## 1 Introduction  
The field of metamaterials has emerged over the past 20 years and inspired numerous innovations in optics, electromagnetics e.g., [1; 2; 3] and more recently in acoustics e.g., [4; 5; 6]. Phononic crystals and acoustic metamaterials are composites engineered to mold elastic wave dispersion through scattering or local resonances to achieve desired spectral and phase properties such as band gaps around specific frequencies. Phononic crystals are composed of a periodic array of scatterers. The mechanism for the formation of band gaps in phononic crystals is a Bragg-like scattering of waves with wavelength comparable to the dimension of the period of the crystal or the crystal lattice constant [7]. This characteristic limits the use of phononic crystals as low-frequency filters. However, low-frequency filters can be achieved by using a different class of acoustic metamaterials that comprise a series of locally resonating units which are not necessarily periodic. [PERSON] et al. [8] demonstrated that such assemblies are capable of muting waves of wavelengths that are orders of magnitude longer than the lattice constant. By tuning the properties of the individual units and their arrangement, the metamaterial can act as a low-frequency band-gap filter (blocking the incoming elastic energy within certain frequency bands) or wedge (converting the mode and diverting the incident wave). The studies of resonators that followed have been mostly parametric in nature and focused on designing elements with strong frequency-coupled characteristics that will yield band gaps about a given center frequency [9; 10; 11]. As noted above, the field of elastodynamic metamaterials is relatively new, but nonetheless presents a wide variety of resonator design methodologies [9; 10; 11; 12; 13]. An experiment conducted by [PERSON] et al. [14] found that cylindrical rods adhered to a plate waveguide could be used to prohibit the propagation of the A0 Lamb wave mode at low frequencies (<11 kHz). Soon thereafter, a paper by [PERSON] et al. [15] sought to determine what characteristic of the cylindrical rods contributed to the A0 Lamb wave mode band gap. They found that the rods vibrated in an axial mode which applied a \"clamping\"-like effect to the waveguide. That is, the rods would vibrate in such a way that the out-of-plane displacement at their bases was minimized. They also compared the frequencies at which the minimal displacements occurred with the band gaps reported in [PERSON] et al. 's paper and found a good agreement between the two spectra. The spectrum detailed in [PERSON] et al. 's paper was calculated using a vibration model subjected to a harmonic forcing function. Upon further investigation, we found that the frequencies at which minimum displacement occurred were equal to the resonant frequencies of an axially vibrating, fixed-free beam. Since these resonant frequencies have well-known solutions, this finding presented itself as a very straightforward method for designing sub-wavelength resonators for the A0 Lamb wave mode to create band gaps around specific frequencies. However, this approach was only shown to be effective for low-frequency A0 Lamb wave modes which have primarily out-of-plane displacement. The purpose of this article is to extend this concept to design resonators that prohibit the propagation of low-frequency S0 Lamb wave modes and to determine its applicability at higher frequencies. To accomplish this, two resonator designs, one designed based on a frequency matching approach and the other based on the sole concept of clamping, were tested to see how well they can impede the propagation of a 50 kHz S0 Lamb wave. These resonators are hereafter referred to as the frequency-matched resonators and the clamping resonators, respectively. While the design of the frequency-matched resonators is straightforward (based on resonance), the theoretical basis for the design of the clamping resonators is more involved and requires the full attention of a separate publication.