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2019年 第40卷 第8期    刊出日期：2019-08-01

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论文

Coupled flapwise-chordwise-axial-torsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation

Jin ZENG, Hui MA, Kun YU, Zhitao XU, Bangchun WEN

2019, 40(8):  1053-1082.  doi:10.1007/s10483-019-2506-6

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A rotating pre-twisted and inclined cantilever beam model (RPICBM) with the flapwise-chordwise-axial-torsional coupling is established with the Hamilton principle and the finite element (FE) method. The effectiveness of the model is verified via comparisons with the literatures and the FE models in ANSYS. The effects of the setting and pre-twisted angles on the dynamic responses of the RPICBM are analyzed. The results show that:(i) the increase in the setting or pre-twisted angle results in the increases in the first-order flapwise and torsional frequencies while the decrease in the first-order chordwise frequency under rotating conditions; (ii) a positive/negative setting angle leads to a positive/negative constant component, while a positive/negative pre-twisted angle leads to a negative/positive constant component; (iii) when the rotation speed is non-zero, the pre-twisted angle or non-zero setting angle will result in the coupled flapwise-chordwiseaxial-torsional vibration of the RPICBM under axial base excitation.



Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium

S. MONDAL, S. A. SAHU, K. K. PANKAJ

2019, 40(8):  1083-1096.  doi:10.1007/s10483-019-2505-6

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The frequency of the Love-type surface waves in a bedded structure consisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to have a constant initial stress. The Wentzel-Kramers-Brillouin (WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses (tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.

Modified strip saturated models for two equal collinear cracks with coalesced zones in piezoelectric media

S. SINGH, K. SHARMA, R. R. BHARGAVA

2019, 40(8):  1097-1118.  doi:10.1007/s10483-019-2507-6

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Two equal collinear cracks with coalesced interior electric saturation zones are analytically studied for two-dimensional (2D) arbitrary polarized semipermeable piezoelectric media based on a modified strip saturated model. The strip saturated model is modified here by varying the strip saturated constant electric displacement condition to the polynomially varying electric displacement conditions. Based on the linear, quadratic, and cubic electric displacement conditions on the inner and outer saturated zones, different modified strip saturated models are proposed and studied for two equal collinear cracks. With the Stroh formalism and the complex variable technique, these fracture problems are reduced into different types of non-homogeneous Riemann Hilbert problems in unknown generalized complex potential functions. These mathematical problems are then solved with the Riemann-Hilbert approach to obtain the stress and electric displacement components at any point of the domain. The explicit expressions for the outer saturated zone length, the crack opening potential (COP), the crack opening displacement (COD), and the local intensity factors (LIFs) are derived. A numerical study is presented for the modified strip saturated model in 2D arbitrary polarized semipermeable PZT-4 material. The obtained results are compared with those of the strip saturated model, and the effects of the polynomially varying saturation condition on the saturated zones and the applied electrical loadings are presented.

In-plane dynamics of a fluid-conveying corrugated pipe supported at both ends

Yingjie WANG, Qichang ZHANG, Wei WANG, Tianzhi YANG

2019, 40(8):  1119-1134.  doi:10.1007/s10483-019-2511-6

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The dynamics and stability of fluid-conveying corrugated pipes are investigated. The flow velocity is assumed to harmonically vary along the pipe rather than with time. The dimensionless equation is discretized with the differential quadrature method (DQM). Subsequently, the effects of the mean flow velocity and two key parameters of the corrugated pipe, i.e., the amplitude of the corrugations and the total number of the corrugations, are studied. The results show that the corrugated pipe will lose stability by flutter even if it has been supported at both ends. When the total number of the corrugations is sufficient, this flutter instability occurs at a micro flow velocity. These phenomena are verified via the Runge-Kutta method. The critical flow velocity of divergence is analyzed in detail. Compared with uniform pipes, the critical velocity will be reduced due to the corrugations, thus accelerating the divergence instability. Specifically, the critical flow velocity decreases if the amplitude of the corrugations increases. However, the critical flow velocity cannot be monotonously reduced with the increase in the total number of the corrugations. An extreme point appears, which can be used to realize the parameter optimization of corrugated pipes in practical applications.

Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

S. M. ABO-DAHAB, A. M. ABD-ALLA, A. A. KILANY

2019, 40(8):  1135-1154.  doi:10.1007/s10483-019-2504-6

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The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.

Nonlinear primary resonance analysis for a coupled thermo-piezoelectric-mechanical model of piezoelectric rectangular thin plates

Xun WANG, Chunxia XUE, Haitao LI

2019, 40(8):  1155-1168.  doi:10.1007/s10483-019-2510-6

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A model of piezoelectric rectangular thin plates with the consideration of the coupled thermo-piezoelectric-mechanical effect is established. Based on the von Karman large deflection theory, the nonlinear vibration governing equation is obtained by using Hamilton's principle and the Rayleigh-Ritz method. The harmonic balance method (HBM) is used to analyze the first-order approximate response and obtain the frequency response function. The system shows non-linear phenomena such as hardening nonlinearity, multiple coexistence solutions, and jumps. The effects of the temperature difference, the damping coefficient, the plate thickness, the excited charge, and the mode on the primary resonance response are theoretically analyzed. With the increase in the temperature difference, the corresponding frequency jumping increases, while the resonant amplitude decreases gradually. Finally, numerical verifications are carried out by the Runge-Kutta method, and the results agree very well with the theoretical results.

An irreducible polynomial functional basis of two-dimensional Eshelby tensors

Zhenyu MING, Liping ZHANG, Yannan CHEN

2019, 40(8):  1169-1180.  doi:10.1007/s10483-019-2502-6

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The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.

Numerical analysis of the interaction of 3D compressible bubble clusters

Hui GUAN, Jincheng WANG, Zhijun WEI, Chuijie WU

2019, 40(8):  1181-1196.  doi:10.1007/s10483-019-2509-6

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Based on the bubble dynamic theory and the compressible two-phase flow solver of the open source software OpenFOAM, a numerical simulation study is carried out on the interactions of bubble clusters in a closed volume. The bubble dynamics and interactions of a single bubble, two bubbles, and four bubbles are investigated under the working conditions without and with the presence of a free surface. Through a parametric study, the qualitative patterns of the variations of the bubble collapse period, the volume compressibility, the bubble pressure peak value, and the breakdown, fusion, and separation phenomena with the parameters such as the bubble pressure, the radius size, the bubble spacing, and the distance from the free surface are obtained. The main factors affecting the bubble morphology and the dynamic characteristics are summarized from numerous parameter experiments. It is shown that, in the absence of a free surface, the main factors are the relative size of the bubbles, the pressure of the liquid, and the pressure differences among the bubbles, while in the presence of a free surface, the main factor is the pressure of the liquid between the upper surface of the bubble and the free surface.

Turbulent combustion modeling using a flamelet generated manifold approach-a validation study in OpenFOAM

Tao LI, Fanfu KONG, Baopeng XU, Xiaohan WANG

2019, 40(8):  1197-1210.  doi:10.1007/s10483-019-2503-6

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An OpenFOAM based turbulence combustion solver with flamelet generated manifolds (FGMs) is presented in this paper. A series of flamelets, representative for turbulent flames, are calculated first by a one-dimensional (1D) detailed chemistry solver with the consideration of both transport and stretch/curvature contributions. The flame structure is then parameterized as a function of multiple reaction control variables. A manifold, which collects the 1D flame properties, is built from the 1D flame solutions. The control variables of the mixture fraction and the progress variable are solved from the corresponding transport equations. During the calculation, the scalar variables, e.g., temperature and species concentration, are retrieved from the manifolds by interpolation. A transport equation for NO is solved to improve its prediction accuracy. To verify the ability to deal with the enthalpy loss effect, the temperature retrieved directly from the manifolds is compared with the temperature solved from a transport equation of absolute enthalpy. The resulting FGM-computational fluid dynamics (CFD) coupled code has three significant features, i.e., accurate NO prediction, the ability to treat the heat loss effect and the adoption at the turbulence level, and high quality prediction within practical industrial configurations. The proposed method is validated against the Sandia flame D, and good agreement with the experimental data is obtained.

Wavelet analysis of stagnation point flow of non-Newtonian nanofluid

M. HAMID, M. USMAN, R. U. HAQ, Z. H. KHAN, Wei WANG

2019, 40(8):  1211-1226.  doi:10.1007/s10483-019-2508-6

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The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson's fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.