be as low as 6%, although the area coverage of the resonators constitutes around 50% of the host plate area. Recently, the authors developed a lightweight elastomeric half cylindrical resonator for vibration suppression of an aluminum panel [37]. The peak amplitude of plate vibration around 140 Hz was reduced by 8 dB by applying only four resonators on the plate accounting for a mass ratio of just 3.3% and the area coverage of 1.7% of the plate surface. These functionalities were achieved by exploiting the multimodal nature of the locally resonant elastomeric attachments [37]. Rather than devise resonators from add-on elements, researchers have investigated resonators realized by cut-outs from a host structure [38], [39], [40]. Yet, to date the operating frequency ranges of such cut-out resonators are high considering structure-borne vibrations, such as in the kHz range, and the cut-out resonators require a large area coverage. Ulz and Semercigil [41] studied the dynamic responses of a clamped plate with a single cut-out resonator and discuss the possibility to employ such resonators for low frequency vibration attenuation. While an important step to address the outstanding needs for effective lightweight and minimally intrusive application of vibration absorbers to continuous structures, the discussion of resonator design and positioning is limited in terms of frequency responses for achieving vibration control [41].

This research explores an approach for cut-out resonators in non-load-bearing plates that provides vibration suppression at low frequencies without excessive use of the plate surface area. By examining the resonant mechanisms of the cut-outs, the linear modes are exploited to capitalize on the cut-out resonator positioning for multi-mode vibration attenuation. The following sections of this report detail computational and experimental efforts undertaken to characterize the modal nature of the resonators and to analyze the vibration attenuation mechanisms of the resonators integrated with a host plate structure. The findings and implications from the insights of this research are summarized in the final section.

Section snippets

Modal characteristics of the cut-out resonators

The host structure with cut-out resonators considered in this research is schematically shown in Fig. 1(a). The host structure is a 3 mm thick acrylic rectangular plate. In order to avoid reducing necessary mechanical performance of the plates via the cut-out inclusions, we envision that the host structure plate is involved in a non-load-bearing application, such as serving as a cover over other mechanical or structural members, yet still essential in the vibration transmission scenario. The

Experimental and finite element investigation methods

The experimental system is a 3 mm thick, clamped acrylic plate that includes cut-out resonators, as shown in Fig. 2(a). A laser cutter (Epilog, Mini/Helix 8000, Golden, CO, USA) is used to cut the exterior shape of the acrylic plate, the mounting holes in the plate for clamping, as well as potential cut-out resonators employed. The area of the acrylic plate inside the clamped edges is 203.2 mm by 241.3 mm. The clamping frame is placed on foam supports to minimize coupling between dynamics

Results and discussions

This section leverages integrated FE and experimental efforts to investigate the mechanisms leading to vibration attenuation in rectangular plates having cut-out resonators. The plates with resonators are classified by labels such as C1, S2, and F3. The characters C, S, and F respectively refer to the clamped plate, simply-supported plate, and freely-suspended plate. The numbers 1, 2, and 3 represent the plates respectively designed to mitigate the first, second, third modes of the plate

Conclusions

This research investigates the mechanisms of plate vibration attenuation for cut-out resonators. Via FE and experimental efforts, the studies reveal that embedding the resonators at locations offering high bending moment gradient and arranging the central resonator beam along a nodal line of bending moment can best excite the first resonator eigenmode. As a result, maximum vibration attenuation occurs by exploiting these design conditions. Moreover, this design principle is extensible to any

CRediT authorship contribution statement

Sih-Ling Yeh: Conceived the ideas of the research, Carried out the theoretical and experimental research efforts, Analyzed the data and processed conclusions, Edited the manuscript. Ryan L. Harne: Conceived the ideas of the research, Analyzed the data and processed conclusions, Edited the manuscript.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This project is supported by the National Science Foundation, United States Faculty Early Career Development Award (No. 2054970).

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