Search Results (48)

To investigate the oscillation modes of iced transmission lines, this study introduces a forcing term into the galloping equation and applies two discretization approaches: Discrete Method I (DMI), which directly transforms the partial differential equation into an ordinary differential form, and Discrete Method II (DMII), which first averages dynamic tension along the span. The finite element method is employed to validate the analytical solutions. Using a multiscale approach, amplitude-frequency responses under primary, harmonic, and internal resonance are derived. Results show that DMII yields larger galloping amplitudes and trajectories than DMI, with lower resonant frequencies and weaker geometric nonlinearities. In harmonic resonance, superharmonic and subharmonic modes (notably 1/2) are more easily excited. Under 2:1:2 internal resonance, amplitude differences in the vertical (z) direction are more sensitive to the discretization method, whereas the 1:1:1 case shows minimal variation across directions. These findings suggest that the choice of discretization significantly influences galloping behavior, with DMII offering a more conservative prediction. Full article

The theory of orbital forcing as formulated by Milankovitch involves the mediation by the advance (retreat) of ice sheets and the resulting variations in terrestrial albedo. This approach poses a major problem: that of the period of glacial cycles, which varies over time, as happened during the Mid-Pleistocene Transition (MPT). Here, we show that various hypotheses are called into question because of the finding of a second transition, the Early Quaternary Transition (EQT), resulting from the million-year period eccentricity parameter. We propose to complement the orbital forcing theory to explain both the MPT and the EQT by invoking the mediation of western boundary currents (WBCs) and the resulting variations in heat transfer from the low to the high latitudes. From observational and theoretical considerations, it appears that very long-period Rossby waves winding around subtropical gyres, the so-called “gyral” Rossby waves (GRWs), are resonantly forced in subharmonic modes from variations in solar irradiance resulting from the solar and orbital cycles. Two mutually reinforcing positive feedbacks of the climate response to orbital forcing have been evidenced: namely the change in the albedo resulting from the cyclic growth and retreat of ice sheets in accordance with the standard Milankovitch theory, and the modulation of the velocity of the WBCs of subtropical gyres. Due to the inherited resonance properties of GRWs, the response of the climate system to orbital forcing is sensitive to small changes in the forcing periods. For both the MPT and the EQT, the transition occurred when the forcing period merged with one of the natural periods of the climate system. The MPT occurred 1.25 Ma ago, when the dominant period shifted from 41 ka to 98 ka, with both periods corresponding to changes in the Earth’s obliquity and eccentricity. The EQT occurred 2.38 Ma ago, when the dominant period shifted from 408 ka to 786 ka, with both periods corresponding to changes in the Earth’s eccentricity. Through this paradigm shift, the objective of this self-consistent approach is essentially to spark new debates around a problem that has been pending since the discovery of glacial–interglacial cycles, where many hypotheses have been put forward without, however, fully answering all our questions. Full article

This study examines the hydrodynamic response and structural stability of an eccentric conical floating structure, a return capsule for manned space missions, to ensure safe water landings. Using numerical simulations and experiments, we evaluated how center-of-mass offsets, displacement volume control, and environmental factors, including waves, currents, and wind, affect capsule stability. In still water, lateral center-of-mass offsets strongly affect stability through nonlinear restoring moments, whereas foam-based displacement control reduces motion amplitude and tilt angle. In dynamic sea conditions, wave parameters dominate motion, with surge displacement and pitch angle varying by wavelength and sea state. At higher sea states, nonlinear phenomena, including subharmonic resonance, amplify pitch angle extrema, compromising safety margins. This research offers key insights for evaluating and improving return capsule safety, highlighting the importance of complex multi-physics interactions in marine environments. Full article

The aim of this study is to examine the behavior of subharmonics in a one-dimensional cavity filled with a bubbly liquid, leveraging the nonlinear softening phenomenon of the medium at high amplitudes to enhance subharmonic generation. To this purpose, we use a numerical model developed previously that solves a coupled differential system formed by the wave equation and a Taylor-expanded Rayleigh–Plesset equation. This system describes the nonlinear mutual interaction between ultrasound and bubble vibrations. We carry out several different simulations to measure the response of the subharmonic component $f/2$ and the acoustic source frequency signal f when the cavity is excited over a range around the linear resonance frequency of the cavity (the resonance value obtained at low pressure amplitudes). Different source amplitudes in three different kinds of medium are used. Our results reveal several new characteristics of subharmonics as follows: their generation is predominant compared to the source frequency; their generation is affected by the softening of the bubbly medium when acoustic pressure amplitudes are raised; this specific behavior is solely an acoustically-related phenomenon; their behavior may indicate that the bubbly liquid medium is undergoing a softening process. Full article

Unique in mammals, the vocal generator of mysticete species comprises membranes covering the two arytenoid cartilages that vibrate as the airflow passes through the trachea from the lungs to the laryngeal sac. By adjusting the airflow as well as the spacing and orientation of the two cartilages, mysticetes control the vibrations and vary acoustic qualities of the produced sounds, including the duration, amplitude, and frequency modulation of vocalizations. Humpback whales control sound production in this way to construct a complex vocal repertoire, including vocalizations with or without harmonics as well as pulsed sounds. Some vocalizations within humpback whale songs, called units, exhibit non-linearities such as frequency jumps and chaos. Here, we further describe non-linear features of units, including two additional non-linearities: subharmonics and biphonation. Subharmonics within units are probably due to higher air flow rates and to the acoustic modes of internal resonators. Biphonic vocalizations are likely generated either by an asymmetric opening of the arytenoid cartilages or by the passage of the air flow at two separate positions along the membranes. Our analyses revealed acoustic non-linearities in vocalizations emitted by six different singers during multiple breeding seasons and from populations in different oceans, suggesting that singing humpback whales often produce units with non-linear features. Full article

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. Full article

Near-inertial waves (NIWs), a special form of internal waves with a frequency close to the local Coriolis frequency, are ubiquitous in the ocean. NIWs play a crucial role in ocean mixing, influencing energy transport, climate change, and biogeochemistry. This manuscript briefly reviews the generation and propagation of NIWS in the oceans. NIWs are primarily generated at the surface by wind forcing or through the water column by nonlinear wave-wave interaction. Especially at critical latitudes where the tidal frequency is equal to twice the local inertial frequency, NIWs can be generated by a specific subclass of triadic resonance, parametric subharmonic instability (PSI). There are also other mechanisms, including lee wave and spontaneous generation. NIWs can propagate horizontally for hundreds of kilometers from their generating region and radiate energy far away from their origin. NIWs also penetrate deep into the ocean, affecting nutrient and oxygen redistribution through altering mixing. NIW propagation is influenced by factors such as mesoscale eddies, background flow, and topography. This review also discussed some recent observational evidence of interactions between NIWs from different origins, suggesting a complicated nonlinear interaction and energy cascading. Despite the long research history, there are still many areas of NIWs that are not well defined. Full article

Inspired by the fact that flying insects improve their power conversion efficiency through resonance, many soft robots driven by dielectric elastomer actuators (DEAs) have achieved optimal performance via first-order modal resonance. Besides first-order resonance, DEAs contribute to multiple innovative functions such as pumps that can make sounds when using multimodal resonances. This study presents the multimodal resonance of a rectangular planar DEA (RPDEA) with a central mass bias. Using a combination of experiments and finite element modeling (FEM), it was discerned that under a prestretch of 1.0 × 1.1, the first-, second-, and third-order resonances corresponded to vertical vibration, rotation along the long axis, and rotation along the short axis, respectively. In first-order resonance, superharmonic, harmonic, and subharmonic responses were activated, while only harmonic and subharmonic responses were observed in the second- and third-order resonances. Further investigations revealed that prestretching tended to inhibit third-order resonance but could elevate the resonance frequencies of the first and second orders. Conveniently, both the experimental and FEM results showed that the frequencies and amplitudes of the multimodal resonances could be tuned by adjusting the amplitudes of the excitation signals, referring to the direct current (DC) amplitude and alternating current (AC) amplitude, respectively. Moreover, instead of linear vibration, we found another novel approach that used rotation vibration to drive a robot with soft bristles via hopping locomotion, showcasing a higher speed compared to the first-order resonance in our robot. Full article

This paper examines a time delay in position and velocity to minimize the nonlinear vibration of an excited Duffing oscillator (DO). This model is highly beneficial for capturing the nonlinear characteristics of many different applications in engineering. To achieve an estimated uniform solution to the problem under consideration, a modified homotopy perturbation method (HPM) is utilized. This adaptation produces a more accurate precise approximation with a numerical solution (NS). This is obtained by employing Mathematica software 12 (MS) in comparison with the analytical solution (AS). The comparison signifies a good match between the two methodologies. The comparison is made with the aid of the NS. Consequently, the work allows for a qualitative assessment of the results of a representative analytical approximation approach. A promising stability analysis for the unforced system is performed. The time history of the accomplished results is illustrated in light of a diverse range of physical frequency and time-delay aspects. The outcomes are theoretically discussed and numerically explained with a set of graphs. The nonlinear structured prototype is examined via the multiple-scale procedure. It investigates how various controlling limits affect the organization of vibration performances. As a key assumption, according to cubic nonlinearity, two significant examples of resonance, sub-harmonic and super-harmonic, are explored. The obtained modulation equations, in these situations, are quantitatively investigated with regard to the influence of the applied backgrounds. Full article

A new power receiving unit (PRU) is proposed in this paper for resonant wireless power transfer (WPT), which is characterized by the capability of attracting high power from the power transmitting unit (PTU). The resonant WPT is designed for delivering the electrical power to the PRU attached on an electrical vehicle (EV) chassis 50 cm away from a PTU installed on the ground. The proposed PRU uses only the passive elements such as inductors, diodes, and capacitors, which need no initial power from the EV. It is then applicable for charging a battery to several hundred volts for even a first-time charging battery. For a resonant WPT at a switching frequency of 4 MHz, the proposed PRU behaves as a negative impedance converter (NIC) itself in the subharmonics of 4 MHz. The NIC effect plus the subharmonic oscillation causes an instability current charging the battery connected to the PRU. In this paper, we simulated the PRU and performed the experiment. The experiment demonstrated a battery charging of 150 W from 50 cm away using three D-mode GaN HEMT transistors via the instability current ramp. The power transfer efficiency (PTE) improved as the power delivered to the load (PDL) increased. The peak PTE was 65% in the present findings. The simulation analysis showed that the circuit allowed itself be used to much higher power transfer when it is implemented with more GaN HEMT transistors connected in parallel. The theoretical derivation of the PRU circuit is also used to support both the experimental and simulation results. Full article

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. Full article

Based on the dynamic characteristics of the axle box front cover of high-speed trains in the subharmonic resonance state, the nonlinear single-degree-of-freedom (SDOF) model was proved to be reasonable, and reasons for the ineffectiveness of the common prevention methods for preventing bolt failure were analyzed firstly. Then, dynamic stress of the bolt was simulated by innovatively adopting the linear method based on frequency response analysis. The stress simulation method was verified to be practical under the subharmonic resonance state by analyzing and comparing the experimental and numerical results of the bolted front cover. It was proved that the linear method was accurate enough to simulate the dynamic stress of bolts, which is of great engineering significance. In addition to the transverse resonance stress of bolts caused by drastic vertical vibration of the front cover, the tensile resonance stress at the root of the first engaged thread was too large to be neglected on account of the first-order bending modes of bolts. Next, equivalent stress amplitude of the multiaxial stresses was obtained by means of the octahedral shear stress criterion. Finally, fatigue life of bolts was predicted in terms of S-N curve suitable for bolt fatigue life analysis. It argued that the bolts were prone to multiaxial fatigue failure when the front cover was in subharmonic resonance for more than 26.8 h, and the fatigue life of bolts could be greatly improved when the wheel polygonization was eliminated by shortening the wheel reprofiling interval. Full article

A pressure sensor, located for four months in the middle of a 1275 m-long taut deep-ocean mooring in 2380 m water depth above a seamount with sub-surface top-buoys and seafloor anchor-weight, demonstrates narrow-band spectral peaks of deterministic well-predictable signals with equivalent 0.5 m amplitudes at uncommon sub-harmonic frequencies f*/4, f*/2, 3f*/4 of the local near-inertial frequency f* = 1.085f, where f denotes the Coriolis parameter. None of these sub-harmonics can be associated with oceanographic motions, which are dominated by super-inertial internal waves that are more broadband and less predictable. No corresponding peaks are found in spectra of other observables like current velocity (differences), temperature, and pressure in the top buoy of the mooring. The mid-cable pressure sensor was mounted on a nearly 1 kN weighing non-swiveled frame. Its data are hypothesized to reflect a resonant mechanical oscillation of the high-tensioned elastic steel mooring cable under repeated short-scale Strouhal cable vibrations induced by vortex-shedding due to water-flow drag and/or possibly by tidal baroclinic motions that are about 50% larger near the sloping seafloor of the seamount than mid-depth thereby modifying the mooring-cable in a helical shape. Cable dynamics and mooring-motion considerations yield inconclusive results to explain the observations. Hypothesizing, the observations suggest, cable dynamically, sub-harmonic drainage of helix-shape source at non-tidal semidiurnal center-frequency (M₂ + S₂)/2 = 3f*/2, physically, the measurement of Earth rotation thereby mimicking a Foucault–Wheatstone device, and, oceanographically, the relative vortex-rotation ζ/2 = 0.085f being possibly induced by water-flow interacting quasi-permanently with the nearby seamount by a topographic obstruction, so that total local near-inertial frequency f* = f + ζ/2. Full article

In the controlled source radiomagnetotelluric (CSRMT) sounding method, a horizontal magnetic dipole, HMD (vertical loop) or a horizontal electric dipole, and HED (grounded line) are used as sources. When working with HMD, the source is usually tuned to resonance to increase the current in the loop. However, the disadvantage of this approach is the narrow frequency range realized in the CSRMT method (1–12 kHz) and the short operating distance from the source (600–800 m). The need to tune the source to resonance at each selected frequency reduces the efficiency of the survey. In the case of using HED for sounding, measurements are performed in a wider frequency range of 1 to 1000 kHz, and along with the signal of the base frequency, its subharmonics are measured. In this case, emitted signal measurements are possible at a distance of up to 3–4 km from the source. At the same time, the disadvantage of using HED is that it requires grounding, the arrangement of which requires additional time when working on frozen ground or dry stony soil. We consider the possibilities of generation and registration of signals of subharmonics of base frequencies when applying the CSRMT method with loop sources—HMD and VMD (horizontal loop). A matching unit (MU) based on a step-up transformer was developed, which increases the output voltage of the CSRMT transmitter. In a field test with base frequencies of 20, 40, and 80 kHz, the signal amplitudes increased by a factor of two to four for subharmonics at frequencies of 60–200 kHz and by up to 10–13 times for subharmonics at frequencies of 200–500 kHz due to transformation of signal spectrum provided by MU. The possibility of using odd subharmonics of base frequencies for inversion has been demonstrated in the results of field experiments with different sources (HED, HMD, and VMD). This expands the frequency range of the method when working with loop sources and increases the survey’s effectiveness. The use of loop sources in the CSRMT method is especially advantageous for winter work in Arctic regions. Full article

Power grids are a combined system where the electrical energy produced by the power plants is transmitted to consumers. This forms a specific interdependence where the recipients have a significant impact on the power quality. Therefore, the nonlinear loads connected by households and industrial customers cause current and voltage distortion in the power networks. This creates the need for accurate measurement of nonsinusoidal voltage and current composed not only from the fundamental component but also containing higher harmonics, interharmonics, and subharmonics. In order to ensure high transformation accuracy of distorted current and voltage, the inductive instrument transformers have to be tested in these conditions. Many papers describe their behavior during the transformation of sinusoidal current or voltage. Nowadays, the scientific field in this scope is focused on the evaluation of their exploitation properties for distorted signals. The common problem of inductive instrument transformers is the self-generation of low-order higher harmonics to the secondary current or voltage. In the case of the inductive VTs, an additional problem results from the resonance caused by the parasitic capacitance of the primary winding. The proposed solutions to compensate for the values of current or voltage errors and phase displacement of inductive instrument transformers are also analyzed. Full article