Amplitude-modulated Mode Research Articles

Optimization of a vibro-impact damper design using MATLAB tools

The paper studies the dynamics of a vibro-impact system consisting of a main (primary) structure and a vibro-impact damper coupled to it. A vibro-impact damper is a vibro-impact nonlinear energy sink (VI NES). The optimal damper design should provide the best vibration mitigation for the primary structure. The optimization procedures for finding the optimal NES design are carried out using standard MATLAB tools. We used different MATLAB programs, namely surf program, which graphically shows the ranges of parameter pairs to be optimized; fminsearch and fminconprograms, which search for local minima of the objective function. It is shown that the optimization procedure itself is ambiguous and contains a sufficient amount of arbitrariness. Its result is also ambiguous. It is due to the presence of the many possible sets of damper parameters that can provide maximum mitigation of the main structure vibrations. We do not use the genetic algorithm gabecause it selects random intermediate results and yields randomly selected parameter sets from the optimal parameters manifold. Setting the objective function and its parameters plays a crucial role in the optimization process. We have chosen the maximum total energy of the primary structure as the objective function. Each resulting variant of the damper parameter set should be carefully tested and analyzed. We compared the five obtained optimal designs for dampers with two different masses. When analyzing them, we observed different motion modes, namely periodic modes of different periodicity with different number of impacts per cycle, with different ratio of bodies motion periods: 1:1 resonance with resonance capture and 2:1 resonance; amulti-periodic mode with many impacts per cycle, which turned out to be an amplitude-modulated mode – Amplitude Modulated Signal . The final decision on the optimal damper design may be made taking into account various engineering considerations regarding its mass and other parameters. It should be based on the options obtained as a result of the optimization procedure.

Noise analysis and modeling for a digital control architecture for Lissajous frequency-modulated MEMS gyroscope with amplitude-modulated readout

We report a digital control architecture that demodulates both amplitude-modulated (AM) and frequency-modulated (FM) rate information simultaneously from a gyroscope working in Lissajous frequency-modulated (LFM) mode. The angular rate information is derived from both quadrature (X and Y) resonance modes of the gyroscope simultaneously. A noise model for the AM signal processing channel of the LFM gyroscope is built, analyzed and compared with that of a conventional AM gyroscope, which shows that methods to improve the performance of the conventional AM gyroscope can also be applied to the AM signal processing channel of the LFM gyroscope. The angular rate output obtained from the AM information of the LFM gyroscope has better noise characteristics, which therefore supplements the low precision inadequacy of the FM signal channel of the LFM mode. Tests on the same gyroscope working in different control architectures are conducted. The angle random walk (ARW) and bias instability (BI) of the AM channel of the proposed architecture are 0.51 deg √h−1 and 1.8 deg h−1, respectively, which are better than the results obtained from the FM channel in the same architecture, with values of 0.99 deg √h−1 and 4.3 deg h−1, respectively. Also ARW amd BI of the same gyroscope working in conventional AM mode is 0.50 deg √h−1 and 5.2 deg h−1, respectively.

Identification and suppression of driving force misalignment angle for a MEMS gyroscope using parametric excitation

We report for the first time an implementable method to identify and suppress the driving force misalignment angle for a MEMS gyroscope working either in amplitude modulated (AM) or Lissajous frequency modulated (LFM) mode using parametric excitation. By introducing driving force misalignment angle into gyroscope dynamic equations, we illustrate that gyroscope angular rate output is affected by driving force misalignment angle and cross-axis damping jointly. We propose parametric excitation as a way to both identify and calculate the driving force misalignment angle. The identification results for a gyroscope working in both AM and LFM mode are similar, which indicates the effectiveness of the proposed identification method. Instead of using traditional amplitude control loop by adjusting the driving force, we do the automatic gain control by adjusting the parametric pump voltage so that a fixed drive voltage can be used, which also indicates fixed force coupling. Experimental results show that after suppression, the bias instability (BI) of AM mode is improved from 4.7° h−1 to 2.3° h−1 and the BI of LFM mode is improved from 1.4° h−1 to 0.9° h−1 which is the lowest result reported for LFM gyroscope.

A singular vorticity wave packet within a rapidly rotating vortex: spiralling versus oscillating motions

This paper considers a free vorticity wave packet propagating within a rapidly rotating vortex in the quasi-steady regime, a long time after the wave packet strongly and unsteadily interacted with the vortex. We study a singular, nonlinear, helical and asymmetric shear mode inside a linearly stable, columnar and axisymmetric vortex on the $f$-plane. The amplitude-modulated mode enters resonance with the vortex at a certain radius $r_{c}$, where the phase angular speed is equal to the rotation frequency. The singularity in the modal equation at $r_{c}$ strongly modifies the flow in the three-dimensional helical critical layer, the region around $r_{c}$ where the wave/vortex interaction occurs. This interaction generates a vertically sheared three-dimensional mean flow of higher amplitude than the wave packet. The chosen envelope regime assumes the formation of a mean radial velocity of the same order as the wave packet amplitude, leading to the streamlines exhibiting a spiral motion in the neighbourhood of the critical layer. Radar images frequently show such spiral bands in tropical cyclones or tornadoes. Through matched asymptotic expansions, we find an analytical solution of the leading-order equations inside the critical layer. The generalized Batchelor integral condition applied to the quasi-steady, three-dimensional motion inside the separatrices yields a leading-order, non-uniform three-dimensional vorticity. The critical-layer pattern, strongly deformed by the mean radial velocity, loses its symmetries with respect to the azimuthal and radial directions, which makes the leading-order mean radial wave fluxes non-zero. Finally, a stronger wave/vortex interaction occurs with respect to previous studies where a steady neutral vortical mode or an envelope of larger extent was involved.

The polarization characteristics of ELF/VLF waves generated via HF heating experiments of the ionosphere by EISCAT

This paper presents the experimental results of modulation and heating of the ionosphere using the European Incoherent Scatter facility in Troms ϕ, Norway, heating facility. The frequency characteristics of the excited extremely low frequency (ELF)/very low frequency (VLF) radiation sources in the amplitude modulated (AM) and dual-beam beat-wave (BW) modes are compared, and the polarization of the horizontal ELF/VLF magnetic field received at 15 km from the heating facility is studied. The results show that in the AM mode, the amplitude of the ELF/VLF signal decreases as the radiation frequency increases when the amplitude of the ELF/VLF signal reaches the maximum at 2017 Hz. In the BW mode, the maximum appears at 2017 Hz, but the overall amplitude of the ELF/VLF signal increases as the radiation frequency increases. The AM and BW modes have different frequency characteristics on ELF/VLF radiation sources formed by modulation and heating of the ionosphere. When the frequency is low, the amplitude of the ELF/VLF signal excited by the AM mode is greater than that excited by the BW mode, but as the frequency increases, the BW mode performs better than the AM mode. Under the same background conditions, the polarization characteristics of the ELF/VLF radiation signals excited by the AM and BW modes are different. The former tends to produce circularly polarized waves, while the latter produces linearly polarized waves.

Practical loss tangent imaging with amplitude-modulated atomic force microscopy

Amplitude-modulated (AM) atomic force microscopy (AFM), also known as tapping or AC mode, is a proven, reliable, and gentle imaging method with widespread applications. Previously, the contrast in AM-AFM has been difficult to quantify. AFM loss tangent imaging is a recently introduced technique that recasts AM mode phase imaging into a single term tan δ that includes both the dissipated and stored energy of the tip-sample interaction. It promises fast, versatile mapping of variations in near-surface viscoelastic properties. However, experiments to date have generally obtained values larger than expected for the viscoelastic loss tangent of materials. Here, we explore and discuss several practical considerations for AFM loss tangent imaging experiments. A frequent limitation to tapping in air is Brownian (thermal) motion of the cantilever. This fundamental noise source limits the accuracy of loss tangent estimation to approximately 0.01<tan δ<5 in air. In addition, surface effects including squeeze film damping, adhesion, and plastic deformation can contribute in a manner consistent with experimentally observed overestimations. For squeeze film damping, we demonstrate a calibration technique that removes this effect at every pixel. Finally, temperature-dependent imaging in a two-component polymeric film demonstrates that this technique can identify temperature-dependent phase transitions, even in the presence of such non-ideal interactions. These results help understand the limits and opportunities not only of this particular technique but also of AM mode with phase imaging in general.

Extended Bandwidth Lorentz Force Magnetometer Based on Quadrature Frequency Modulation

In this paper, a Lorentz force magnetometer demonstrates quadrature frequency modulation operation. The Lorentz force magnetometer consists of a conventional 3-port resonator, which is put into oscillation by electrostatic driving and sensing. The bias current flowing through the resonator is proportional to the displacement, and generates Lorentz force in quadrature with the electrostatic force. As a result, the Lorentz force acts as an equivalent spring and the magnetic field can be measured by reading the change in oscillation frequency. The sensor has a sensitivity of 500 Hz/T with a short-term noise floor of 500 nT $\surd $ Hz. The bandwidth of the sensor is increased to 50 Hz, a factor of 12 greater than that of the same resonator operating in amplitude-modulated mode. The short-term noise floor within 50-Hz bandwidth is comparable with CMOS Hall-effect sensors.

On the reduction of the non-diamond phase in nanocrystalline CVD diamond films

We present photocurrent spectra of nominally undoped nanocrystalline diamond (NCD) films grown on glass substrates by hot filament (HF) and microwave (MW) plasma enhanced chemical vapor deposition (CVD). The spectra were measured in a broad optical range (200–2000 nm) by dual-beam photocurrent spectroscopy (DBP) and Fourier-transform photocurrent spectroscopy (FTPS) in amplitude modulated step scan mode. The NCD films with carefully oxidized surface show photosensitivity and high dark resistivity. Unlike single crystal type IIa diamond with the photonization threshold at 5.5 eV, the photocurrent spectra of NCD films are dominated by the “non-diamond phase” with the photo-ionization threshold at about 0.8 eV. Some HF CVD samples have lower sub-band gap absorption (non-diamond phase contamination). The non-diamond phase content increases after annealing at elevated temperature. The non-diamond phase content can be reduced by exposing NCD to hydrogen plasma at temperature below 350 °C.

The influence of thermal annealing on the electronic defect states in nanocrystalline CVD diamond films

AbstractThe photosensitive, nominally undoped nanocrystalline diamond (NCD) films were grown on insulating substrates at a relatively low temperature below 600 °C. The NCD films were exposed to the hydrogen plasma and then briefly to the oxide plasma. This treatment significantly reduced the surface conductivity and enhanced the bulk photosensitivity. The broad optical spectral range (200–2000 nm) photocurrent and optical absorption spectra were measured by the dual‐beam photoconductivity (DBP), Fourier‐transform photocurrent spectroscopy (FTPS) in amplitude modulated step scan mode, optical transmittance and reflectance and photothermal deflection spectroscopy (PDS). The photoionization cross section spectrum of our NCD films is dominated by the non‐diamond phase with the photo‐ionization threshold energy at about 1 eV. At 350 °C the thermal annealing increased the concentration of defects related to the non‐diamond phase and deteriorated the UV photosensitivity. The significant increase of the optical absorption was observed after annealing at 500 °C. The hydrogenation can reduce to some extend the defects created by the thermal annealing. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

AM and high-harmonic FM laser mode locking

We demonstrate a new technique of active mode locking that combines amplitude-modulated (AM) mode locking at the cavity fundamental repetition rate with frequency-modulated (FM) mode locking at a high harmonic. This method combines the advantages of pulse shortening by high-harmonic mode locking while preserving the higher peak powers available at the fundamental repetition rate. We demonstrate this technique using a Nd:YAG laser that is simultaneously AM mode locked at 80 MHz and FM mode locked at the 22nd harmonic (1.76 GHz). Pulses as short as 16 ps with a peak power of 6.25 kW were measured.

The quadratic property of the human auditory sensation induced by focused amplitude-modulated ultrasound

Three modes of low-intensity (≤100 mW/cm2) monotone amplitude-modulated (AM) ultrasound are focused on the region of the human cochlear and the human auditory response patterns are observed. The AM ultrasonic signal is defined as f(t) cos ωt, where f(t) is the monotone modulation signal and ω is the angular frequency of the ultrasonic carrier. The three modes of f(t) cos ωt are: (1) carrier-suppressed AM mode, cos Ωt cos ωt; (2) square-rooted AM mode, (1+cos Ωt)1/2 cos ωt; (3) standard AM mode, (1+cos Ωt) cos ωt, where Ω is the angular frequency of the monotone. They are applied in sequence to stimulate the subject. The pattern of auditory sensation of the subject to the ultrasonic stimulations follows the square of the modulation signal, f2(t), which are: (1) cos2 Ωt; (2) [(1+cos Ωt)1/2]2; (3) (1+cos Ωt)2. The subject senses the pure tone of 2Ω for the first mode of the ultrasonic stimulation, the pure tone of Ω for the second mode of the ultrasonic stimulation, and the mixed tones of Ω with relatively weaker intensity of 2Ω for the third mode of the ultrasonic stimulation. The response patterns reveal that the AM ultrasound induced human auditory sensation has the property of f2(t). This quadratic property is similar to the parametric demodulation of the focused AM ultrasound in water which has the form of d/dt[f2(t)], (B≫1) [Novikov, NonlinearUnderwaterAcoustics (Acoustical Society of America, Woodbury, NY, 1987), pp. 86–95]. [Work partially supported by Electro-Stim Corp.]