Low-order Modes Research Articles

Modal characteristics analysis and vibration control of long-span cable-stayed-suspension hybrid bridge based on strain energy method

The research on the modal characteristic analysis of long-span bridges is crucial for vibration analysis and control, yet literature regarding the modal characteristics of long-span bridges remains limited. This study thus aims to introduce a strain energy-based damping model to estimate the modal damping of long-span cable-supported bridges. Two different systems of cable-supported bridges are analyzed, and the strain energy proportions and modal damping ratios of various substructures for each mode are calculated. Based on the analysis of modal strain energy results, a strategy to control the vibration of long-span bridges is proposed and validated using the finite element methods. The results indicate that the main girder exhibits the highest strain energy proportion in low-order lateral bending modes, while it is the main cable in low-order vertical bending modes. Different substructures in higher-order modes contribute to the strain energy in varying proportions. For a specific mode, increasing the material damping of the substructure with the highest strain energy proportion effectively suppresses the vibration amplitude of the main girder in that mode. Additionally, installing V-shaped damping cables to control the vibration of substructures with higher strain energy proportions effectively suppresses the vibration of the main girder.

Mechanism analysis of the abnormal head-cover vibration of an ultra-high-head pump-turbine operating in pump mode by CFD and FEM

ABSTRACT Hydraulic excitation causes abnormal head-cover vibration in some pump-turbines, particularly as design heads continue to rise. Pump-turbines with heads exceeding 600 m have reported such vibrations in pump mode, and it is urgent to reveal the reasons. A study was conducted on a head-cover of a pump-turbine with a maximum head of 660 m by 3D computational fluid dynamics (CFD) and finite element method (FEM) numerical simulations to investigate the hydraulic excitation source and vibration mechanism. Results show that the intensive vibration is related to the coincidence of frequency and mode between abnormal pressure pulsations with frequency 6–8f n and the low-order wet mode of the head-cover. A new flow pattern termed the rolling vortex was discovered in the vaneless space under high-head pumping conditions. The 6–8f n pressure pulsations result from the interaction between rolling vortices and guide-vanes, similar to the rotor-stator interaction. The flow mechanism of the rolling vortices is that the outflow velocity near the hub at the runner outlet is higher than that near the shroud, due to the positive blade lean angle and the X-shape distorted blades. Suppressing rolling vortices may help eliminate the abnormal head-cover vibration, which will be attempted in further study.

Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation

In this paper, we investigate the dynamics and stability of multi-peak solitons from the coupled nonlinear Schrödinger equation with the fractional dimension based on Lévy random flights. By implementing linear stability analysis and direct simulations, we demonstrate regions where the single and multi-peak modes are stable. Analysis of perturbed coupled solitons confirms the stability of higher-order modes compared to lower-order modes under the same configurations. The stability diagrams show that the force coupling, Lévy index, power, and the nonlinear intensity significantly influence the stability of high-order modes. Our findings indicate that stability is favored in self-defocusing systems with high Lévy indices under weak coupling conditions, with higher-order states exhibiting smaller stability regions.

Mode-dependent analysis of a fiber optic curvature sensor with sensitive zone

In this paper, mode-dependent analysis of fiber optic curvature sensor with precision machined structural imperfections (teeth) as sensitive zone is conducted. Using controlled input or light source launching conditions sensor response is measured for different modes excited in the multimode optical fiber. Study shows that as curvature changes there is significant difference in how sensitive zone affects low and high order modes propagating through the fiber. Obtained measurement results provide further insight into FOCS response and open possibilities for development of new measurement approaches which represent a significant step forward for FOCS based measurement systems. Guidelines for maximizing sensor sensitivity, increasing measurement reliability and even avoiding intensity based measurement by measuring changes in the width of the sensor’s output light intensity distribution are discussed in this work.

Insights into turbulent flow structure and energy dissipation in centrifugal pumps: A study utilizing time-resolved particle image velocimetry and proper orthogonal decomposition

The purpose of the study is to investigate the flow structure and energy dissipation mechanism within centrifugal pump impellers. The velocity fields at the mid-sections of the flow passages of 4- and 5-blade impellers were measured under various flow rates using the Time-resolved Particle Image Velocimetry (TR-PIV) technique; the proper orthogonal decomposition (POD) analysis was performed to extract flow structures with different scales; the dissipation rate was estimated using the large-eddy PIV method; the correlation between turbulent kinetic energy (TKE) and dissipation rate was measured using the cross-correlation analysis. The findings are as follows: impeller with more uniform and stable flow, the scale and energy contribution of large-scale structures in lower order modes are smaller, leading to higher impeller efficiency; large-scale structures identified in the low-order modes correspond to locations of high TKE and dissipation areas; the high velocity gradients within the impeller passage and the interactions between large-scale flow structures encourage the breakup of large-scale turbulent structures into dissipative-scale structures; the correlation between TKE and dissipation rate reflects the extent to which large-scale flow structures within the impeller passage break up into dissipative scales.

Nonlinear Static Bending and Forced Vibrations of Single-Layer MoS2 with Thermal Stress.

Single-layer molybdenum disulfide (MoS2) has been a research focus in recent years owing to its extensive potential applications. However, how to model the mechanical properties of MoS2 is an open question. In this study, we investigate the nonlinear static bending and forced vibrations of MoS2, subjected to boundary axial and thermal stresses using modified plate theory with independent in-plane and out-of-plane stiffnesses. First, two nonlinear ordinary differential equations are obtained using the Galerkin method to represent the nonlinear vibrations of the first two symmetrical modes. Second, we analyze nonlinear static bending by neglecting the inertial and damping terms of the two equations. Finally, we explore nonlinear forced vibrations using the method of multiple scales for the first- and third-order modes, and their 1:3 internal resonance. The main results are as follows: (1) The thermal stress and the axial compressive stress reduce the MoS2 stiffness significantly. (2) The bifurcation points of the load at the low-frequency primary resonance are much smaller than those at high frequency under single-mode vibrations. (3) Temperature has a more remarkable influence on the higher-order mode than the lower-order mode under the 1:3 internal resonance.

Fluid dynamics of a flapping wing interacting with the boundary layer at a flat wall

In this paper, we consider the fluid dynamics of a flapping wing interacting with a boundary layer developed at a no-slip flat wall. Direct numerical simulations are carried out via implementing the non-iterative immersed boundary-lattice Boltzmann method, over a Reynolds number range of 10≤Re≤1000, for a fixed Strouhal number of St = 0.3 and for a given symmetric plunging and pitching flapping motion. The interactions between the wing and the boundary layer are modulated by varying the mean distance of the wing to the wall H0. The results indicate that the presence of the boundary layer at the wall amplifies the fluctuations in both lift and drag due to the boundary layer separation, in contrast to the pure ground effect. This separation also leads to the decrease in both average lift and average drag over one flapping cycle when H0 is low. When it comes to the flow patterns in the wake, it generally gets more complex for a low H0 and/or a high Re. Secondary vortices can be observed for Re≥500 in the present configuration, which either evolve by themselves or interact with the vortices in the wake while being convected downstream and dissipated via viscosity. In the end, a dynamic mode decomposition analysis is performed to explore further the flow structures in the wake. One observes the sheltering effect of the boundary layer that the vortices in the wake are prevented from penetrating the boundary layer, while this effect will not hold if the vortex intensity is sufficiently high, such as the low order mode of the case for Re≥1000 in this study.

Making the unmodulated Pyramid wavefront sensor smart

Almost all current and future high-contrast imaging instruments will use a Pyramid wavefront sensor (PWFS) as a primary or secondary wavefront sensor. The main issue with the PWFS is its nonlinear response to large phase aberrations, especially under strong atmospheric turbulence. Most instruments try to increase its linearity range by using dynamic modulation, but this leads to decreased sensitivity, most prominently for low-order modes, and makes it blind to petal-piston modes. In the push toward high-contrast imaging of fainter stars and deeper contrasts, there is a strong interest in using the PWFS in its unmodulated form. Here, we present closed-loop lab results of a nonlinear reconstructor for the unmodulated PWFS of the Magellan Adaptive Optics extreme (MagAO-X) system based on convolutional neural networks (CNNs). We show that our nonlinear reconstructor has a dynamic range of >600 nm root-mean-square (RMS), significantly outperforming the linear reconstructor that only has a 50 nm RMS dynamic range. The reconstructor behaves well in closed loop and can obtain >80% Strehl at 875 nm under a large variety of conditions and reaches higher Strehl ratios than the linear reconstructor under all simulated conditions. The CNN reconstructor also achieves the theoretical sensitivity limit of a PWFS, showing that it does not lose its sensitivity in exchange for dynamic range. The current CNN’s computational time is 690 µs, which enables loop speeds of >1 kHz. On-sky tests are foreseen soon and will be important for pushing future high-contrast imaging instruments toward their limits.

Cladding-pumped laser and amplifier for E- and S-bands based on multimode bismuth-doped graded-index fibers: toward "watt-level" output power.

In this Letter, we investigated the potential scalability of output power of a cladding-pumped laser and a power amplifier (booster) based on a multimode Bi-doped fiber (BDF) using the mode-selection approach. We fabricated the multimode double-clad graded-index (GRIN) fiber with a confined Bi-doped germanosilicate glass core with a diameter of ≈30 and ≈60 µm. Using femtosecond (fs) inscription technology with high spatial resolution, Bragg gratings of a special transverse structure allowing the selection of low-order modes were written into the core of BDFs. The operation features of the cladding-pumped multimode bismuth-doped GRIN fiber lasers with the inscribed Bragg gratings with various reflection coefficients were investigated. In addition, the behavior of the output power and the beam quality (M2 parameter) of the optical radiation of the developed devices was studied. The CW laser and booster operating at nearly 1.45 µm with maximum output powers of ≈0.8 and ≈1 W, respectively, based on the 60-µm-core BDF under pumping by multimode laser diodes at 808 nm were developed, which are, to the best of our knowledge, the most powerful cladding-pumped BDF devices to date. Near single-mode lasing (M2 <1.3) is demonstrated for a 30-µm-core fiber. The experimental data open new possibilities to achieve higher powers in cladding-pumped BDF sources, which are more cost-effective compared to core-pumped counterparts.

Vibration of black phosphorus nanotubes via orthotropic cylindrical shell model

Black phosphorus nanotubes (BPNTs) may have good properties and potential applications. Determining the vibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designing optimized nanodevices. In this paper, the mechanical behaviour and vibration property of BPNTs are studied via orthotropic cylindrical shell model and molecular dynamics (MD) simulation. The vibration frequencies of two chiral BPNTs are analysed systematically. According to the results of MD calculations, it is revealed that the natural frequencies of two BPNTs with approximately equal sizes are unequal at each order, and that the natural frequencies of armchair BPNTs are higher than those of zigzag BPNTs. In addition, an armchair BPNTs with a stable structure is considered as the object of research, and the vibration frequencies of BPNTs of different sizes are analysed. When comparing the MD results, it is found that both the isotropic cylindrical shell model and orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of the longer BPNTs better. However, for the vibration of shorter and thinner BPNTs, the prediction of the orthotropic cylindrical shell model is obviously superior to the isotropic shell model, thereby further proving the validity of the shell model that considers orthotropic for BPNTs.

Time-varying propagation model and dynamic-feedback-phase correction for multiplexed orbital angular momentum beams in atmospheric turbulence.

Freespace optical (FSO) communication in an outdoor setting is complicated by atmospheric turbulence (AT). A time-varying (TV) multiplexed orbital angular momentum (OAM) propagation model to consider AT under transverse-wind conditions is formulated for the first time, and optimized dynamic correction periods for various TV AT situations are found to improve the transmission efficiency. The TV nature of AT has until now been neglected from modeling of OAM propagation models, but it is shown to be important. First, according to the Taylor frozen-turbulence hypothesis, a series of AT phase screens influenced by transverse wind are introduced into the conventional angular-spectrum propagation analysis method to model both the temporal and spatial propagation characteristics of multiplexed OAM beams. Our model shows that while in weak TV AT, the power standard deviation of lower-order modes is usually smaller than that of higher-order modes, the phenomena in strong TV AT are qualitatively different. Moreover, after analyzing the effective time of each OAM phase correction, optimized dynamic correction periods for a dynamic feedback communication link are obtained. An optimized result shows that, under the moderate TV AT, both a system BER within the forward-error-correction limit and a low iterative computation volume with 6% of the real-time correction could be achieved with a correction period of 0.18 s. The research emphasizes the significance of establishing a TV propagation model for exploring the effect of TV AT on multiplexed OAM beams and proposing an optimized phase-correction mechanism to mitigate performance degradation caused by TV AT, ultimately enhancing overall transmission efficiency.

Acoustic arrival predictions using oceanographic measurements and models in the Beaufort Sea.

Acoustic propagation in the Beaufort Sea is particularly sensitive to upper-ocean sound-speed structure due to the presence of a subsurface duct known as the Beaufort duct. Comparisons of acoustic predictions based on existing Arctic models with predictions based on in situ data collected by Seaglider vehicles in the summer of 2017 show differences in the strength, depth, and number of ducts, highlighting the importance of in situ data. These differences have a significant effect on the later, more intense portion of the acoustic time front referred to as reverse geometric dispersion, where lower-order modes arrive prior to the final cutoff.

Research on frequency-variation square ratio in damage identification technique for single column platforms

This paper attempts to utilize lower order harmonics and modes of vibration consisting of “square ratios of frequency variations” as structural damage susceptibility characteristics. This is followed by the development of the frequency-based method. Firstly, this paper derives the theoretical formulation of the square ratio of frequency variation method. Secondly, a finite element model of a single column platform is established. Then the damage is simulated using the reduced modulus of elasticity to localize the damage. The result is shown to be feasible. Thirdly, a model of the offshore single column platform is constructed, and the damage is simulated using cracks on the column. The “frequency variation square ratio” is valid, so the method can be used in reality. This method is applied to the single column platform model, suitable for a beam structure. It is very effective for the single column damage identification at different damage levels, and can also initially locate the damage. This method has high practical application value and reference value for future studies.

Experimental study of turbulent flow in lower plenum with flow skirt of reactor pressure vessel of pressurized water reactor

The turbulent flow in lower plenum of reactor pressure vessel (RPV) of pressurized water reactor (PWR) is an important phenomenon for design of flow mixing device. A high-precision matched index of refraction (MIR) technique is requisite for time-resolved particle image velocimetry (TR-PIV) measurements in RPV with complicated internals. In this study, turbulent flow in a scaled-down RPV model was measured by TR-PIV under different Reynolds numbers (Re) and asymmetrical flow rate with aid of the high-precision MIR technique of sodium iodide (NaI) solution and acrylic. The time-averaged flow structures include flow separation at the corner of lower support plate, fluid bifurcation around the lower edge of flow skirt, flow turning upward below the vortex suppression plate, horizontal jets at holes of flow skirt, vertical jets at holes of vortex suppression plate, improving turbulent mixing and Reynolds stresses in the lower plenum. The coherent structures were studied by proper orthogonal decomposition (POD) analysis. The flow skirt and vortex suppression plate break down large vortices through them. With Re increasing, Reynolds stresses decrease fast, and the energy fractions of low-order modes transfer into high-order modes, because turbulent vortices break up. In the case of asymmetrical flow rate, the time-averaged velocity and Reynolds stress decrease slightly, and the cumulative energy fraction decreases at flow skirt and vortex suppression plate.

Model Reduction of a Continuous System with Friction-Induced Vibration Considering Separation and Re-Contact

The friction-induced vibration of a continuous system consisting of two flexible beams in sliding contact to represent a brake system is studied in this paper. Besides the motion of relative sliding when the two beams are in contact, the separation of beams may also happen in the system dynamics. The complex eigenvalue analysis for the stability of the steady sliding state and the transient dynamic analysis for the characteristics (intensity and periodicity) of the steady-state responses of the system are carried out. Moreover, the results obtained using different numbers of beam modes are acquired and compared. It is found that only a few low-order beam modes need to be incorporated to get accurate results of the stability of the steady sliding state and the steady-state responses of the continuous frictional system, which therefore theoretically justify the omission of high-order modes of continuous structures when investigating the friction-induced vibration of continuous systems and thereby greatly reduce the computational cost. Additionally, the inclusion of the separation and re-contact behavior has a significant effect on the number of required modes for accurate steady-state responses compared with that when no separation is considered, which also verifies the important role of the separation and re-contact behavior in the system dynamics. Besides, a reduced dynamic model that can produce identical dynamic behaviors to those of the continuous frictional system is constructed, with the structural parameters of the reduced model derived from the several key low-order modes of beams.

Revisiting anapoles in a single high-index dielectric structure

High-index dielectric structures support electric and magnetic Mie resonance. Through careful manipulation of geometric parameters, destructive interference can be induced between electric multipole moments and toroidal multipole moments. This leads to the formation of anapoles, which are characterized by quenched scattering in the far field and giant enhancement in the near field. Here, we revisit the formation mechanism of anapole states in a single dielectric structure with a high refractive index from an eigenmode perspective. We find that scattering efficiency is mainly determined by the intrinsic phase governed by the leaky mode of the structure and the extrinsic phase induced by the frequency deviation from resonance. It is also demonstrated that the anapole modes in a two-dimensional cylinder and a three-dimensional sphere can only occur in the following two situations: (1) when only one mode is involved, the combined phase of intrinsic and extrinsic phase should be equal to 2π at a certain frequency (anapole frequency), which is very close to the resonance frequency. Generally, these types of anapoles are low-order anapoles since low-order resonant modes (i.e., magnetic (electric) dipole and quadrupole) are well separated. (2) If two or more leaky modes are involved, the combined phase for each mode must be 2π at the same frequency located between the two resonances. This corresponds to the high-order anapoles. It is also found that more anapole states will emerge with increasing refractive index. Our results may provide new perspectives for designing high-order anapoles with more freedom.

Analysis of Dynamic Characteristics of Rotor Sail Using a 4DOF Rotor Model and Finite Element Model

The interest in wind-assisted ship propulsions (WASPs) is increasing to improve fuel efficiency and to reduce greenhouse gas emissions in ships. A rotor sail, one of the typical WASPs, can provide auxiliary propulsive force by rotating a cylinder-shaped structure based on the Magnus effect. However, due to its huge rotating structure, a meticulous evaluation of the influence on the ship structure and dynamical stability of the rotating structure should be conducted in the design stage. In this respect, an analysis of the rotating structure for a 30 m height and 3 m diameter rotor sail was conducted in this study. First, a 4DOF (four-degree-of-freedom) model was derived to simplify the dynamics of the rotor sail. Using the 4DOF model, natural frequencies for four low-order modes of the rotor sail were calculated, and frequency responses at support points were predicted. Next, a comparison and validation with the finite element model of the rotor sail were carried out. For the 1st and 2nd natural frequencies, a difference of approximately 0.3 Hz was observed between the 4DOF model and the finite element model, confirming the effectiveness of the 4DOF model for low-order modes. In analysis with changes in the bearing supporting stiffnesses, it was verified that lower support bearings have a significant impact on rotor dynamics compared to upper support bearings. Vibration response at the upper support was also confirmed through frequency response analysis caused by imbalance at Thom disk and mid-plate. Additionally, when estimating the eccentricity of the Thom disk as imbalance, a limit of eccentricity error could be set as 24 mm. The presented modeling procedures and analysis results can be references during early design stage of a novel rotor sail structure.

Thermal effect on the modal characteristics of the rotor of a typical cryogenic turbine for helium refrigerator

The helium turbine is a critical component of the cryogenic system for nuclear fusion devices. To ensure the turbine's steady functioning and avoid resonance, it is essential to understand and clarify the influence of key factors on its modal characteristics. This paper investigates the influence of thermal effect, fluid-structure interaction and rotational effects on the intrinsic frequency of a helium turbine used in the Comprehensive Research Facility for Fusion Technology (CRAFT) cryogenic system. The effects of coefficient of thermal expansion, thermal conductivity and Young's modulus on the intrinsic frequency of the rotor are explored, considering these thermal factors that vary with temperature. The results indicate that thermal effect has the greatest influence on the intrinsic frequency of the rotor over rotational effectand fluid-structure interaction. Lower-order modes are more sensitive to changes in thermal conductivity, while higher-order modes are more sensitive to changes in Young's modulus at low temperatures. The intrinsic frequency of the rotor is more sensitive to changes in the thermal factors of the shaft rather than the thermal factors of the impellers.

Fluid-Dynamic Mechanisms Underlying Wind Turbine Wake Control with Strouhal-Timed Actuation

A reduction in wake effects in large wind farms through wake-aware control has considerable potential to improve farm efficiency. This work examines the success of several emerging, empirically derived control methods that modify wind turbine wakes (i.e., the pulse method, helix method, and related methods) based on Strouhal numbers on the O(0.3). Drawing on previous work in the literature for jet and bluff-body flows, the analyses leverage the normal-mode representation of wake instabilities to characterize the large-scale wake meandering observed in actuated wakes. Idealized large-eddy simulations (LES) using an actuator-line representation of the turbine blades indicate that the n=0 and ±1 modes, which correspond to the pulse and helix forcing strategies, respectively, have faster initial growth rates than higher-order modes, suggesting these lower-order modes are more appropriate for wake control. Exciting these lower-order modes with periodic pitching of the blades produces increased modal growth, higher entrainment into the wake, and faster wake recovery. Modal energy gain and the entrainment rate both increase with streamwise distance from the rotor until the intermediate wake. This suggests that the wake meandering dynamics, which share close ties with the relatively well-characterized meandering dynamics in jet and bluff-body flows, are an essential component of the success of wind turbine wake control methods. A spatial linear stability analysis is also performed on the wake flows and yields insights on the modal evolution. In the context of the normal-mode representation of wake instabilities, these findings represent the first literature examining the characteristics of the wake meandering stemming from intentional Strouhal-timed wake actuation, and they help guide the ongoing work to understand the fluid-dynamic origins of the success of the pulse, helix, and related methods.

Experimental investigation of Rayleigh wave propagation in a locally resonant metamaterial layer resting on an elastic half-space

In this experimental investigation, we explore the propagation characteristics of surface Rayleigh waves in a Locally Resonant Metamaterial (LRM) layer positioned on an elastic half-space. The study focuses on characterizing the dispersion and attenuation properties of these waves and validating analytical and numerical models of the LRM. For practical purposes, we utilize a thin-plate sample and construct the LRM layer, featuring multiple rows of sub-wavelength resonators, by machining the resonators at one edge of the plate. Employing a piezoelectric transducer coupled to the plate and a laser vibrometer, we actuate and receive the surface-like waves propagating at the plate edge. Two resonant layer configurations, comprising 3 and 5 rows of resonators, corresponding to heights of ∼0.6λh and λh, where λh represents the reference wavelength of Rayleigh waves, are examined. The experimental observations reveal the hybridization of the fundamental surface mode at the resonant frequency of the embedded resonators, leading to the creation of a low-frequency bandgap. This bandgap, attributed to the local resonance mechanism, exhibits a remarkable attenuation of surface wave amplitudes. To support our experimental findings, we conduct both analytical and numerical studies. These analyses demonstrate the confinement of the lowest-order surface mode within the frequency ranges proximate to the resonators’ resonance. The insights gained from this experimental study contribute to the advancement of strategies for mitigating surface waves through the application of resonant metamaterials and metastructures.