Circumferential Modes Research Articles

Critical speed and frequency behavior of rotating joined FG-CNTRC conical-conical shells

This paper provides information on critical speed and frequency behavior of rotating joined functionally graded carbon nanotube reinforced (FG-CNTRC) conical-conical shells. Furthermore, frequency bifurcation as a consequence of rotational effects is investigated. The shell is assumed to be composed of an isotropic polymer matrix that is reinforced by uniformly or functionally distributions of carbon nanotubes (CNTs). The structure’s kinematics originates from the first order shear deformation theory (FSDT). To derive spin-based motion equations, Coriolis and centrifugal forces together with initial hoop tensions are propounded through the Hamilton’s principle. Moreover, matching and boundary conditions are ascertained to supplement the governing equations. To discretize the governing equations meridionally, the generalized differential quadrature (GDQ) technique is employed. After validity checking, some significant parameters like cones’ angles, rotation speed, edge supports, CNT volume fractions and dispersion patterns that play effective roles on the critical speed and vibration characteristics are examined. It is revealed that by enhancing spinning speed, frequencies of different FG patterns converge. In addition, difference between backward and forward frequencies decreases as the circumferential mode number increases.

Bending failure analysis of level ice with temperature-gradient effect under inclined structure collision

To better investigate ice-structure collision, it is important to obtain the failure mechanisms of level ice under different loading cases. The present study aimed to explore the bending failure of level ice using the extended finite element method. The temperature-gradient effect in the thickness direction of level ice is studied by the improved ice model. The numerical model is verified by comparing the location of bending crack and the collision load observed from a published field test. It is proved that the temperature-gradient has a significant effect on the collision process. Based on the validated model, different crack forms of level ice caused by bending failure under different loading parameters are investigated. It reveals two modes of cracks, i.e. radial and circumferential modes. A parametric sensitivity analysis demonstrates the crack mode will transform from radial to circumferential mode with the increase of loading angle, rate and area. Besides, the conversion mechanism of two crack modes is investigated by analyzing the distribution of yield factor and the principal stress. When the load is slighter, the level ice is mainly deformed locally, causing radial cracks. When the load is violent, more energy will be absorbed by ice. The level ice is mainly deformed integrally, causing circumferential crack.

The effect of mean flow on the intrinsic thermoacoustic instabilities in the duct and annular combustion chambers

Thermoacoustic instability in the combustion chamber of gas turbines, aero and rocket engines has become a topic concern. In this paper, a new instability phenomenon in the field of the thermoacoustic instability - Intrinsic ThermoAcoustic instabilities (ITA) is studied. The classic thermoacoustic instability is caused by the coupling among acoustic disturbances, flow fluctuations and heat release pulsations. When the influence of acoustic disturbance is removed, there is still a thermoacoustic instability phenomenon in the combustion chamber, which is known as ITA. In the previous research on ITA, the scholars found that the ITA is mainly determined by the flame response, but many scholars neglected the influence of the mean flow and entropy waves. In this paper, the influence of the mean flow on the ITA mode in the duct and annular combustion chambers is studied by constructing a low-order acoustic network model. At the same time, it also explores the influence of other parameters on the ITA mode. The mean flow greatly affects the growth rate of the ITA mode, and has little effect on its frequency in the duct combustion chamber model. This is also the main reason for neglecting the effect of mean flow on the ITA mode in previous studies. In addition, the influence of other parameters on the ITA mode is also reflected in the growth rate. In the annular combustion chamber, a new ITA mode, which does not meet the −π criterion, is found. And the increase of Mach number makes all ITA modes more unstable. The circumferential mode number has a great influence on the high frequency ITA mode. In addition, the ITA mode has a significant effect on the thermoacoustic mode of the system in the annular combustion chamber.

Numerical and Experimental Investigations of Modal Coherence Characteristics for the Determination of Broadband Noise in Flow Ducts

This paper presents a detailed investigation about the modal coherence characteristics of turbomachinery noise. The modal coherence characteristics of ducted noise at high frequencies are investigated by establishing three kinds of ducted sound source distribution models. The results are consistent with the acoustic experimental results of a single-stage axial fan. The results show that acoustic modes of different orders are mutually incoherent, and radial modes within the same circumferential mode have a great degree of coherence. This paper successfully conducted an acoustic measurement on turbomachinery noise by rotating microphone arrays. The acoustic experimental results show that the coherence of some modes has little impact on the measurement of incident acoustic waves in the flow duct, while it leads to about 3 dB deviation in the prediction of the reflected modal sound power and has little influence on the spectral shape of reflected acoustic waves. It was demonstrated that the experimentally measured modal coherence functions give an inner sense of the spatial noise source distribution and enable the investigation of mode scattering within the propagation. Based on the modal coherence characteristics obtained in this paper, more theoretical and methodological studies can be carried out for the turbomachinery broadband noise test.

Damping and Frequency Response Characteristics of Functionally Graded Fiber-Reinforced Composite Cylindrical Shells

This paper presents research on the modal damping and frequency response of functionally graded fiber-reinforced composite cylindrical shells considering the internal damping. Based on the Love shell theory and energy approach, the dynamical equations of cylindrical shells are established. In the process of variable separation, the Haar wavelet series and trigonometric functions are respectively to represent the axial and circumferential modes. Based on the microscopic damping prediction method and multi-cell model of hybrid materials, the equivalent damping and elastic characteristics of composite materials are determined. Then the damping and frequency response characteristics are solved by the complex modulus method. The present analysis is validated by comparing the results with those in the literature and finite element simulation. The effects of fiber content and distribution, lamination and geometry configuration on damping and frequency response properties are further analyzed. The analysis show that the damping decreases monotonically with the increase of fiber volume fraction. The damping behaviors may be improved by changing the fiber distribution type and stacking sequence. Increasing the internal damping of composites can obviously reduce the vibration amplitude in the resonance region, especially in the high frequency range.

Numerical study of the effect of the corrugated baffle on the acoustic characteristics of the combustion chamber

Combustion instability caused by the amplification of sound waves is called acoustic or high-frequency instability, which can cause severe damage to the system. Adding baffles is one of the methods of passive instability control. Depending on the geometry of the chamber and the type of application, different baffles are used. In this research, the effect of the longitudinal corrugated baffle on the acoustic characteristics of the combustion chamber is investigated numerically. The quality of each baffle configuration is determined by examining their influence on the essential parameters such as natural frequency shift and damping factor. Modal and harmonic analyses for the acoustic field are conducted to investigate the effect of baffles installed in the combustion chamber. According to the obtained results, the addition of baffle shifts resonant frequencies. In other words, a combustor with baffles is more effective in controlling the instabilities than that without baffles. In addition, it increases the damping factor in the first–second circumferential (tangential) modes, making the system more stable. Also, a quantitative assessment of the acoustics by adding baffles shows that combustion chamber finds a better condition from stability point of view, and the bandwidth increase affects the combustion stability.

Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.

Optical diagnostics and multi-point pressure sensing on the knocking combustion with multiple spark ignition

Engine knock is an abnormal combustion phenomenon that limits the thermal efficiency and service life of spark-ignition engines. A better understanding of the knock mechanisms and characteristics is beneficial to knock alleviation and engine efficiency improvement. In this study, a metal liner with four evenly-spaced spark plugs in the periphery of the combustion chamber is designed to initiate knock from different positions. Four spark strategies are applied to the single-cylinder optical research engine and six pressure sensors are utilized to analyze the local pressure oscillations in the cylinder. The knocking combustion is investigated by simultaneous 72 kHz high-speed imaging and 6-point pressure sensing. The experimental results indicate that using multiple spark-ignition could promote knock intensity, advance the start of auto-ignition and introduce more acoustic resonance modes. The center pressure sensor is more sensitive to the first radial resonant mode (0, 1) of the knock pressure oscillation, while the side sensors are more sensitive to the first and second circumferential resonant modes (1, 0) and (2, 0). The knock onset judged by natural flame photography is earlier than that by pressure analysis because the auto-ignition event happens first and induces the subsequent pressure fluctuation. Natural flame luminosity analysis demonstrates that the initial auto-ignition sites only cause weak pressure oscillations, and the instantaneous combustion of the remaining end-gas increases the heat release rate significantly and gives rise to more violent pressure oscillations. Statistically, the maximum amplitude of pressure oscillation follows an exponential relationship with the peak mean flame luminosity. The end-gas resides in the gaps among the flame fronts generated by different spark strategies while the first auto-ignition sites are not evenly distributed in the end-gas zone. This fact gives insights into the local temperature non-uniformity of the end gas zone that affects the spatial distributions of the initial auto-ignition sites in the cylinder.

Achieving cylindrical duct modes generation in spinning mode synthesizer via a least-square identification of the global calibration factor

Spinning Mode Synthesizer is an effective engine noise test rig for aero-engine noise propagation and radiation research. Spinning mode generation is realized through amplitude modulation and phase shift between individual loudspeakers. The target spinning mode is not the primary mode. It is even submerged in the undesired modes due to the system error of artificial source generators, especially the magnitude and phase mismatch of loudspeakers. In this paper, a global calibration factor is used to minimize the effect of loudspeaker nonuniformity in mode generation. The mode generation process of the calibrated system is mainly divided into two steps. The first step is to identify the calibration factors of individual loudspeakers with an optimized microphone array, which is used primarily for mode analysis. No particular error sensor or additional devices is used in the measurement. The theoretical complex source strengths are multiplied by the calibration factor to calibrate artificial source generators. The second step is to carry out mode generation experiments using the calibrated system, and Radial Mode Analysis is used to analyze the mode components in the duct. A spinning mode synthesizer with three axially spaced rows of loudspeakers is introduced, and each row consists of 12 excitation units. The maximum controllable circumferential mode order is m = 9, and the maximum controllable radial mode order is n = 2. It has been proven that the calibrated system can generate the target mode more precisely, and the mode coefficient signal-to-noise ratio (SNRA) of any propagable mode is greater than 10 dB in the operating frequency range.

Noise Characteristics of Automobile Cooling Fan Based on Circumferential Mode Analysis

Abstract The fan is the main component of the cooling system of an automobile engine. A typical automobile cooling fan consists of a shrouded axial fan, stator vanes, a deflector, and a cover. With recent developments in the automobile industry, the increase in the speed of rotation and blade load of cooling fans has increased the noise generated by them. To reduce it, it is important to analyze the characteristics of this noise. This paper uses an acoustic test to examine the characteristics of flow and noise of automobile cooling fans. The frequency spectrum and far-field radiation of the noise of the fan are first analyzed through far-field measurements, and the influence of the single rotor, tip clearance of the blade, and cover on fan noise is studied. The distribution of the mode spectrum and characteristics of sound propagation of discrete tonal noise are then examined using the circumferential mode test. The influence of the flow structure on fan noise is also studied. The flow characteristics and distribution of the source of noise of the automobile cooling fan are then used to analyze the influence of the structure of the fan on the noise generated by it. The results can help develop designs to reduce the noise of automobile cooling fans.

Knocking characteristics of a high pressure direct injection natural gas engine operating in stratified combustion mode

Abstract Knocking becomes an increasingly important issue in direct injection natural gas engines with the application of new combustion modes. In this article, the knocking characteristics of natural gas engine operating in stratified combustion mode were studied with the aid of cylinder pressure oscillations and combustion parameters. The results indicated that knocking tendency will be stronger when operating in stratified combustion mode. The first to the fourth circumferential modes and the first radial mode are the featured modes for knocking behavior, while knocking is more serious when the duration of 10–50% of total energy released is shorter.

Single‐sweep pulmonary vein isolation using the new third‐generation laser balloon—Evolution in ablation style using endoscopic ablation system

The endoscopic ablation system (EAS) is an established ablation device for pulmonary vein isolation (PVI) in patients with atrial fibrillation (AF). The novel X3 EAS is now equipped with a contiguous circumferential ablation mode (RAPID mode). To determine the feasibility of single-shot fashioned ablation using X3. Consecutive patients who underwent AF ablation using X3 were enrolled. We assessed the acute procedural data focusing on "Single-sweep PVI" defined as successful PVI with a single RAPID mode energy application, and on "first-pass isolation" defined as successful PVI after initial circular lesion set. One hundred AF patients (56% male, age: 68 ± 10 years, 66% paroxysmal AF) were analyzed. A total of 379 of 383 PVs (99%) were isolated with X3. Single-sweep PVI and first-pass-isolation were achieved in 214 PVs (56%) and in 362 PVs (95%), respectively. Single-sweep PVI rates varied across PVs with higher rates at the superior PVs (61.2% vs. inferior PVs: 49.5%, p = .0239) and at PVs with maximal ostial diameter <24 mm (57.6% vs. >24 mm: 36.8%, p = .0151). The mean total procedure and fluoroscopy times were 43.0 ± 10 and 4.0 ± 2 min, respectively. In none of the patients an acute thromboembolic event (stroke or transient ischemic attack) or a pericardial effusion/tamponade occurred. A single transient phrenic nerve palsy was observed. The new X3 EAS allows for single-shot fashioned ablation in terms of single-sweep PVI in half or more of PVs. The new RAPID ablation mode leads to an improved rate of first-pass isolation associated with very short procedure times without compromising safety.

Effects of injection strategy on the knocking behavior of a pilot ignited direct injection natural gas engine

Pilot ignited direct injection natural gas engines have become a research focus due to the high thermal efficiency and low emissions. However, when stratified combustion mode is adopted, more attention should be paid to the knocking behavior. In this paper, the effects of injection strategy on the knocking behavior of a pilot ignited direct injection natural gas engine have been studied. The results indicated that the knocking intensity will be increased at advanced natural gas injection timing, delayed diesel injection timing and raised injection pressure. The three major resonance modes that dominate the pressure oscillations are the first circumferential mode, the third circumferential mode and the first radial mode. Advancing natural gas injection has negative effects on cyclic variations of indicated mean effective pressure while have negligible effects on the cyclic variations of combustion duration. After correlation analysis of parameters, it was found that knocking behavior is highly correlated with maximum heat release rate, combustion duration and maximum combustion pressure, whereas has weak correlations with combustion phasing and cyclic variations.

Numerical study of enhanced Rayleigh streaming in resonant cylindrical shells

We have numerically demonstrated a type of enhanced Rayleigh streaming in a resonant cylindrical shell (CS) by using the limiting velocity method. It is found that the main characteristics of the resonant streaming field resemble those of classical Rayleigh streaming in a rigid cylindrical cavity. Nevertheless, the maximum velocity of the demonstrated streaming in the resonant CS is significantly higher than that of classical Rayleigh streaming in a rigid cylindrical cavity under the same acoustic conditions. In addition, the velocity of the demonstrated streaming at the low resonant frequency is higher than that at the high resonant and non-resonant frequencies in the shell. The enhancement of the demonstrated streaming originates from the resonant excitation of non-leaky circumferential modes intrinsic to the CS, characterizing with the enhanced gradient acoustic fields in the viscous boundary layer around its inner surface. This type of streaming may be of interest for acoustofluidic devices in many applications such as particle manipulation and liquid mixing.

Simulation of the frequency split of the fundamental air cavity mode of a loaded and rolling tire by using steady-state transport analysis

It has been found that when a tire deforms due to loading, the fundamental air cavity mode splits into two due to the break in geometrical symmetry. The result is the creation of fore-aft and vertical acoustic modes near 200 Hz for typical passenger car tires. When those modes couple with structural, circumferential modes having similar natural frequencies, the oscillatory force transmitted to the suspension can be expected to increase, hence causing increased interior noise levels. Further, when the tire rotates, the frequency split is enlarged owing to the Doppler effect resulting from the airflow within the tire cavity. The current research is focused on determining the influence of rotation speed on the frequency split by using FE simulation. In particular, the analysis was performed by using steady-state transport analysis which enables vibroacoustic analysis in a moving frame attached to tire in the frequency domain. The details of the modeling are described and results are given for a tire under different rotation speeds, presented in terms of dispersion curves that illustrate the interaction between structural and acoustical modes. The results are compared to those for static tires and tires spinning without translational velocity to highlight the effects of rolling.

Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization

The presented paper is the first attempt to apply deep learning for predicting the frequency characteristics of a magneto-electro-elastic (MEE) annular nano/microdisk (MEEAD). The optimum amount of the factors participating in the mechanism of the fully connected neural network are achieved through the optimizer based on the momentum. The positive side of the mentioned approach employed in this investigation would be due to its high accuracy along with lower epochs required for training the multi-layered network. This scrutinization would be semi-computational research that estimates the vibrational behavior of a MEEAD employing a non-classical continuum model known as the modified couple stress (MCS) model. First-order shear deformation theory (FSDT) and shell model would be provided for presenting their displacement fields. Then, Kelvin-Voight theory has been applied to model the viscoelastic foundation. Its non-classical governing equations, as well as related boundary conditions (BCs) of small-scaled MEEAD, would be achieved by considering the symmetric spinning gradient along with higher-order stress tensors for the strain energy. The provided non-classical theory would be able to capture the small scale in the MEEAD employing just one length scale of a material factor, then, the mathematical modeling of MEEAD according to the classical theory would be able to be recovered from the provided model by eliminating the material length scale factor. Ultimately, the non-classical governing equations would be solved by applying the generalized differential quadrature (GDQ) approach for multifarious BCs. Moreover, parametric research has been conducted to analyze the influences of the viscoelastic foundation, length scale factor, geometry of MEE, radial and circumferential mode number, radius ratio, and BCs on the frequency behavior of the MEEAD by applying MCST. The outcomes reveal that there would be a crucial radius ratio in which the relationship between these elements and crucial inserted voltage alters from direct to indirect relation.

On the vibro-acoustic response of a cylindrical shell submerged near a free sea surface

A vibro-acoustic model of a structurally excited cylindrical shell of infinite length submerged in a heavy fluid at a finite distance from a free surface is presented. Expressions for the shell displacement, the acoustic pressure in the interior cavity of the shell and the acoustic pressure at all field locations in the exterior domain are analytically derived. The formulation for the exterior acoustic pressure is developed using the image method and Graf's addition theorem. Results for the structural and acoustic responses of the cylindrical shell submerged at a finite distance from the free surface and in an unbounded fluid domain are compared. The effects of the shell circumferential modes, interior cavity resonances and proximity of the free surface on the shell acoustic responses are examined. New mechanisms influencing the low frequency vibro-acoustic response of a submerged hull near a fluid boundary are described.

Circumferential crack modeling of thin cylindrical shells in modal deformation

An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element including the crack is divided into three sub-elements with four nodes in which the stiffness matrix is enriched. The crack characteristics are included in the finite element method relations through conversion matrices and a rotational spring corresponding to the crack. Conversion matrices obtained by applying continuity conditions at the crack tip are used to transform displacements of the middle nodes to those of the main nodes. Moreover, another technique, called spring set, is represented based on a set of springs to model the crack as a separated element. Components of the stiffness matrix related to the separated element are incorporated while the geometric boundary conditions at the crack tip are satisfied. The effects of the circumferential mode number, the crack depth and the length of the cylinder on the critical buckling load are investigated. Experimental tests, ABAQUS modeling and results from literature are used to verify and validate the results and derived relations. In addition, the crack effect on the natural frequency is examined using the vibration analysis based on the conversion technique.

Higher order electro-magneto-elastic free vibration analysis of piezomagnetic nano panel

Abstract This paper investigates electro-magneto-elastic free vibration responses of piezomagnetic cylindrical nano panel subjected to electro-magneto-mechanical loads based on third-order theory. Third-order shell theory is used for description of the displacement field. The zero transverse shear strains are obtained using the third-order displacement field. Hamilton’s principle is employed to obtain the governing equations of motion. The nano panel is subjected to a coupling of magnetic and electric loads, including a linear function along with the thickness direction and a 2D function along with the axial and circumferential directions. To account the effect of nanoscale in governing equations, the Eringen nonlocal elasticity theory is used. The numerical results are obtained to investigate the impact of significant parameters such as axial and circumferential mode numbers, the nanoscale parameter, applied electromagnetic potentials, and length-to-radius ratio. It is concluded that an increase in initial electric potential and a decrease in magnetic potential lead to an increase in natural frequencies of the nano panel.

Free Vibration Analysis of Multiphase Magneto-Electro-Elastic Composite Conical Shells

Objectives: In the present article, free vibration of multiphase Magneto-Electro-Elastic (MEE) conical shell having a uniform thickness is examined for Clamped-Free (C-F) boundary condition. Method: The study is carried out using a semi-analytical approach for different volume fractions (Vf ) 0, 0.2, 0.6 and 1.0 of BaTiO3 in BaTiO3-CoFe2O4 smart composite conical shell for three different semi-vertex angles 20o,35o and 50o. The piezoelectric (Pe) and piezomagnetic (Pm) phase on natural frequencies of MEE truncated conical shells are discussed for different circumferential modes. Findings: The parametric study indicates that natural frequency decrease with an increase in Vf of BaTiO3 in magnetoelectro-elastic truncated conical shells. Novelty: Studies on MEE constant thickness truncated conical shell using BaTiO3 and CoFe2O4 as (Pe) & (Pm) smart composite for clamped-free boundary condition to analyse the effect of the frequency with different semi-vertex angle and cone heights. Present commercial FEA software tools are limited to 2 coupling fields. In this research, coupling between 3 fields considered for MEE material. Hence, a computer code is developed to study the influence coupling between electric, elastic and magnetic fields, which can be used for any combinations of boundary conditions and volume fractions. Keywords: MagnetoElectroElastic (MEE); axisymmetric constant thickness conical shell; Smart Composites; volume fraction; free vibrations; finite element method