Natural Resonant Modes Research Articles

A Comprehensive Seismic Monitoring of the Pillar Threatening the World Cultural Heritage Site Chauvet‐Pont d'Arc Cave, Toward Rock Damage Assessment

AbstractFragile geological features must undergo frequent structural health assessments to prevent catastrophic failure events. The mechanical behavior of natural sites is largely guided by vibrations of the earth and environmental exposure, but damage is rarely assessed, except empirically. The Chauvet‐Pont d’Arc cave, a UNESCO World Heritage Site, represents a shining example of fragility that would benefit from monitoring. It is overhung by a rock column known as Abraham's pillar that extends out from the cliff like a natural tuning fork. For this study, we monitored dancing movements of this pillar for over 2 years to analyze its elastic response to weather conditions. Using ambient‐seismic‐noise‐based methods, we identified the pillar's first two natural resonance modes. Through extensive monitoring of the site, we observed the striking temporal evolution of these two resonance frequencies on hourly, daily, seasonal, and pluriannual scales in response to changes in air temperature and insolation. Based on thermo‐acousto‐elastic modeling with a simplified 3D geometric structure, we determined how thermally‐induced stress stiffening affects the rock material, by applying convective and radiative heat fluxes to the model. From the results obtained, we suggest a novel quantitative method based on daily observations that can estimate the level of damage within the rock material. Our work provides a foundation for distinguishing between reversible processes and damage for hazard studies in the frame of climate change. Such knowledge is crucial not only for the preservation of heritage sites but also for enhancing risk assessment protocols and informing conservation efforts worldwide.

On the use of combined surface integral equations for the analysis of high contrast penetrable objects

AbstractAccurate solutions of electromagnetic scattering problems involving objects made of materials with large permittivity contrasts are considered. Problems are formulated with different commonly used combined surface integral equations (SIEs). All studied formulations are discretised through the method of moments with rooftop basis functions over flat quadrilaterals represented as bilinear surfaces, with razor‐blade functions being used for the testing procedure. The accuracy of the results is first investigated in detail for several frequencies and permittivity values using different numerical measures. It is shown that numerical instabilities may appear at frequencies corresponding to the physical resonances of the object, in particular in the near field and for large material parameter contrasts. The example of a dielectric resonator (DR) with cubic geometry is considered for the purpose of analysis, especially since to achieve smaller DR type antennas, it is necessary to use higher contrast materials. The accuracy of the combined surface integral equations to determine the natural resonant modes of the DR is investigated. It is found that the resonance modes can be accurately determined by exploring the radar cross section (RCS) of the DR in free space only if a proper combination of the electric and magnetic fields equations is applied.

Numerical study on knock characteristics and mechanism of a heavy duty natural gas/diesel RCCI engine

In this paper, the knock phenomenon of reactivity controlled compression ignition (RCCI) engine fueled with natural gas/diesel was numerically studied. The knock mechanism of the RCCI engine is explained and the strategy of suppressing knock is put forward. The knock characteristics were studied by setting monitoring points in different spaces positions of the cylinder. The results show that the pressure oscillation amplitude at the center and edge of the cylinder is large under the high load condition of RCCI engine. In addition, the knock mechanism was studied by using pressure difference method, maximum amplitude of pressure oscillation, important components, temperature isosurface, pressure fluctuation and heat release rate. The results show that the knock of RCCI engine is mainly caused by the end-gas auto-ignition. The pressure difference results show that the characteristic frequency is consistent with the natural resonance mode (0,1) of the cylindrical combustion chamber. On this basis, the effects of pilot oil injection timing and compression ratio on engine knock are further studied. It is confirmed that diesel knock and end-gas knock may exist simultaneously in the same cycle when RCCI engine knock occurs. And diesel knock occurs before top dead center, and end-gas knock occurs after top dead center. Proper adjustment of pilot oil injection timing and reduction of compression ratio can effectively suppress engine knock.

Wall-Meshed Cavity Resonator-Based Wireless Power Transfer Without Blocking Wireless Communications With Outside World

In order to address the issue of wireless communication signal blocking in the traditional cavity resonance wireless power transfer (CR WPT), a wall-meshed cavity resonator constructed of the meshed metallic walls is proposed together with an analytical design method. This cavity resonator can not only generate and confine the electromagnetic waves of natural resonant modes inside the cavity resonator, but also support wireless communications with outside. The wall-meshed cavity resonator is analytically designed by the known theoretical equations without time-consuming optimizations and verified by electromagnetic simulations and experiments. The results show that the proposed CR WPT system can achieve simultaneous wireless power transfer in the cavity and wireless communications with outside. The maximum power transfer efficiency is higher than 85%. The power transfer efficiency exceeds 60% within about 70% areas inside the wall-meshed cavity. For wireless communication signals passing through the wall-meshed cavity, the attenuation at 2.1 GHz (4G), 2.45 GHz (Wi-Fi), and 3.5 GHz (5G) is about 6.0 dB, 5.1 dB, and 3.8 dB, respectively. Additionally, the safety performance of the proposed CR WPT system is numerically investigated by the specific absorption rate analysis of a human torso model.

Synthesis, Control, and Excitation of Characteristic Modes for Platform-Integrated Antenna Designs: A design philosophy

Electrically compact antennas that exploit the characteristic modes (CMs) of their platforms have recently attracted much attention in military and terminal device antenna research. Conventionally, to design an antenna on a platform, the antenna element is first synthesized in a stand-alone manner, without explicitly considering the platform structure. Electromagnetic compatibility issues may arise since the size of the antenna is usually comparable to the wavelength of operation. In contrast, CM-based platform-integrated antenna design takes advantage of the natural resonant modes of the platforms to achieve the desired properties, such as multiband/wideband operation, polarization or pattern reconfigurability, high isolation between ports (in the case of multiport antennas), and achievement of the specified gain.

A newly MEMS vacuum gauge with multi-modes for low vacuum measurement

A Micro-Electro-Mechanical-System (MEMS) resonant vacuum gauge (RVG) based on the electrostatic nonlinearity for low vacuum measurement was introduced. Different natural resonance modes of the sensing unit were driven for vacuum measurement. There were three modes driven under different pressure to measure the relationships between resonance frequency and gas pressure, including the second-order resonant mode (the second mode in short), the third mode and the fourth mode. The second mode was independent of gas pressure variation. The third mode measurement range nearly covered 1–500 Pa, and the linear fitting showed an excellent output linearity (R2 = 0.995) and resolution (more than 0.5 Pa). The measurement range of the fourth mode covered 1–4000 Pa, and the fitting results showed high linearity (R2 = 0.997) and about 1 Pa of resolution.

Analysis of Modal Excitation in Wideband Slot-Loaded Microstrip Patch Antenna Using Theory of Characteristic Modes

In this communication, modal excitation of characteristic modes in the ultrawideband (UWB) slot-loaded microstrip patch has been investigated. A comprehensive analysis of modal excitation due to straight and L-probe feed reveals physical insight about antenna behavior due to feeding structure. This communication analyzes the modal effect of feed inclusion in two steps, i.e., before and after excitation. The application of characteristic modes to antenna bandwidth enhancement serves as a demonstration of the broad utility of the theory of characteristic modes (TCM), where multiple resonant modes participate simultaneously to broaden the bandwidth. This communication also examines the potential capability of natural resonant modes to contribute to the impedance bandwidth upon excitation. The slot-loaded antenna exhibits 35% impedance bandwidth with the straight probe feed, but bandwidth increased up to 81% by changing the feed to L-probe. Hence, impedance bandwidth has been enhanced up to 46% (approx) by exciting particular resonant modes via changing and optimizing a feed structure.

Experimental investigation on special modes with narrow amplification diagrams in harbor oscillations

In studies on harbor oscillations, modes with extremely narrow amplification diagrams are common. The numerical simulation results obtained by Bellotti (2007) and Ma et al. (2020) for these modes (termed as extreme modes) based on regular waves are first validated by physical experiments in this study. Moreover, we investigate whether the extreme mode can be induced by irregular waves and solitary waves. Results show that considering an external force of steady-state waves, extreme modes cannot be triggered in the laboratory as they require an enormous amount of time (such as hundreds of wave periods) to reach full development. This phenomenon is consistent with the research of Bellotti (2007) and Ma et al. (2020). For an external force of solitary waves, extreme modes can be excited. The solitary wave enters and leaves the harbor within a brief period. Some energy is then trapped within the harbor and distributes over various wave components within a very short time, while a majority of the energy concentrates near the natural (resonant) modes of the harbor (i.e., resonant modes are triggered without experiencing the same development process as in the cases induced by steady-state waves). The phenomenon where extreme modes can be triggered by solitary waves is observed and explained in this work for the first time. Once extreme modes are triggered, they decay very slowly. Tsunamis are usually studied through solitary waves and are the main contributor to destructive harbor oscillations, though they are uncommon relative to irregular oceanic waves. Hence, the negative effect of extreme modes on vessels and mooring systems needs to be further studied.

Quasinormal-Mode Non-Hermitian Modeling and Design in Nonlinear Nano-Optics

Based on quasinormal-mode theory, we propose a novel approach enabling a deep analytical insight into the multi-parameter design and optimization of nonlinear photonic structures at subwavelength scale. A key distinction of our method from previous formulations relying on multipolar Mie-scattering expansions is that it directly exploits the natural resonant modes of the nanostructures, which provide the field enhancement to achieve significant nonlinear efficiency. Thanks to closed-form expression for the nonlinear overlap integral between the interacting modes, we illustrate the potential of our method with a two-order-of-magnitude boost of second harmonic generation in a semiconductor nanostructure, by engineering both the sign of $\chi^{(2)}$ at subwavelength scale and the structure of the pump beam.

Modification of higher order natural mode in metamaterial loaded patch antenna

Usually microstrip patch antennas radiate at the broadside direction. Instead of the broadside direction, if a patch antenna radiates in a different direction in a controlled way, it may open a novel way of antenna array miniaturisation. For conventional patch antennas, higher order resonance modes are usually considered entirely useless due to the splitting of the maximum radiated power. In this work, a generic process of modifying the higher order natural resonance mode has been proposed by using metamaterial. Owing to this modification, maximum radiation in a particular direction has been achieved while the gain of the side lobe has been decreased at a great instinct. Furthermore, the main lobe is far shifted than the conventional broadside direction. Interestingly, the proposed dual band antenna radiates in two different directions in two different radiating bands, which can be very useful for the possible miniaturisation of printed antenna array.

On Characteristic Eigenvalues of Complex Media in Surface Integral Formulations

Although the surface integral equations (SIEs) have been extensively used in solving electromagnetic problems of penetrable objects, there are still open issues relating to their application to the Theory of Characteristic Modes (CMs). This letter demonstrates that when an SIE is used to solve for the CMs of a dielectric or magnetic object, the resulting eigenvalues are unrelated to the reactive power of the object, unlike the eigenvalues of perfect electric conductors. However, it is proposed that the classical eigenvalues, which provide useful physical insights, can be extracted from the SIE CM solution using Poynting's theorem. Large discrepancies between the SIE CM eigenvalues and the proposed eigenvalues, as well as the eigenvalue-derived characteristic quantities, are highlighted using a numerical example. The modal resonances, as predicted by the proposed eigenvalues, closely match those obtained for natural resonance modes.

Analysis of Electromechanical Interaction in Aircraft Generator Systems

The supply of electrical power is usually achieved by a generator driven from a prime mover by some form of mechanical drivetrain. Such an electromechanical system will have natural resonant modes in both the electrical and mechanical subsystems. The electrical generator provides a coupling between the subsystems, transferring not only useful power, but also disturbances between the electrical and mechanical domains. These disturbances may excite resonances resulting in cross-domain (electromechanical) interaction. This can lead to lifetime reduction in the mechanical components and instability in the electrical network, resulting in poor reliability for the wider system and potentially catastrophic component failure. Electromechanical interaction is particularly critical in power generation systems onboard aircraft, because the generator is driven by a gas turbine via an inherently low-stiffness drive train. It is then critical to identify electromechanical interaction at the design stage so that these issues can be avoided. However, predicting the occurrence of interaction through simulation is challenging, requiring multidomain models operating with different time scales. This paper analyzes an aircraft auxiliary power offtake to produce a reduced-order mechanical drivetrain model, allowing the modal frequencies to be predicted and cross-domain interactions to be modeled. A purpose-built electromechanical test platform is used to validate the model and demonstrate how electrical disturbances are passed through the generator to the mechanical system and affect the electrical network. Future research will use the test bed to demonstrate strategies for avoiding or suppressing unwanted interactions.

Evolution of microwave ferromagnetic resonance with magnetic domain structure in FeCoBSi antidot arrays

Magnetic domain structure of FeCoBSi antidot array thin films of varying thickness were characterized using surface magneto-optic Kerr effect. Vibrating sample magnetometry and microstrip transmission line measurements helped to associate the microwave magnetic analysis of the antidot arrays with hysteresis studies. The domain structure evolution from quasi-continuous domains to strip domains induced by the competing exchange and dipolar interaction resulted in the change of ferromagnetic resonance from multi-band to single-band. Hence, the mechanisms of multi-resonance are proposed to be related to domain wall motion, natural resonance and spin wave modes. This phenomenon can be used to control the magnetization dynamics in spin wave devices.

Experimental study natural resonance modes of sound of a hydrophone and sediment discharge measurement

Experimental study natural resonance modes of sound of a hydrophone and sediment discharge measurement

Optical measurements of self-induced oscillations

High speed digital holographic interferometry is used to measure the self-induced mechanical oscillations produced by frequency signals near the first natural resonance mode of a rectangular polyester membrane. The external excitation produces very low mechanical amplitude levels in the membrane. This non-invasive optical technique has high temporal and spatial resolution allowing large data acquisition and hence allowing the processing of thousands of recorded images acquired in a CMOS camera set at 5000 frames per second (fps).

The improvement of microwave properties for Co flakes after silica coating

Sub-micrometer cobalt flakes were successively fabricated by hydrazine reduction in aqueous solution, the flakes were coated with silica layers by the hydrolysis method. Their microwave and static magnetic properties were investigated. The silica coated cobalt flakes are characterized with high resonance frequency at 4 GHz, and the real part of permeability μ′ were greatly improved when frequency was lower than resonance frequency. The improvement is ascribed to the suppression of eddy current loss after silica coating. The spectra of complex permeability were fitted with the Landau–Lifshitz–Gilbert equation and the resonance mode is proved to be the natural resonance mode.

Microwave Magnetic Properties and Natural Resonance of ∊-Co Nanoparticles

Owing to the novel crystal structure, ∊-Co nanoparticles with an average diameter of 12nm are synthesized and the microwave magnetic properties of the epoxy resin composite with 50vol% ∊-Co particles are measured in the frequency range 0.1–7 GHz. The experimental resonance frequency (4.7 GHz) matches well with the values obtained by the theoretical calculation with the Kittel equation and fitting the experimental permeability dispersion curve via the Landau–Lifshitz equation. Hence the resonance peak is attributed to natural resonance mode. This work is believed to be beneficial for further understanding microwave applications of the novel ∊-Co nanoparticles.

Eigenmode Analysis of a Two Element Segmented Capped Monopole Antenna

The behavior of a two element segmented capped monopole antenna is described in terms of three natural resonances of the antenna structure. A numerical eigenmode solver is used to derive the resonant frequency and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -factor of the natural resonances, as well as the impedance properties of these modes when excited individually. The impedance of the antenna is described as a lumped element network, where the component values of the network are determined from the impedance parameters of the resonant modes and the static properties of the antenna structure. The model is applied to predict the behavior of the antenna when a lumped element inductor is used to connect the two segments. The inductor tunes the properties of one of the three resonances, enabling the impedance bandwidth to be optimized. The analysis is then extended to predict the behavior of the antenna when the two vertical elements have different radii, a configuration that enables wide bandwidth operation without the use of an inductor. The modal analysis accurately predicts the impedance and far-field properties of the antennas. Analyzing the antenna in terms of its natural resonant modes provides physical insights into both its behavior and the fundamental limitations of its performance.

Characteristic Polarization States Estimation in an Ultrawideband Context: A Frequency Approach

The concept of characteristic polarization states (CPSs) is extended to an ultrawideband (UWB) context. This is achieved by a sparse representation of the target UWB scattering spectrum by a set of frequency bands associated with the target natural resonance modes. The polarization description involves using the average power within each resonant frequency band to derive the Kennaugh power matrix and, subsequently, a set of CPSs using the Lagrangian optimization procedure. To validate this, preliminary feature sets are formed by extracting robust information from each derived CPS and then implementing a correlation measure criterion from which the relationships between these preliminary feature sets as a function of resonance order are established. These relationships are invariant to range and target orientation about the radar-target direction and are robust to noise.

Innovative automatic resonant mode identification for nano-scale dynamic full-field characterization of MEMS using interferometric fringe analysis

A dynamic 3D nano-scale surface profilometer was successfully developed for novel automatic resonant frequency identification using stroboscopic interferometric principle. With rapid increase in the application of micro electromechanical systems (MEMS) to industries, the needs of accurate dynamic characterization have become a major challenge in design and fabrication. In view of such, an interferometric microscopy was developed using LED stroboscopic interferometry to achieve dynamic full-field profilometry and characterization of MEMS with a measurement bandwidth exceeding 1 MHz. Most importantly, a novel detection algorithm was also developed employing interferogram fringe density measure for automatic resonant frequency identification. Natural resonant modes of a series of microstructures can be accurately detected, giving values consistent with theoretical ones. To verify the effectiveness of the developed methodology, an AFM cantilever microbeam and a cross-bridge microbeam were measured to analyze their full-field resonant vibratory shapes. Our experimental results confirmed that the resonant vibration of the tested beams can be fully characterized while achieving an accuracy in vertical measurement of 3–5 nm with a vertical measurement range of tens of micrometers.