Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

Acknowledgements H.N.G.W. is grateful for support for this work by the ONR (grant number N00014-15-1-2933), managed by D. Shifler, and the DARPA MCMA programme (grant number W91CRB-10-1-005), managed by J. Goldwasser.Peer reviewedPostprintPostprintPostprintPostprin

The effects of tine coupling and geometrical imperfections on the response of DETF resonators

This paper presents a two-degree-of-freedom analytical model for the electromechanical response of double ended tuning fork (DETF) force sensors. The model describes the mechanical interaction between the tines and allows investigation of the effect of a number of asymmetries, in tine stiffness, mass, electromechanical parameters and load sharing between the tines. These asymmetries are introduced during fabrication (e. g., as a result of undercut) and are impossible to completely eliminate in a practical design. The mechanical coupling between the tines induces a frequency separation between the in-phase and the out-of-phase resonant modes. The magnitude of this separation and the relative intensity of the two modes are affected by all the asymmetries mentioned above. Two key conclusions emerge: (i) as the external axial compressive load is increased, the in-phase mode reaches zero frequency (buckling) much faster than the out-of-phase (i. e., operational) mode, resulting in a device with a decreased load range. (ii) During the operation, balanced excitation is essential to guarantee that the out-of-phase mode remain significantly stronger than the in-phase mode, thus allowing sharp phase locked loop locking and hence robust performance. The proposed model can be used to assess the magnitude of asymmetries introduced by a given manufacturing process and accurately predict the performance of DETF force sensors. For the specific sensor characterized in this study, the proposed model can capture the full dynamic response of the DETF and accurately predict its maximum axial compressive load; by contrast, the conventional single-DOF model does not capture peak splitting and overpredicts the maximum load by similar to 18%. The proposed model fits the measured frequency response of the electromechanical system and its load-frequency data with coefficient of determination (R-2) of 95.4% (0.954) and 99.2% (0.992), respectively

A RESONANT TUNING FORK FORCE SENSOR WITH UNPRECEDENTED COMBINATION OF RESOLUTION AND RANGE

This paper presents a double-ended tuning fork (DETF) force sensor with a resolution of 7nN and a range of 0.12N. The resonator has a scale factor of 216 kHz/N, a Q-factor exceeding 60,000 at 3mTorr ambient pressure and a zero-load resonant frequency of 47.6 kHz. The sensor and the complete readout circuit are fully embedded in a compact 65 mm x 52 mm printed circuit board (PCB). The PCB is mounted on a micro-stage and coupled with an off-the-shelf displacement actuator to realize an economical, versatile and robust micro mechanical test frame with unprecedented combination of force and displacement resolutions and ranges

Nanoscale investigation of two-photon polymerized microstructures with tip-enhanced Raman spectroscopy

We demonstrate the use of tip-enhanced Raman spectroscopy (TERS) on polymeric microstructures fabricated by two-photon polymerization direct laser writing (TPP-DLW). Compared to the signal intensity obtained in confocal Raman microscopy, a linear enhancement of almost two times is measured when using TERS. Because the probing volume is much smaller in TERS than in confocal Raman microscopy, the effective signal enhancement is estimated to be ca. 104. We obtain chemical maps of TPP microstructures using TERS with relatively short acquisition times and with high spatial resolution as defined by the metallic tip apex radius of curvature. We take advantage of this high resolution to study the homogeneity of the polymer network in TPP microstructures printed in an acrylic-based resin. We find that the polymer degree of conversion varies by about 30% within a distance of only 100 nm. The combination of high resolution topographical and chemical data delivered by TERS provides an effective analytical tool for studying TPP-DLW materials in a non-destructive way