Chapter 8 Three-Dimensional Mechanical Metamaterial for Vibration Suppression Brittany C. Essink and Daniel J. Inman Abstract Decades of research have been conducted on vibration suppression, cancellation, and absorption methods. Recently, distributed arrays of resonators have been implemented in host structures creating devices termed mechanical metamaterials, also known in the literature as metastructures. The benefit of using mechanical metamaterials as opposed to traditional added absorbers is the structure is initially designed including the absorbers instead of adding them after creation, saving time and weight. Additionally, these structures remain capable of bearing loads without adding additional mass. Where past research has focused on designing and optimizing metastructures based on single degree of freedom excitations, the research presented in this paper focuses on a device capable of vibration suppression under excitation in three directions; longitudinal, transverse, and torsional. This accommodation is necessary for these devices to be implemented in non-laboratory settings to account for excitation from multiple directions. This paper presents experimental data and a preliminary finite element model for a three-dimensional mechanical metamaterial vibration suppression system. Experimental results compare the structure with blocked absorbers to free absorbers to demonstrate vibration reduction bandwidths of 358 Hz in the longitudinal direction, 24 Hz in the transverse direction, and a frequency shift of 40 Hz in the torsional direction. These promising results show that a metastructure can be effectively designed to suppress vibrations in all three directions of excitation with further motivation to explore optimization of the absorber system for maximum suppression bandwidth. Keywords Mechanical metamaterial · Metastructure · Multidirectional excitation · Vibration supression 8.1 Introduction Methods of suppressing and canceling vibration have been widely investigated by scientists and engineers alike. The majority of these suppression methods can be either classified as active or passive vibration systems. Active systems require energy input into the system and control of an actuator to suppress the vibrations whereas passive systems will operate without any additional energy input or control system. Historically, one of the most investigated vibration systems is a tuned mass damper, or TMD. This simple 1DOF system can be added to an existing structure and tuned through the structural and forcing parameters to suppress the vibration of the host structure. More recently, this TMD concept has been expanded upon and compounded to create a distributed array of tuned mass absorbers throughout a system. This concept is called a mechanical metamaterial, also known as a metastructure. The efficacy of these metastructures for vibration reduction using a chiral design has been demonstrated by Zhu et al. [1]. Other researchers such as Sun et al. and Pai et al. have focused on the traditional tuned mass damper system to achieve broadband absorption in both vibration and acoustics [2, 3]. Previous work in the metastructure field used distributed absorber designs for axial vibration suppression. Hobeck et al. [4] investigated preliminary modeling and experiments for the passive axial metastructure system while Reichl and Inman [5] delved into both passive and active axial suppression including tuning the dampers separately for varying suppression effects. Oftentimes, vibrations are restricted to unidirectional excitation which is achievable in a lab setting but is not often the type of excitation experienced by a structure in the field. The work of Drouard et al. [6] added suppression of torsional vibration to the original axial design for a 2D structure. The research presented in this paper builds upon these works and incorporates the transverse degree of freedom for a metastructure capable of suppression in three dimensions. This paper includes a brief description of the preliminary finite element modeling for this structure, with a main focus on the experimental results. B. C. Essink ( ) · D. J. Inman Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA e-mail: essinkb@umich.edu © Society for Experimental Mechanics, Inc. 2020 N. Dervilis (ed.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12243-0_8 43
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