Order Resonance Research Articles

Planar dual-band bandpass filter with regular harmonic suppression

Abstract This paper presents a dual-band bandpass filter with regular harmonic suppression. The proposed third-order filter consists of two microstrip stepped impedance resonators and single substrate integrated waveguide resonator. The mismatches in their higher order resonant frequencies are utilized to suppress the regular harmonics. The passbands are centered at f1 = 2.4 GHz and f2 = 3.5 GHz with fractional bandwidths of 5% and 7.5%, respectively. The measured midband insertion and return losses are better than 2.55 and 14.5 dB for the first, whereas for the second band, they are better than 1.95 and 14 dB. The filter offers at least 33 dB suppression of first three higher order regular harmonics of f1 and f2.

Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells

This study utilizes a semi-analytical approach to examine the nonlinear dynamic responses of multilayer functionally graded (MFG) cylindrical shells reinforced by FG spiral stiffeners (FGSSs), which may have symmetric or asymmetric angles, under a thermal condition. It is presumed that the temperature is distributed across the thickness direction. The shell includes three layers: an outer ceramic-rich layer, a middle FG layer, and an inner metal-rich layer. By applying classical shell theory (CST), the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the problem of nonlinear vibrations (NVs) has been addressed. Furthermore, the method of multiple scales (MMSs) is applied to investigate the nonlinear vibrational characteristics of the MFG cylindrical shells reinforced by FGSS, particularly focusing on the 1:2:4 internal resonance and the subharmonic resonance of order 1/2. This study finds that FG spiral stiffeners with symmetric or asymmetric angles and ambient temperature significantly affect the vibrational properties of the MFG cylindrical shells reinforced by spiral stiffeners.

Purcell gain equalized zero-mode waveguide

We refresh the design of zero-mode waveguides (ZMWs) by introducing metamaterials that makes the zeroth order resonant mode existence. Of particular importance, the resulting electromagnetic field exhibits nearly constant distribution but not a trivial solution of Maxwell’s equation, showing great advantage to equalize the excitation rate of molecules throughout the waveguides. A closed form expression for the wave impedance is derived which is verified by the finite-difference time-domain simulations. Benefitted from the cavity Purcell effect which is lacking in existing ZMWs, fluorescence amplification and lifetime reduction are simultaneously enhanced. A practical design where the excitation volume reduced down to sub-zeptoliter and the fluorescence lifetime shortened to picosecond scale is illustrated. This result makes single molecule real time (SMRT) sensing of biochemical reactions at biophysically relevant concentrations (~ μM) possible, combining off-the-shelf ultrafast lasers.

Acoustic Effects of Uneven Polymeric Layers on Tunable SAW Oscillators

Surface acoustic wave (SAW) sensors in tunable oscillator configuration, with a deposited polymeric layer, were used to investigate the layer’s impact on the oscillator’s resonant frequency. The SAW oscillators were tuned by means of variable loop amplification. Full-range amplification variation led to a resonant frequency increase of ~1.7 MHz due to the layer’s nonlinear reaction. The layer’s morphology and location resulted in a specific resonant frequency–amplitude dependence. Five types of layers were used to test the causal linkage between the layers’ morphological parameters or positioning and the SAW oscillator’s resonant frequency. The frequency variation trend is almost linear, with a complex minute variation. Small amplitude sigmoids occur at certain attenuation values, due to layer acoustic resonances. Multiple sigmoids were linked with layer resonances of different orders. A good correlation between the layer’s thickness and resonance position was found.

Simulations of non-integer upconversion in resonant six-wave scattering

Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [Malkin and Fisch, Phys. Rev. E 108, 045208 (2023)]. The high order resonance is a unique non-integer multiple of a driving pump frequency resulting in a frequency upshift by a factor of ≈3.73. We demonstrate the presence, unique requirements, and growth of this mode numerically. Through tuning waves to high amplitude, in a mildly underdense plasma, the six-photon process may grow more than other non-resonant but lower order processes. The growth of the high frequency mode remains below the nonlinear growth regime. However, extending current numerical results to more strongly coupled resonances with longer pulse propagation distances suggests a pathway to significant upconversion.

Numerical and experimental analysis on the whirl orbit with inner loop in cracked rotor system

Cracks in rotor systems are generated because of internal as well as external heavy loading conditions. The external loading conditions could be attributed to thermal gradients (such as in turbomachinery) or other environmental conditions that result in cracks developments. The internal loading conditions can be attributed to cyclic fatigue loading during continuous and recurrent shaft's running which is the most common cause for cracks propagation. The presence of cracks in rotor systems induces nonlinearities into the system which affects its whirl response. Many published literature on cracked rotors have indicated that when the rotational speed is at sub-critical resonance of order 1/n (1/2, 1/3,1/4, etc.…) of the critical rotational speed, the fundamental whirl orbit takes patterns including inner loop/loops of order (n-1) or outer loop/loops of order (n+1) depending on the critical whirling direction. The present study investigates the strong impact of the magnitude of unbalance force on whirling pattern with inner loop in a cracked rotor. Numerical analysis is carried out on the mathematical model of the considered cracked rotor. The unbalance force magnitude is observed to be the main factor affecting the inner loop pattern in the whirl orbit rather than the ½ of the critical resonance speed. Accordingly, the appearance of inner loop in shaft's whirl orbit due to crack propagation in the rotor system is found here to be present before and after passing through resonance speed. This inner loop whirl orbit pattern is not restricted to be associated with ½ of the critical rotational speed as believed in plenty of literature. This kind of whirling is observed to be strongly depending on the unbalance force magnitude rather than the subcritical resonance speed. The experimental results also validate the numerical simulation findings. Therefore, the whirl orbits of the cracked rotor can be categorized into pre-resonance whirl orbit (Pr-WO), resonance whirl orbit (R-WO) and post-resonance whirl orbit (Po-WO) based on the magnitude of the unbalance force. The resultant numerical and experimental findings on the whirl orbit with inner loop can provide a robust insight into the cracked rotor whirl behavior.

Evidence for transit-timing variations of the 11 Myr exoplanet TOI-1227 b

TOI-1227 b is an 11 Myr old validated transiting planet in the middle of its contraction phase, with a current radius of 0.85 Rj. It orbits a low-mass pre-main sequence star (0.170 M⊙, 0.56 R⊙) every 27.4 days. The magnetic activity of its young host star induces radial velocity jitter and prevents good measurements of the planetary mass. We gathered additional transit observations of TOI-1227 b with space- and ground-based telescopes, and we detected highly significant transit-timing variations (TTVs). Their amplitude is about 40 min and their dominant timescale is longer than 3.7 yr. Their most probable origin is dynamical interactions with additional planets in the system. We modeled the TTVs with inner and outer perturbers near first and second order resonances; several orbital configurations provide an acceptable fit. More data are needed to determine the actual orbital configuration and eventually measure the planetary masses. These TTVs and an updated transit chromaticity analysis reinforce the evidence that TOI-1227 b is a planet.

Higher-order resonance of single-crystal diamond cantilever sensors toward high f‧Q products

MEMS resonant sensing devices require both HF (f) and low dissipation or high quality factor (Q) to ensure high sensitivity and high speed. In this study, we investigate the resonance properties and energy loss in the first three resonance modes, resulting in a significant increase in f‧Q product at higher orders. The third order resonance exhibits an approximately 15-fold increase in f‧Q product, while the Q factor remains nearly constant. Consequently, we achieved an ultrahigh f‧Q product exceeding 1012 Hz by higher-order resonances in single-crystal diamond cantilevers.

Multi-condition stability analysis and lightweight research of mining wide-body dump truck compartment

This paper proposes a multi-condition optimization method based on single condition optimization and weight. This method analyzes and discusses various working states of the wide-body dump truck and optimize its structure. Firstly, the modal shape and natural frequency of the carriage under modal conditions are analyzed using the finite element method. Combined with the mechanic’s theory, the carriage’s force, deformation, and stress are studied under the turning and partial load conditions. This part provides a basis for subsequent stability analysis and lightweight research. According to the filtering white noise method and differential equation method, the f-class road model and the vehicle system dynamics model are established in MATLAB to study the influence of road vibration on the stability of the dump truck during operation. The carriage vibration data prove that the road vibration causes the low order resonance of the carriage and affects the stability of the dump truck. This part provides a basis for the subsequent stability optimization. Based on the above analysis, a multi-objective genetic algorithm based on the response surface is used to optimize the structural parameters of the carriage under partial load conditions, turning conditions and modal conditions, to realize the optimization of stability, mass, stress and deformation of the carriage. Finally, the entropy weight method is used to fuse the optimization results of the three working conditions. The correctness of the comprehensive optimization results is verified, and the wide-body dump truck carriage optimization is realized, proving the feasibility of the proposed method.

Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions

Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions

Analysis of electromechanical coupling modal and dynamic response characteristics of permanent magnet gear transmission system considering variable load condition

In order to study the influence of electromagnetic (EM) effect and load change on the modal characteristics and dynamic response of gear transmission system driven by permanent magnet synchronous motor (PMSM), a electromechanical coupling dynamic model is established. The composite air gap permeability coefficient is introduced, and the formula of permanent magnet flux linkage under the influence of space harmonic and cogging effect is derived. The variation laws of gear meshing stiffness and bearing support stiffness under the influence of load change are simulated and analyzed. The natural frequency and vibration modal under different load, flux linkage and PI controller gain are revealed. On this basis, the influence of EM effect and load change on the resonance domain is analyzed through frequency sweep analysis and time domain simulation. Results indicate that the 1st order natural frequency and resonance amplitude will increase with the load, and the influence of PMSM EM excitation will gradually dominate. The increase of the flux linkage and speed loop controller gain Kpω will reduce the 1st order natural frequency. When Kpω =123, a new mode appears, and there is a modal transition between the new mode and mode 1 when Kpω =161. The research results can provide theoretical guidance for improving the transmission performance and structure optimization design of the permanent magnet gear transmission system.

Terahertz bow-tie diode based on asymmetrically shaped AlGaN/GaN heterostructures

Asymmetrical shaping of AlGaN/GaN heterostructures containing a conductive layer of two-dimensional electron gas (2DEG) was used for the development of bow-tie (BT) diodes for room temperature terahertz (THz) detection. Considering operation of the THz BT diode in the unbiased mode as preferable for practical applications, we investigated the diodes with an obvious asymmetry of IV characteristics, which was found to be more pronounced with the decrease of an apex width, resulting in the sensitive THz detection. A nonuniform heating of carriers in a metalized leaf of the BT diode was attributed as the main mechanism that caused the rectification of THz waves. The responsivity and noise-equivalent power (NEP) at the fundamental antenna frequency of 150 GHz were up to 4 V/W and 2 nW/√Hz, respectively. Such high sensitivity of BT diodes allowed us to measure for the first time the response spectrum of the asymmetric BT antenna demonstrating fundamental and higher order resonances in good agreement with finite-difference time-domain simulation data in a broad spectrum range. The detailed investigation of the lowand high-frequency noise characteristics of AlGaN/GaN BT diodes revealed that only thermal noise needs to be considered for the unbiased operation, the value of which was relatively low due to a high density of 2DEG enabling low resistivity values. Moreover, we observed that the responsivity of BT diode scales with its resistance, revealing that tapering of the diode apex below a few microns could be ineffective in applications which require low NEP values.

Hamiltonian Hopf bifurcations near a chaotic Hamiltonian resonance

The 1:2:3 Hamiltonian resonance is one of the four genuine first order resonances which is non-integrable. For this resonance, chaotic behavior of the normal form has been shown due to the existence of a transverse homoclinic orbit on the energy manifold. Considering the detuning parameters, in the mirror symmetric cases of the Poisson manifold, by a reduction theory and computing the classical normal form of non-degenerate Hamiltonian Hopf bifurcation, we show there are just non-degenerate Hamiltonian Hopf bifurcations. However in the general case by considering some case studies and specially of FPU (Fermi–Pasta–Ulam) chains for a fiber passaging 1:2:3 resonance, we may deal with complex dynamics and specially Hamiltonian Hopf bifurcation in a complicated region. Actually, we can see some special Krein collisions in a complex region.

MEMS Electrostatically Driven Coupled Beam Filter Banks.

MEMS bandpass filters based on electrostatically driven, mechanically coupled beams with in-plane motion have been demonstrated up to the VHF band. Filters higher than second order with parallel plate drives have inherent tuning difficulties, which may be resolved by adding mass-loaded beams to the ends of the array. These beams deflect for DC voltages, and thus allow synchronized electrostatic tuning, but do not respond to in-band AC voltages and hence do not interfere with dynamic synchronization. Additional out-of-band responses may be damped, leaving the desired response. The principle is extended here to close-packed banks of filters, with adjacent arrays sharing mass-loaded beams that localize modes to sub-arrays. The operating principles are explained using a lumped element model (LEM) of the equations of motion in terms of resonant modes and the reflection of acoustic waves at discontinuities. Performance is simulated using the LEM and verified using the more realistic stiffness matrix method (SMM) for banks of up to eight filters. Similar or dissimilar filters may be combined in a compact arrangement, and the method may be extended to higher order resonances and alternative coupled resonator systems.

Nonlinear Dynamic Analysis of an Electrostatically Actuated Clamped-Clamped Beam and Excited at the Primary and Secondary Resonances.

This work investigates the primary and secondary resonances of an electrostatically excited double-clamped microbeam and its feasibility to be used for sensing applications. The sensor design can be excited directly in the vicinity of the primary and secondary resonances. This excitation mechanism would portray certain nonlinear phenomena and it would certainly lead in increasing the sensitivity of the device. To achieve this, a nonlinear beam model describing transverse deflection based on the Euler-Bernoulli beam theory was utilized. Then, a reduced-order model (ROM) considering all geometric and electrical nonlinearities was derived. Three different techniques involving time domain, fast Fourier transforms (FFTs), and frequency domain (FRCs) were used to examine the appearance of subharmonic resonance of order of one-half under various excitation waveforms. The results show that higher forcing levels and lower damping are required to activate this resonance. We note that as the forcing increases, the size of the instability region grows fast and the size of the unstable region increases rapidly. This, in fact, is an ideal place for designing bifurcation inertia MEMS sensors.

Holistically Nested Edge Detection and particle filtering for subtle vibration extraction

Extracting and analyzing subtle motion via optical sensing techniques is becoming a more important research area within the vibration community. Computer vision approaches and machine learning architecture have been adopted to contest the complexity concerning hand instrumentation of sensors. Pre-treatment using a stochastic pattern for optical analysis or traditional wired sensing is not always permitted for large structures. In this work, Holistically Nested Edge Detection (HED) is utilized to highlight high-spatial-frequency content features in images for structural dynamic analysis. Following the accentuation of edge features, phase-based motion magnification (PMM) is used to amplify motion that is not visible to the naked eye. This permits the band-passing of higher order resonant frequencies for structural dynamic evaluation. Implementation of two-dimensional particle filtering (PF) is utilized to track the accentuated edge features in the presence of ghosting artifacts that appear post magnification. Within this work, compared to traditional edge-thresholding, the combination of HED and PF (HED-PF) is more proficient to handle noise and ultimately improves magnified image quality and modal parameter extraction. Uncertainties related to using PF for vibration measurement are analytically presented to provide guidance on the behavior of the algorithm. To demonstrate the effectiveness of HED-PF, experimental modal testing takes place on both a tier-structure and cantilever beam to demonstrate the approaches’ capability in handling varying sorts of excitation. Finally, introduction of background occlusions and non-ideal lighting scenarios are used to test the limitations of the approach. Ultimately, this will highlight HED-PF’s robust tracking capabilities compared to the current state of the art.

Pseudo-resonance phenomenon of valveless piezoelectric pump

Volumetric piezoelectric pumps are widely used in the field of microfluidic drive due to their simple structure, flexible design, and absence of magnetic interference. As driven by the volume change of the pump chamber, the majority of this kind of pumps work under the first order resonance frequency, where the volume change is the largest. However, the experimental parts or data of many studies reflect a phenomenon that a flow rate peak exists in the non-resonance frequency range. This phenomenon has not been studied or explained in depth, and goes against conventional vibration theories. In this study, we define this phenomenon as the pseudo-resonance phenomenon, and the corresponding flow rate peak is named as the pseudo-resonance flow rate peak. First, a non-single-channel composite tapered tube valveless piezoelectric pump (NCTVP) was designed, which reproduced the pseudo-resonance phenomenon reported in the literature. Through displacement measurement experiments, it was demonstrated that the vibration mode of the piezoelectric vibrator was B00 mode when the pseudo-resonance phenomenon occurred. Then, frequency sweeping experiments and flow field observation experiments were conducted, it can be obtained that the pseudo-resonance phenomenon is caused by the reaction force of the water to the piezoelectric vibrator, and the reaction force is generated by the impact of two streams. Finally, based on the experiment results, a theoretical model was established; it was deduced that the first order resonance flow rate peak was caused by the flow resistance difference between the forward and reverse flows of the tapered tubes in NCTVP, and that the pseudo-resonance flow rate peak was caused by the water hammer effect. By applying the pseudo-resonance phenomenon, another flow rate peak was obtained in the non-resonance frequency range without changing the mechanical structure, which can enable piezoelectric micro nano pump to obtain extra flow rate or pressure without changing the constraint boundary conditions.

Broadband muffler with acoustic bright and dark modes for refrigerator noise control

In the present paper, a system composed of a two-port waveguide and two quarter wavelength tubes (QWTs) with different cross section sizes is proposed. The narrow tube performs the dark mode and the wide tube plays the bright mode. Perfect absorption can be achieved at the optimal interval between the tubes when sound waves are incident from the port close to the narrow tube. Besides first order resonance, the system with two QWTs has more high-order resonances in the concerning frequency range, which is demonstrated by simulation and verified by experiments. A strategy of resonance frequency tuning is further adopted to develop a muffler which can achieve near-perfect broadband absorption. Moreover, the straight QWTs are folded so that a compact structure is obtained. A sample of the muffler is fabricated and tested. A transmission loss (TL) of 5.2 dBA is obtained in the frequency range up to 6400 Hz. Except for the target frequency region, high-order resonances also contribute notably from 1800 to 6400 Hz. The design process is applied to a refrigerator, and noise reductions of 4.2 dBA and 2.6 dBA are achieved in the frequency range up to 6400 Hz on both sides of the compressor compartment. Due to the flexibility of the folded QWTs and distinct contributions of the high-order resonances, an extensive application of the muffler can be expected.

Analytic solutions of linear neutral and non-neutral delay differential equations using the Laplace transform method: featuring higher order poles and resonance

In this article, we extend the Laplace transform method to obtain analytic solutions for linear RDDEs and NDDEs which have real and complex poles of higher order. Furthermore, we present first-order linear DDEs that feature resonance phenomena. The procedure is similar to the one where all of the poles are order one, but requires one to use the appropriate modifications when using Cauchy’s residue theorem for the poles of higher order. The process for obtaining the solution relies on computing the relevant infinite sequence of poles and then determining the Laplace inverse, via the Cauchy residue theorem. For RDDEs, the poles can be obtained in terms of the Lambert W function, but for NDDEs,the complex poles, in most cases, must be computed numerically. We found that an important feature of first-order linear RDDES and NDDES with poles of higher order is that it is possible to incite the resonance phenomena, which in the counterpart ordinary differential equation cannot occur. We show that despite the presence of higher order poles or resonance phenomena, the solutions generated by the Laplace transform method for linear RDDEs and NDDEs that have higher order poles are still accurate.

Agency and Strategy: Chastity Exemplars in an Early Qing Anthology

This article reads exemplary biographies of chaste widows and women who committed suicide to preserve their chastity in the 1656 Yuding Nei ze yanyi 御定内則衍義 (Imperially Commissioned Expanded Meaning of the “Inner Standards”) by Fu Yijian 傅以漸 (1609–1665, jinshi 1646). In this anthology commissioned by the Shunzhi emperor on behalf of his mother, Fu's commentary emphasizes both the agency of individual women and the mutual resonance of personal virtue and political order. He not only praises the exemplars' virtue but also their agency, intelligence, and strategy. He explicitly acknowledges the different factors that could make chastity more difficult and states that in some situations, multiple courses of action were possible. He comments both on his heroines' political ability and on the political importance of recognizing chastity. Finally, in a context where women's chastity was often linked to political loyalism to the fallen Ming, Fu uses these biographies in a very different way: he presents chastity exemplars of conquered dynasties as foils to the decadent society around them. His commentary is thus recognizably tailored to his audience's circumstances as Manchu and Mongolian imperial women and his own as a Chinese male scholar at the beginning of the Qing.