Asymmetric Gap Research Articles

The NaNO3–KNO3 phase diagram

Many papers have been published in relation to the NaNO3–KNO3 phase diagram determination in the last 160 years. These papers fall in two categories: (1) the solid–liquid equilibrium is assumed to be of the eutectic type, and (2) the solid–liquid equilibrium is considered as a loop with a minimum. The discordance between the two views is related to the slow transition kinetics that complicate the assessment of thermal ‘fluctuations’, and also to the appearance of a metastable form of potassium nitrate. The main result of this paper is the experimental phase diagram constructed with new experimental data so that we can assure that the second option is correct. This phase diagram is defined by a eutectoid invariant, an asymmetric immiscibility gap and a continuous solid solution with a minimum of melting point. Additionally, the ABθ model simulates correctly the experimental piece of evidence.

Fano resonances and strong field enhancements in arrays of asymmetric plasmonic gap-antennas

In this paper, we numerically study the optical responses of arrays of asymmetric plasmonic gap antennas and show that they support Fano resonances due to symmetry-breaking. The resonance properties can be controlled by the asymmetry. Quality factors more than 30 are achieved, and an enhancement of the electric field exceeding 40 times is predicted to be obtained in antennas with 10-nm wide gaps at the resonance in the near-infrared range. Furthermore, similar designs can be applied in the THz range, and even higher quality factors and stronger field enhancements can be realized. The combination of Fano resonances with gap effects of metallic nanostructures provides an effective way for improvement in light trapping and field enhancement and may find applications in nonlinear optics, sensing, photothermal heat generation, and other areas.

Double Fano resonances in plasmon coupling nanorods

Fano resonances are investigated in nanorods with symmetric lengths and side-by-side assembly. Single Fano resonance can be obtained by a nanorod dimer, and double Fano resonances are shown in nanorod trimers with side-by-side assembly. With transverse plasmon excitation, Fano resonances are caused by the destructive interference between a bright superradiant mode and dark subradiant modes. The bright mode originates from the electric plasmon resonance, and the dark modes originate from the magnetic resonances induced by near-field inter-rod coupling. Double Fano resonances result from double dark modes at different wavelengths, which are induced and tuned by the asymmetric gaps between the adjacent nanorods. Fano resonances show a high figure of merit and large light extinction in the periodic array of assembled nanorods, which can potentially be used in multiwavelength sensing in the visible and near-infrared regions.

Tunneling modes and giant Goos–Hänchen effect of a symmetric heterostructure containing negative-zero-positive index metamaterials

The photonic band gaps and the corresponding tunneling modes in a symmetric heterostructure containing negative-zero-positive index metamaterials (NZPIM) are studied systematically. The zero- $$\bar{n}$$ gap is found to be insensitive to incident angle in contrast to the Bragg gap. Due to the linear dispersion of NZPIM, there exists an asymmetric Dirac point band gap which is always absent of the defect tunneling mode. The tunneling modes inside the gaps and the corresponding giant positive and negative Goos–Hanchen shifts are further investigated. Our results may have potential application in integrated optics and optical devices and also suggest analogous phenomena of valence electron in graphene superlattice.

Ultrathin flexible dual band terahertz absorber

We propose an ultrathin and flexible dual band absorber operated at terahertz frequencies based on metamaterial. The metamaterial structure consists of periodical split ring resonators with two asymmetric gaps and a metallic ground plane, separated by a thin-flexible dielectric spacer. Particularly, the dielectric spacer is a free-standing polyimide film with thickness of 25µm, resulting in highly flexible for our absorber and making it promising for non-planar applications such as micro-bolometers and stealth aircraft. Experimental results show that the absorber has two resonant absorption frequencies (0.41THz and 0.75THz) with absorption rates 92.2% and 97.4%, respectively. The resonances at the absorption frequencies come from normal dipole resonance and high-order dipole resonance which is inaccessible in the symmetrical structure. Multiple reflection interference theory is used to analyze the mechanism of the absorber and the results are in good agreement with simulated and experimental results. Furthermore, the absorption properties are studied under various spacer thicknesses. This kind of metamaterial absorber is insensitive to polarization, has high absorption rates (over 90%) with wide incident angles range from 0° to 45° and the absorption rates are also above 90% when wrapping it to a curved surface.

Gravitational Kaluza-Klein modes in the string-cigar braneworld

In this work we analyze the properties of the gravitational Kaluza-Klein (KK) modes in two stringlike braneworlds, the thin Gherghetta-Shaposhnikov (GS) model and the thick string-cigar model. The string-cigar model is a smooth generalization of the GS model that undergoes a Ricci geometrical flow. We find a new massless mode in both models satisfying the respective Schr\"odinger equations. By means of a numerical analysis, we obtain the complete graviton spectrum and its respective eigenfunctions. The KK spectrum exhibits the usual linear regime for large discrete index $n$ and we find a new decreasing regime for small $n$. Moreover, there is an asymmetric mass gap between the massless mode and the massive KK tower. The mass gap in the GS model is bigger than in the string-cigar model. In addition, the mass gap remains invariant upon the geometrical flow. It turns out that in the string-cigar model the brane structure smoothes and amplifies the KK modes near the brane core. The presence of a potential well in the string-cigar scenario allows the existence of resonant massive gravitons for small masses.

Experimental study along the magnesio-hornblende-glaucophane join

Amphiboles have played a leading role in metamorphic petrology, from helping to define several metamorphic facies to forming the basis of geothermobarometry, if their thermodynamic mixing properties can be calibrated to the temperature and pressure of formation. Compositional variations of sodium- and sodium-calcium-amphiboles may reveal important information about paleo-subduction zones but have not been studied as much as the more common calcium-amphiboles. In this study we investigate the mixing properties of amphibole solid solutions between magnesio-hornblende and glaucophane [ B Ca 2 C (Mg 4 Al) T (AlSi 7 )O 22 (OH) 2 - B Na 2 C (Mg 3 Al 2 ) T (Si 8 )O 22 (OH) 2 ] as a binary sub-join within the ternary amphibole system tremolite-glaucophane-tschermakite where the principal substitutions are Ca for Na at the B, Al for Mg at the C, and Al for Si at the T crystallographic sites. Amphiboles were made from mixtures of reagent oxides at 10 mol% increments between magnesio-hornblende and glaucophane, formed in a piston-cylinder press at 735-860 °C and 1.3-2.5 GPa for 72-216 h giving good yields (92-100 wt%). A positive deviation is present in the volume-composition plot, even after correcting volumes for non-binary components, supporting the presence of a positive deviation in the enthalpy of mixing (ΔH mix ) along this join. Fourier transform infrared spectra (FTIR) were obtained in the range of 350-4000 cm -1 for the mid-infrared spectra (MIR) for the purpose of estimating the extent of short-range ordering and for autocorrelation analysis, and, in the 650-50 cm -1 , for far-infrared spectra (FIR) for autocorrelation analysis. Autocorrelation analysis gave δΔCorr values, which further support a positive deviation in the ΔH mix along the magnsio-hornblende-glaucophane join, although the δΔCorr maximum did not occur at the calcium-poor (i.e., glaucophane-rich) portion of the join as expected. Synthetic end-member glaucophane and magnesio-hornblende were mixed in a molar ratio of 1:1 and allowed to equilibrate by homogenization for variable durations in the range of 600-800 °C at 2.0 GPa to determine the maximum-width of the miscibility gap. These compositional re-equilibration experiments suggested the presence of an asymmetric miscibility gap (steeper toward glaucophane) with a critical-point below 700 °C. Combining the results of this study with previously published results on the tremolite-glaucophane join allowed refinement of several asymmetric formalism mixing parameters (i.e., W Gl,Ts = 20 kJ, α Ts = 1.2) and modeling of the miscibility gap within the tremolite-glaucophane-tschermakite ternary system. The results showed that the composition of the critical point is very close to the maximum in the autocorrelation parameter δΔCorr, as one would predict. An important implication of this study is that low-temperature immiscibility between calciumand sodium-rich amphiboles may be more important than the role of pressure, as proposed by Brown (1977), in accounting for the change in B-site Na contents of metamorphic amphiboles.

A Novel Fluid Structure Interaction-EHD Model and Optimization Procedure for an Asymmetrical Axially Balanced External Gear Machine

This article presents a novel fluid structure interaction (FSI) model for lateral lubricating interfaces in an asymmetrically balanced external gear pump. Due to the asymmetry in the geometry of the floating lateral bushes responsible for sealing the displacement chambers in such machines, the lubricating interfaces on either side of the gears have been modeled as distinct but coupled lubricating films. An elastohydrodynamic (EHD) lubrication regime was modeled in all simulations and film thickness predictions for both lubricating interfaces have been achieved. The novel FSI model for the asymmetric lateral gaps is then used in an automatic optimization procedure to design the optimal axial balance in the reference external gear machine (EGM). The optimal axial balance is achieved by determining the optimal balance area on the lateral bush by considering specific design variables associated with it. The procedure aims to find the best feasible design solution that minimizes the total power losses in the lubricating interfaces while also minimizing the nonuniformities in the orientation of these gaps between two significant operating conditions of the EGM. The developed procedure highlights the potential to virtually design the axial balance in EGMs—which represent a key design aspect of pressure compensated EGM—by using an advanced FSI-EHD model.

Diagnostic Challenge of Sulcus Vocalis Made Easier

ABSTRACT Objectives To introduce a simple diagnostic test performed with white light laryngoscopy for the diagnosis of sulcus vocalis. Materials and methods This is a retrospective observational study. A total of 14 patients with voice-related complaints and a phonatory gap on examination were included. Obvious structural and neuromuscular glottic pathologies were excluded. Phonatory gap was measured using white light rigid laryngoscopy with the technique described here. Findings were then correlated with stroboscopy. Results All 14 patients (10 U/L and 4 B/L), observed to have an asymmetric phonatory gap on white light rigid laryngoscopy, were diagnosed with sulcus vocalis. Conclusion An asymmetric phonatory gap, as seen on white light laryngoscopy and measured with the simple technique mentioned here, should make the laryngologist suspect a sulcus vocalis. However, the diagnosis needs to be confirmed by stroboscopy. How to cite this article Nerurkar NK, Gupta HK, Shedge AE. Diagnostic Challenge of Sulcus Vocalis Made Easier. Int J Phonosurg Laryngol 2015;5(2):39-41.

Spin asymmetric band gap opening in graphene by Fe adsorption

Abstract The adsorption of Fe atom on graphene is studied by first-principles Density Functional Theory. The structural, electronic, and magnetic properties are analyzed at different coverages, all preserving C6v symmetry for the Fe adatom. We observed that binding energies, magnetic moments, and adsorption distances rapidly converge as the size of the supercell increases. Among the considered supercells, those constituted by 3n graphene unit cells show a very peculiar behavior: the adsorption of a Fe atom induces the opening of a spin-dependent gap in the band structure. In particular, the gap amounts to tenths of eV in the majority spin component, while in the minority one it has a width of about 1 eV for the 3 × 3 supercell and remains significant even at very low coverages (0.25 eV for θ ≃ 2%). The charge redistribution upon Fe adsorption has also been analyzed according to state of the art formalisms indicating an appreciable charge transfer from Fe to the graphene layer.

Heterotypic gap junctions at glutamatergic mixed synapses are abundant in goldfish brain

Gap junctions provide for direct intercellular electrical and metabolic coupling. The abundance of gap junctions at “large myelinated club ending (LMCE)” synapses on Mauthner cells (M-cells) of the teleost brain provided a convenient model to correlate anatomical and physiological properties of electrical synapses. There, presynaptic action potentials were found to evoke short-latency electrical “pre-potentials” immediately preceding their accompanying glutamate-induced depolarizations, making these the first unambiguously identified “mixed” (i.e., chemical plus electrical) synapses in the vertebrate CNS. We recently showed that gap junctions at these synapses exhibit asymmetric electrical resistance (i.e., electrical rectification), which we correlated with total molecular asymmetry of connexin composition in their apposing gap junction hemiplaques, with connexin35 (Cx35) restricted to axon terminal hemiplaques and connexin34.7 (Cx34.7) restricted to apposing M-cell plasma membranes. We now show that similarly heterotypic neuronal gap junctions are abundant throughout goldfish brain, with labeling exclusively for Cx35 in presynaptic hemiplaques and exclusively for Cx34.7 in postsynaptic hemiplaques. Moreover, the vast majority of these asymmetric gap junctions occur at glutamatergic axon terminals. The widespread distribution of heterotypic gap junctions at glutamatergic mixed synapses throughout goldfish brain and spinal cord implies that pre- vs. postsynaptic asymmetry at electrical synapses evolved early in the chordate lineage. We propose that the advantages of the molecular and functional asymmetry of connexins at electrical synapses that are so prominently expressed in the teleost CNS are unlikely to have been abandoned in higher vertebrates. However, to create asymmetric coupling in mammals, where most gap junctions are composed of connexin36 (Cx36) on both sides, would require some other mechanism, such as differential phosphorylation of connexins on opposite sides of the same gap junction or on asymmetric differences in the complement of their scaffolding and regulatory proteins.

Thermal evolution of the band edges of 6H-SiC: X-ray methods compared to the optical band gap

The band gap of semiconductors like silicon and silicon carbide (SiC) is the key for their device properties. In this research, the band gap of 6H-SiC and its temperature dependence were analyzed with silicon 2p X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS) allowing for a separate analysis of the conduction-band minimum (CBM) and valence-band maximum (VBM) components of the band gap. The temperature-dependent asymmetric band gap shrinking of 6H-SiC was determined with a valence-band slope of +2.45×10−4eV/K and a conduction-band slope of −1.334×10−4eV/K. The apparent asymmetry, e.g., that two thirds of the band-gap shrinking with increasing temperature is due to the VBM evolution in 6H-SiC, is similar to the asymmetry obtained for pure silicon before. The overall band gap temperature-dependence determined with XAS and non-resonant XES is compared to temperature-dependent optical studies. The core-excitonic binding energy appearing in the Si 2p XAS is extracted as the main difference. In addition, the energy loss of the onset of the first band in RIXS yields to values similar to the optical band gap over the tested temperature range.

Solid solutions and phase transitions in (Ca,M2+)M2+Si2O6 pyroxenes (M2+ = Co, Fe, Mg)

The effect of the substitution of Ca with Co, on the phase transition and on the extension of the miscibility gap, was studied to model the general mechanism of phase transitions and solid solutions in (Ca,M 2+ )M 2+ Si 2 O 6 pyroxenes. Eleven pyroxenes with composition Ca 1−x Co 1+x Si 2 O 6 , (0 ≤ × ≤ 1) were therefore synthesized by piston cylinder at P = 3 GPa, and T between 1100 and 1350 °C. The samples were characterized by SEM-EDS, XRD powder diffraction, and TEM. The results were compared with those of Ca-Fe and Ca-Mg pyroxenes. The phase diagram of Ca-Co pyroxenes is similar to that of Ca-Fe and Ca-Mg ones, with a wide asymmetric miscibility gap, and higher solubility in the Ca-rich side of the gap. The solubility on the Ca-rich side of the gap is related to the radius of the cation substituting. The cell parameters of the Ca-Co pyroxenes undergo a sudden change at the composition of about 0.4 Ca apfu, due to the C 2/ c – P 2 1 / c phase transition. The change in volume with composition follows an ideal trend, in the C 2/ c phase, dictated by the ionic size of the substituting cation. Deviation from the C 2/ c behavior are instead observed in the P 2 1 / c field and ascribed to volume strain. The same turnover was found in Ca-Mg, Ca-Fe, and Ca-Mn pyroxenes. The C 2/ c – P 2 1 / c transition occurs with decreasing the M2 average cation radius, down to a critical value between 0.85 and 0.88 A, depending on the series. A stabilization of the C 2/ c phase related to crystal field in Ca-Fe and Ca-Co pyroxenes is suggested by the analysis of the volume strain in the P 2 1 / c field. A key finding is that a miscibility gap may develop either by lattice strain related to cation substitution, within a series where all end-members have the same structure, or for the combined effect of lattice strain and a phase transition, as is the case for pyroxenes.

Design for Triple Band Patch Array Antenna with High Detection Ability

This paper proposes a theoretical analysis of hidden device detection and a design of multiband circular polarization patch array antenna for non-linear junction detector system application. A good axial ratio of circular polarization patch antenna is realized by a new approach that employs inclined slots, two rectangular grooves and a truncated ground for the conventional antenna. A good axial ratio of the 1.5 dB lower is measured by having an asymmetric gap distance between the ground planes of the coplanar waveguide feeding structure. The common ground plane of the linear array has an optimum trapezoidal slot array to reduce the mutual coupling without increasing the distance between the radiators. The higher gain of about 1 dBi is realized by using the novel common ground structure. The measured return loss, gain, and axial ratio of the proposed single radiator, as well as the proposed array antennas, showed a good agreement with the simulated results.

Flow noise induced by small gaps in low-Mach-number turbulent boundary layers

The flow-noise induced by small gaps underneath low-Mach-number turbulent boundary layers at Reθ = 4755 is studied using large-eddy simulation and Lighthill's theory. The gap leading-edge height is 13% of the boundary-layer thickness, and the gap width and trailing-edge height are varied to investigate their effects on surface-pressure fluctuations and sound generation. The maximum surface pressure fluctuations, which increase with gap width and trailing-edge height, occur at the trailing edge or near the reattachment point if there is separation from the trailing edge. The downstream recovery towards an equilibrium boundary layer is significantly faster for gap flows compared to step flows, and the recovery distance scales with the reattachment length for gaps with trailing-edge separation. The acoustic field is dominated by the forward-facing step in the gap and resembles forward-step sound for wide gaps and/or asymmetric gaps with trailing edge higher than leading edge. In these cases, the dominant acoustic source mechanisms are the impingement of the separated shear layer from the leading edge onto the trailing edge and the unsteady separation from the trailing edge, coupled with edge diffraction. For narrow and symmetric gaps, the destructive interference of sound from the leading and trailing edges causes a significant decline in low-frequency sound and thereby creates a broad spectral peak in the mid-frequency range. The effects of gap acoustic non-compactness and free-stream convection are investigated by comparing solutions based on a compact gap Green's function with those from a boundary-element calculation. They are found to be negligible at the typical hydroacoustc Mach number of 0.01, but become significant at Mach numbers as low as 0.1 and moderately high frequencies.

Paragenesis and chemical characteristics of the celsian−hyalophane−K-feldspar series and associated Ba-Cr micas in barite-bearing strata of the Mesoarchaean Ghattihosahalli Belt, Western Dharwar Craton, South India

The upper greenschist - lower amphibolite facies, argillaceous to chemical-exhalative metasedimentary sequence of the Mesoarchaean Ghattihosahalli Schist Belt (GHSB), southern India, has been examined with a special focus on the paragenesis and solid solution characteristics of barian feldspars and associated dioctahedral Ba-Cr-bearing micas. Barian feldspars occur as untwinned porphyroblasts in a recrystallized finely banded matrix of barite, quartz and minor white mica. Idioblastic celsian (Cls98-76Or2-20Ab1-8) and hyalophane (Cls55-39Or35-51Ab10) predate the greenschist-facies foliation, whereas xenoblastic hyalophane (Cls44-35Or45-59Ab8–17) and mantles on celsian (Cls45-35Or42-60Ab13-5) as well as xenoblastic barian K-feldspar (Cls6Or90Ab2) postdate the last fabric-defining event. The preservation of extremely complex zoning patterns down to the micron-scale shows that diffusional homogenization did not operate at fluid-present low to medium-grade conditions (350–550 °C, 3–5 kb). Microstructures indicate that at these conditions barian feldspars deform exclusively by brittle fracturing and do not undergo recrystallization. Barian feldspar compositions confirm the positive correlation of Na-content with temperature and the existence of a narrow asymmetric compositional gap (Cls90-85↔Cls55, ~350 °C) which probably closes at lower amphibolite facies conditions (Xc ~Cls75; Tc ~550 °C). White micas are solid solutions of the end-members muscovite, ganterite (Ba0.5 K0.5)Al2(Al1.5Si2.5)O10(OH)2, paragonite, celadonite with a significant substitution of [VI]Al by Cr. Zoning is a common feature with cores being enriched in Ba. The data document extensive Ba substitution for K from muscovite to ganterite, exclusively controlled by the coupled substitution [XII]K + [IV]Si ↔ [XII]Ba + [IV]Al and strongly dependent on bulk composition. The extent of solid solution from (Ms+Gnt) towards paragonite and celadonite end-members is controlled by the miscibility gap in the (Ms+Gnt)–Pg–Cel pseudoternary, with the Pg-substitution depending on temperature and the Cel-substitution on pressure. [IV]Si values between 3.1 and 3.3 in Ba-poor micas indicate minimum pressures of chemical equilibration in the order of 3–5 kbar, while the most sodian compositions of low-celadonite micas provide an upper temperature estimate of ~550 °C, consistent with P-T estimates for assemblages of metapelites (500–550 °C, 4–5 kb).

Compact Circularly Polarized Antennas Combining Meta-Surfaces and Strong Space-Filling Meta-Resonators

Reduced-size single-feed circularly-polarized (CP) patch antennas are proposed and investigated based on the strategy of combining meta-surfaces and meta-resonators owning strong space-filling capability. They all comprise a slot-loaded square patch printed over a well designed reactive impedance surface (artificial meta-surface with magnetic response at the resonant frequency) for improved antenna performances and size reduction. The complementary crossbar fractal tree (CCFT) slot and three-turn complementary spiral resonators (TCSRs) with asymmetric gap orientation are employed as meta-resonators to render the antennas to radiate CP waves in single-band or dual-band operation and to facilitate further miniaturization. Numerical and experimental results indicate that these antennas owning a maximum size of 0.262λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> × 0.262λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> around 3 GHz exhibit a comparable impedance and axial ratio (AR) bandwidth over 1.05% and high gain of more than 4.15 dBic, predicting promising applications in portable and handheld communication systems.

Asymmetric dust distribution in an eccentric protoplanetary disk as a signpost of a gas giant planet

AbstractThe presence of a cavity in a protoplanetary disk revealed by dust continuum emissions is sometimes postulated as a signpost of an embedded gas giant planet. More peculiarly, dust emissions exterior to the cavity are often observed to be asymmetric. We explore the possibility of the asymmetry as a result of the asymmetric distribution of dust in an eccentric protoplanetary disk under the secular gravitational perturbation of an embedded massive gas giant planet. We find that the surface density of the dust well coupled to the disk gas is enhanced around the apocenter of the disk. In addition, the azimuthal distributions of particles of various sizes can deviate significantly due to different coupling to the gas. Overall, the asymmetric structure exhibits a phase correlation between the gas velocity field and dust density distribution. A Doppler map for an eccentric disk is also presented based on Cycle 1 ALMA observations. Our study potentially provides a reality check as to whether an asymmetric disk gap detected at sub-mm and cm wavelengths is a signpost of a massive gas giant planet.

The significance of an asymmetric extension gap on routine radiographs after total knee replacement

We investigated whether an asymmetric extension gap seen on routine post-operative radiographs after primary total knee replacement (TKR) is associated with pain at three, six, 12 and 24 months' follow-up. On radiographs of 277 patients after primary TKR we measured the distance between the tibial tray and the femoral condyle on both the medial and lateral sides. A difference was defined as an asymmetric extension gap. We considered three groups (no asymmetric gap, medial-opening and lateral-opening gap) and calculated the associations with the Western Ontario and McMaster Universities osteoarthritis index pain scores over time. Those with an asymmetric extension gap of ≥ 1.5 mm had a significant association with pain scores at three months' follow-up; patients with a medial-opening extension gap reported more pain and patients with a lateral-opening extension gap reported less pain (p = 0.036). This effect was still significant at six months (p = 0.044), but had lost significance by 12 months (p = 0.924). When adjusting for multiple cofounders the improvement in pain was more pronounced in patients with a lateral-opening extension gap than in those with a medial-opening extension gap at three (p = 0.037) and six months' (p = 0.027) follow-up.

Impact vibration characteristics of a shrouded blade with asymmetric gaps under wake flow excitations

The vibro-impact mechanism of a rotating shrouded blade with asymmetric gaps is investigated. The Frobenius method is employed to determine the dynamic frequencies and corresponding mode functions of the shrouded blade under the action of dynamic stiffness. The mode functions are used to truncate the governing partial differential equation of the shrouded blade to ordinary differential equations by using the Galerkin method. Taking into account the influence of the rotating speed, the contact stiffness of adjacent blades is assumed to be an equivalent contact spring stiffness which is determined by the bending dynamic stiffness of the blade. Then the average method is employed to obtain the dynamic responses of the primary, the sub-harmonic and the super-harmonic resonances of the shrouded blade with wake flow excitation, respectively. Finally, the dynamical responses of a shrouded blade with a set of typical material constants and geometrical parameters are given to illustrate the influence of the blade shroud gaps on the vibration amplitude.