Mode Amplitudes Research Articles

Galactoseismology in cosmological simulations

Context. Complex models recently became available for studying the dynamics of disk galaxies such as the Milky Way (MW). These models include the global dynamics from dwarf satellite galaxies, dark matter halo structure, gas infall, and stellar disks in a cosmological context. Aims. We use a MW model from a suite of high-resolution hydrodynamical cosmological simulations named GARROTXA to establish the relationship between the vertical disturbances seen in its galactic disk and multiple perturbations from the dark matter halo, satellites, and gas. Methods. We calculated the bending modes in the galactic disk in the last 6 Gyr of evolution. We computed the vertical acceleration exerted by dark matter and gas in order to quantify the impact of these components on the disk, and compared this with the bending behavior with Fourier analysis. Results. We find complex bending patterns at different radii and times, such as an inner retrograde mode with high frequency and an outer slower retrograde mode excited at different times. The amplitudes of these bending modes are highest during the early stages of formation of the thin disk (20 km s−1) and reach up to 8.5 km s−1 in the late disk evolution. We find that the infall of satellite galaxies leads to a tilt of the disk, and produces strong anisotropic gas accretion with a misalignment of 8° with subsequent star formation events and supernovae, creating significant vertical accelerations on the disk plane. The misalignment between the disk and the inner stellar and dark matter triaxial structure, which formed during the ancient assembly of the galaxy, also leads to a strong vertical acceleration of the stars. We also find dark matter subhalos that temporally coincide with the appearance of bending waves in certain periods. Conclusions. We conclude that several agents trigger the bending of the stellar disk and its phase spirals in this simulation, including satellite galaxies, dark subhalos, misaligned gaseous structures, and the inner dark matter profile. These phenomena coexist and influence each other, sometimes making it challenging to establish direct causality.

Expanding the frontiers of cool-dwarf asteroseismology with ESPRESSO

Fuelled by space photometry, asteroseismology is vastly benefitting the study of cool main-sequence stars, which exhibit convection-driven solar-like oscillations. Even so, the tiny oscillation amplitudes in K dwarfs continue to pose a challenge to space-based asteroseismology. A viable alternative is offered by the lower stellar noise over the oscillation timescales in Doppler observations. In this Letter we present the definite detection of solar-like oscillations in the bright K5 dwarf ϵ Indi based on time-intensive observations collected with the ESPRESSO spectrograph at the VLT, thus making it the coolest seismic dwarf ever observed. We measured the frequencies of a total of 19 modes of degree ℓ = 0–2 along with νmax = 5305 ± 176 μHz and Δν = 201.25 ± 0.16 μHz. The peak amplitude of radial modes is 2.6 ± 0.5 cm s−1, or a mere ∼14% of the solar value. Measured mode amplitudes are ∼2 times lower than predicted from a nominal L/M scaling relation and favour a scaling closer to (L/M)1.5 below ∼5500 K, carrying important implications for our understanding of the coupling efficiency between pulsations and near-surface convection in K dwarfs. This detection conclusively shows that precise asteroseismology of cool dwarfs is possible down to at least the mid-K regime using next-generation spectrographs on large-aperture telescopes, effectively opening up a new domain in observational asteroseismology.

Trans-dimensional joint inversion of modal amplitude and arrival- time data for geoacoustic properties in layered muddy sediments

Long-range sound fields in a shallow-water waveguide can be expressed as a summation of several dispersive propagating modes. Modal arrival times as a function of frequency, extracted via warping time-frequency analysis, have been used by many researchers to estimate sound speeds and densities for layered models of the seabed sediments. This paper explores joint inversion of modal amplitude spectra together with arrival times to also estimate sediment-layer attenuations. To consider the common case in underwater-acoustic applications where the source amplitude spectrum is unknown, we include this spectrum as unknown parameters in the inversion, formulated implicitly within the likelihood function. Trans-dimensional Bayesian inversion is applied to estimate marginal probability profiles of the geoacoustic properties, providing quantitative uncertainties. The data considered here were collected on the New England Mud Patch during the 2017 Seabed Characterization Experiment. [Work supported by the Office of Naval Research.]

Temporal evolution of sound pulse in shallow water under conditions of horizontal refraction. Vertical modes and space-time horizontal rays

As is known, to describe horizontal refraction in a shallow water waveguide, the “vertical modes and horizontal rays” approach (Burridge & Weinberg, 1974) is used, within which the two-dimensional eikonal equation for the modal amplitude includes the refractive index determined by the eigenvalues depending on the horizontal coordinates (x,y) and frequency (f). In other words, we have an effective two-dimensional inhomogeneous dispersive medium, to describe the propagation of signals in which, the authors propose to use the so-called space-time rays (Rytov, 1940, Connor & Felsen, 1974, Hillion, 1993) applied for the horizontal plane (STHR). The set of STHRs in a given situation is constructed for each mode. Within the framework of this approach, it is possible to obtain the evolution of the pulses of each mode from the solution of the nonstationary eikonal equation in the horizontal plane or from the corresponding Hamilton-Jacobi equations, obtained using non-local integral wave equation. Examples of constructing STHR in some typical situations (in particular in a wedge) are considered, some specific effects during signal propagation are considered, in particular, the so-called the pulse front tilt, previously discovered in laser optics (Bor & Rasz, 1985). Work was supported by ISF, grant 946/20.

Asymmetry of the Distribution of Vertical Velocities of the Extratropical Atmosphere in Theory, Models, and Reanalysis

Abstract The vertical velocity distribution in the atmosphere is asymmetric with stronger upward than downward motion. This asymmetry is important for the distribution of precipitation and its extremes and for an effective static stability that has been used to represent the effects of latent heating on extratropical eddies. Idealized GCM simulations show that the asymmetry increases as the climate warms, but current moist dynamical theories based around small-amplitude modes greatly overestimate the increase in asymmetry with warming found in the simulations. Here, we first analyze the changes in asymmetry with warming using numerical inversions of a moist quasigeostrophic omega equation applied to output from the idealized GCM. The inversions show that increases in the asymmetry with warming in the GCM simulations are primarily related to decreases in moist static stability on the left-hand side of the moist omega equation, whereas the dynamical forcing on the right-hand side of the omega equation is unskewed and contributes little to the asymmetry of the vertical velocity distribution. By contrast, increases in asymmetry with warming for small-amplitude modes are related to changes in both moist static stability and dynamical forcing leading to enhanced asymmetry in warm climates. We distill these insights into a toy model of the moist omega equation that is solved for a given moist static stability and wavenumber of the dynamical forcing. In comparison to modal theory, the toy model better reproduces the slow increase of the asymmetry with climate warming in the idealized GCM simulations and over the seasonal cycle from winter to summer in reanalysis. Significance Statement Upward velocities are stronger than downward velocities in the atmosphere, and this asymmetry is important for the distribution of precipitation because precipitation is linked to upward motion. An important and open question is what sets this asymmetry and how much it increases as the climate warms. Past work has shown that current theories greatly overestimate the increase in asymmetry with warming in idealized simulations. In this work, we develop a more complete theory and show that it is able to better reproduce the slow increase of the asymmetry with warming that is found over the seasonal cycle from winter to summer and in idealized simulations of warming climates.

Configurable SNAP microresonators induced by axial pre-strain-assisted CO2 laser exposure.

Flexible engineering of the complex shapes of the surface nanoscale axial photonics (SNAP) bottle microresonators (SBMs) is challenging for future nanophotonic technology applications. Here, we experimentally propose a powerful approach for the one-step fabrication of SBMs with simultaneous negative and positive radius variations, exhibiting a distinctive "bump-well-bump" profile. It is executed by utilizing two focused and symmetrical CO2 laser beams exposed on the fiber surface for only several hundred milliseconds. The spectral characteristics of different eigenmodes are analyzed, providing deep insights into the complex physical processes during the CO2 laser exposure. The shapes of the SBMs can be flexibly adjusted by the exposure time, laser power, and applied pre-strains. As a proof of this technique, the developed approach enables the efficient production of a bat SBM, ensuring a uniform field amplitude of the bat mode over the length exceeding 120 µm with 7% deviation. Our proposed technique provides a powerful technique for the efficient fabrication of SBMs with predetermined shapes, laying the groundwork for its applications on microscale optical signal processing, quantum computing, and so on.

Sawtooth suppression by flux pumping on HBT-EP

This study examines the mechanisms underlying sawtooth suppression in the High Beta Tokamak-Extended Pulse (HBT-EP) device. It is observed that strong-intensity sawtooth activities correlate with reduced-amplitude magnetohydrodynamics (MHD) edge modes which are identified as m/n=3/1 external kink modes, while sawtooth suppression correlates with larger and saturated edge mode amplitudes. To further investigate these correlations, the plasma–wall coupling was manipulated by adjusting the positions of the conducting walls in HBT-EP. It was found that strong sawtooth events occur when the normalized wall radius b/a is within a critical value. This implies that the plasma–wall distance must be sufficiently small to ensure effective stabilization of the edge mode. Even slight differences in major radius result in significantly different discharge styles, categorized as ‘sawtoothing discharges’ and ‘sawtooth-suppressed discharges’ respectively. Through a series of mode structure analyses, we confirm the coexistence and coupling of the m/n=1/1 helical core, m/n=2/1 tearing mode, and m/n=3/1 external kink mode during sawtooth-suppression, and that this coupling induces anomalous current broadening. Based on these findings, we conclude that sawtooth suppression in the HBT-EP tokamak is consistent with the process of magnetic flux pumping.

The highest mass Kepler red giants – I. Global asteroseismic parameters of 48 stars

ABSTRACT When low- and intermediate-mass stars evolve off the main sequence, they expand and cool into the red giant stages of evolution, which include those associated with shell H burning (the red giant branch), core He burning (the red clump), and shell He burning (the asymptotic giant branch). The majority of red giants have masses <2 M⊙, and red giants more massive than this are often excluded from major studies. Here, we present a study of the highest mass stars (M > 3.0 M⊙) in the Kepler sample of 16 000 red giants. We begin by re-estimating their global seismic properties with new light curves, highlighting the differences between using the simple aperture photometry and presearch data conditioning of simple aperture photometry light curves provided by Kepler. We use the re-estimated properties to derive new mass estimates for the stars, ending with a final sample of 48 confirmed high-mass stars. We explore their oscillation envelopes, confirming the trends found in recent works such as low mean mode amplitude and wide envelopes. We find, through probabilistic means, that our sample is likely all core He burning stars. We measure their dipole and quadrupole mode visibilities and confirm that the dipole mode visibility tends to decrease with mass.

Adaptive beam with elastic support based on magnetorheological elastomers for modal modulation and vibration suppression

Owing to the wide modulation capability of their magneto-induced modulus, smart structure-based magnetorheological elastomers (MREs) show great promise for vibration control in numerous engineering applications. In conventional smart structure-based MREs, however, vibration absorption or isolation is mainly used for discrete structural systems, and the requirement for vibration control in continuous structures can limit the application of vibration absorbers and isolators. Therefore, it is necessary to resolve the dynamic properties of the continuous structure to obtain modal information. In this paper, different types of smart beams with adaptive elastic support (AES)-based MREs, containing dual-end elastic support, single-end elastic support, and the combination of a fixed end and an AES at an arbitrary location, are developed to tactically influence the dynamics through magneto-mechanical coupling. A dynamic model of thin-walled beams with AES was established by using the improved Fourier series method (IFSM). The numerical results confirm that the effective suppression bandwidth of the beam with MRE-AES can be shifted as a result of the modal modulation-induced energy transfer from low to high frequencies, which requires a decreasing trend of modal amplitude at the response location as the elastic support stiffness increases. According to the modal analysis, the beams with single-end AES and dual-end AES have a decreasing trend of modal amplitude in the global location as stiffness increases. However, the modal amplitude trend of the beam with a fixed end and an AES is not monotonic at certain locations. The experimental results demonstrate that MRE-AES can effectively attenuate the acceleration responses of the beams with single-end AES and with a fixed end and an AES under harmonic excitation. The resonance peaks in the transmission remarkably shift to higher frequencies with increasing magnetic flux.

Synchronous behaviors of three coupled liquid crystal elastomer-based spring oscillators under linear temperature fields.

Self-oscillating coupled systems possess the ability to actively absorb external environmental energy to sustain their motion. This quality endows them with autonomy and sustainability, making them have application value in the fields of synchronization and clustering, thereby furthering research and exploration in these domains. Building upon the foundation of thermal responsive liquid crystal elastomer-based (LCE-based) spring oscillators, a synchronous system comprising three LCE-based spring oscillators interconnected by springs is established. In this paper, the synchronization phenomenon is described, and the self-oscillation mechanism is revealed. The results indicate that by varying system parameters and initial conditions, three synchronization patterns emerge, namely, full synchronous mode, partial synchronous mode, and asynchronous mode. For strongly interacting systems, full synchronous mode always prevails, while for weak interactions, the adjustment of initial velocities in magnitude and direction yields the three synchronization patterns. Additionally, this study explores the impact of several system parameters, including LCE elasticity coefficient and spring elasticity coefficient, on the amplitude, frequency, and synchronous mode of the system. The findings in this paper can enhance our understanding of the synchronization behavior of multiple mutually coupled LCE-based spring oscillators, with promising applications in energy harvesting, soft robotics, signal monitoring, and various other fields.

Predicting Surface Oscillations in Lake Superior from Normal Mode Dynamics

Abstract Satellite observation of sea surface height (SSH) may soon have sufficient accuracy and resolution to map geostrophic currents in Lake Superior. A dynamic atmosphere correction will be needed to remove SSH variance due to basinwide seiching. Here, the dynamics of rotating barotropic gravity modes are examined using numerical models and lake-level gauges. Gravity modes explain 94% of SSH variance in a general circulation model and evolve as forced, damped oscillators. These modes have significant SSH, but negligible kinetic energy (2 J m−2) and dissipation rates (0.01 mW m−2) relative to other motions in Lake Superior. Removing gravity modes from instantaneous SSH allows geostrophic currents to be accurately computed. Complex empirical orthogonal functions (CEOFs) from 50 years of data at eight lake-level gauges show patterns consistent with the first two gravity modes. The frequency spectra of these CEOFs are consistent with forced, damped oscillators with natural frequencies of 3.05 and 4.91 cycles per day (cpd) and decay time scales of 4.5 and 1.0 days. Modal amplitudes from the general circulation model and lake-level gauges are 80% coherent at 1 cpd, but only 50% coherent at 3 cpd, indicating that the atmospheric reanalysis used to force the general circulation model is not accurate at the high natural frequencies of the gravity modes. The results indicate that a dynamic atmosphere correction should combine modeled gravity modes below 1 cpd and observed mode-1 and mode-2 amplitudes (from lake-level gauges) at higher frequencies. An inverted barometer correction is also recommended to account for low-frequency atmospheric pressure gradients that do not project onto gravity modes.

Nonlinear dynamics of multiple Alfvén modes driven by trapped energetic ions in tokamaks: A triplet paradigm

Non-linear dynamics of multiple infernal Alfvén eigenmodes—a subset of global Alfvén eigenmodes in tokamak plasmas with extended low-shear central core [Marchenko et al., Phys. Plasmas 16, 092502 (2009)]—is studied. The analysis is carried out for a mode triplet with toroidal mode-numbers n=1, 2, 3. It was assumed that the n = 1 mode was linearly unstable due to precession resonance with trapped fast ions, whereas the other modes were linearly damped. The modes were coupled due to a non-linearity in a bounce-averaged drift kinetic equation for the distribution function of fast ions. Nonlinear equations for the mode amplitudes and phases are derived and solved numerically. It is found that the temporal evolution of the amplitudes and the phase (responsible for the frequency chirping) of the modes exhibit Hopf bifurcations to stable limit cycles. This can explain a synchronous cyclic destabilization of multiple modes in Alfvén avalanches (sudden growth of amplitudes of the mode cluster with different n and approximately equal frequency spacing) in NSTX and bursting modes in MAST—events, which resulted in enhanced loss of fast ions.

Features of vegetative adaptation to educational activities of primary school children

Purpose. To study the functional state of the autonomic nervous system (ANS), which is involved in the formation of adaptation processes in schoolchildren with different physiological abilities. Material and methods. Three groups of junior schoolchildren were examined: 1st – intellectually gifted children, selected based on the results of specialized scales and tests; 2nd – children with high sports/physical abilities; 3rd (control) – schoolchildren with good academic performance and sports/physical abilities. The functional state of the ANS of children was studied using cardiointervalography. Results. The dynamics of the mode indicators, mode amplitude, variation range, and tension index of regulatory systems (IN) indicated that in group 1 the activity of the sympathetic influences of the ANS predominated, the ratio IN2/IN1 showed hypersympathicotonic reactivity. In group 2, the IN values corresponded to normotonic values. The majority of children in groups 2 and 3 had a normal type of autonomic response. The greatest increase in heart rate and systolic blood pressure during orthostasis was observed in group 1. Conclusion. Multidirectional changes in systolic blood pressure and an increase in diastolic blood pressure of varying degrees of severity were established in children of the study groups, which indicates the heterogeneous nature of vascular reactions to orthostasis. The rhythmogram indicators in group 1 are characterized by the predominance of the activity of the sympathetic influences of the ANS. The identified imbalance in the functional activity of the ANS in children of the 1st group indicates the tension of adaptation processes.

Climatology of atmospheric solar tidal mode effects on ionospheric F2 parameters over the American sector during solar minimum between cycles #23 and #24

This work presents the contribution of solar atmospheric tides (diurnal, semidiurnal, and terdiurnal modes) to the variability of the parameters critical frequency (foF2) and peak height of the F2-layer (hmF2) in the American sector during the transition of solar cycles #23 and #24, a period considered one of the lowest solar activities of the modern era. The Digisonde data available in the GIRO data center were analyzed (12 stations), and the solar tide modes were evaluated regarding their amplitude, latitude, and seasonal dependence. The results showed that the hmF2 and foF2 strongly depend on latitude and seasonality, being more intense in the stations located in the south hemisphere. The same behavior is seen for the tidal amplitude fitted in these parameters, except for hmF2 diurnal tide, which is more intense at latitudes farther from the equator. Moreover, the seasonal variability of the amplitude of hmF2 in most cases presented an annual and semiannual component. A terannual component was also observed in 8 h tide mode in the height and frequency parameters. Likewise, what was observed in foF2, the variability in the mean amplitude and different modes of tides of hmF2 are higher over the sectors located in the southern hemisphere.

Nearly critical superfluids in Keldysh-Schwinger formalism

We examine the effective theory of critical dynamics near superfluid phase transitions in the framework of the Keldysh-Schwinger formalism. We focus on the sector capturing the dynamics of the complex order parameter and the conserved current corresponding to the broken global symmetry. After constructing the theory up to quadratic order in the a-fields, we compare the resulting stochastic system with Model F as well as with holography. We highlight the role of a time independent gauge symmetry of the effective theory also known as “chemical shift”. Finally, we consider the limiting behaviour at energies much lower than the gap of the amplitude mode by integrating out the high energy degrees of freedom to reproduce the effective theory of superfluids.

Non-linear modes of global sea surface temperature variability and their relationships with global precipitation and temperature

Sea surface temperature (SST) modes are comprised of variability that arises from inherently nonlinear processes. Historically, a limitation arises from applying linear statistics to define these modes. Accurate depiction of the complex, non-linear nature of SST modes of variability necessitates the specification of a model capable of producing nonlinear patterns. In this study, we apply an artificial neural network algorithm integrated with autoencoders to analyze the seasonal non-linear global SST modes allowing for improved characterization of the modes and their large-scale temperature and precipitation teleconnections. Our results show that during boreal summer, SST cooling over the central to eastern tropical Pacific co-occurs with the Arctic amplification. In recent decades, the negative SST trend in the central to eastern tropical Pacific, combined with the positive trend in the western tropical Pacific is linked to an increase in the amplitude of SST modes associated with the Arctic warming, resulting in warmer temperatures over large portions of the global land, particularly over Greenland. In boreal winter, El Niño Southern Oscillation (ENSO) is the prominent global SST mode. The distinct spatiotemporal patterns of ENSO modes are associated with unique effects on regional land temperature and precipitation. The central Pacific El Niño is more associated with the combination of warm and dry conditions over Western Australia, and the northern part of South America. Conversely, the central to eastern El Niño is more associated with the combination of warm and dry conditions over parts of Southern Africa, and the northern part of South America. The spatiotemporal patterns and trends in the amplitude of the analyzed non-linear global SST modes alongside their regional influences on temperature and precipitation are discussed. The broader impact of this study is on the potential of neural networks in effectively delineating non-linear global SST modes and their associations with regional climates.

Unconventional Charge-Density-Wave Gap in Monolayer NbS2.

Using scanning tunneling microscopy and spectroscopy, for a monolayer of transition metal dichalcogenide H-NbS2 grown by molecular beam epitaxy on graphene, we provide unambiguous evidence for a charge density wave (CDW) with a 3 × 3 superstructure, which is not present in bulk NbS2. Local spectroscopy displays a pronounced gap on the order of 20 meV at the Fermi level. Within the gap, low-energy features are present. The gap structure with its low-energy features is at variance with the expectation for a gap opening in the electronic band structure due to a CDW. Instead, comparison with ab initio calculations indicates that the observed gap structure must be attributed to combined electron-phonon quasiparticles. The phonons in question are the elusive amplitude and phase collective modes of the CDW transition. Our findings advance the understanding of CDW mechanisms in 2D materials and their spectroscopic signatures.

Prediction of Vertical Vibrations of a CNC Router Type Geometry

Mechanical vibrations represent an important problem in machining processes performed by machine tools. They affect surface quality, tool life, and productivity. In extreme situations, chattering may appear, which can dramatically reduce the tool life. CNC router machines are particularly sensitive to vibrations, with their structure bearing resemblance to a composition of beams that are uniform in cross-section. These CNC machines are commonly used for different tasks, like engraving, cutting, and 3D printing. This work proposes a modeling methodology for vibration systems that consist of coupled thin beams subjected to vertical vibration. This methodology is used to model vertical vibrations in a CNC router machine. For this, the geometry is decomposed into beams of uniform cross-sections that are coupled at their ends. Each beam is modeled by means of the classical theory of Bernoulli–Euler for thin beams. The boundary conditions are determined by the beam couplings. In the system thus defined, fundamental frequencies are calculated using the bisection method, and then the modes are computed for the corresponding frequencies. The modal amplitudes, being time-dependent, are modeled as a state space system, considering the first m frequencies. In order to provide support to the modeling methodology, simulation experiments are performed for validation, comparing the results provided by models built with the proposed methodology against finite element models and an experimental setting with a real structure. Moreover, an analysis of the vibration model focusing on a specific component of the equipment is presented to illustrate the usefulness and flexibility of the models obtained with the proposed methodology.

Evolution of weak, homogeneous turbulence with rotation and stratification

This article concerns the time-evolution, spectral structure and scaling of weak turbulence subject to rotation and stable stratification. The flow is expressed as a combination of particular solutions, referred to as modes, of the linearised governing equations without viscosity or diffusion. Modes are of two types: oscillatory ones which represent inertial-gravity waves and time-independent ones that express a non-propagating (NP) component of the flow. The presence of the NP component, which plays an active role in the dynamics apart from in the case of pure rotation, renders wave-turbulence analysis problematic because the NP mode is non-dispersive. Equations are derived for the time evolution of the modal amplitudes, evolution which is due to nonlinearity and visco-diffusion. Subsequent analysis assumes that one or other (or both) of the Rossby and Froude numbers is small (weak turbulence). Given this assumption, the NP component is found to evolve independently of the wave one and a numerical scheme, similar to, though significantly different from classical direct numerical simulation, is used to determine its time evolution. The treatment of the wave component assumes its amplitude is large compared with the NP one, otherwise there are seemingly intractable difficulties of closure in the analysis. Given this further assumption, the wave component decouples from the NP one. Evolution equations for the wave spectra are derived using wave-turbulence analysis and are integrated numerically. As might be expected, these equations indicate that nonlinear coupling of wave modes is dominated by resonances. Results are given for both the NP and wave components.

Nonlinear dynamics of graphene-reinforced aluminum matrix composite aero-engine blade in thermal environment

This paper analyzes the nonlinear dynamic behaviors of the graphene-reinforced aluminum-based aero-engine blade under the primary resonance using the amplitude-frequency response curves, bifurcation diagram, Lyapunov exponent and Poincaré map. The lateral aerodynamic load, longitudinal aerodynamic load, centrifugal force and temperature are investigated for the graphene-reinforced aluminum-based aero-engine blade. Three kinds of configurations for the functionally graphene-reinforced gradient are considered. The effective Young's modulus of the composite material is given by Halpin-Tsai mode. The rule of the mixture gives other material properties. The results demonstrate that the bifurcation diagrams of the modal amplitude for the blade with the lateral aerodynamic load, longitudinal aerodynamic load and temperature have the periodic-chaos dynamic evolution process under the disturbance of the engine rotation speed. When the disturbance amplitude reaches a specific value, a new round of the periodic-chaos dynamic evolution will be continued. The results also clearly indicate that the aero-engine blade has the rich and complex nonlinear dynamic behaviors which include the hyperchaos, chaos, almost periodic, typical period-doubling bifurcation and anti-period-doubling bifurcation vibrations. This research is more helpful for the engineers to understand the nonlinear dynamic behavior of the blade.