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2020年 第41卷 第7期    刊出日期：2020-07-01

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论文

Research on linear/nonlinear viscous damping and hysteretic damping in nonlinear vibration isolation systems

Zhong ZHANG, Muqing NIU, Kai YUAN, Yewei ZHANG

2020, 41(7):  983-998.  doi:10.1007/s10483-020-2630-6

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A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance. In this paper, a generalized vibration isolation system is established with nonlinear stiffness, nonlinear viscous damping, and Bouc-Wen (BW) hysteretic damping. An approximate analytical analysis is performed based on a harmonic balance method (HBM) and an alternating frequency/time (AFT) domain technique. To evaluate the damping effect, a generalized equivalent damping ratio is defined with the stiffness-varying characteristics. A comprehensive comparison of different kinds of damping is made through numerical simulations. It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes. The linear damping, hysteretic damping, and nonlinear viscous damping are suitable for the small-amplitude, medium-amplitude, and large-amplitude conditions, respectively. The hysteretic damping has an extra advantage of broadband isolation.



Dynamic analysis of wind turbine tower structures in complex ocean environment

Guanzhong LIU, Xingming GUO, Li ZHU

2020, 41(7):  999-1010.  doi:10.1007/s10483-020-2624-8

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Studying and analyzing the dynamic behavior of offshore wind turbines are of great importance to ensure the safety and improve the efficiency of such expensive equipments. In this work, a tapered beam model is proposed to investigate the dynamic response of an offshore wind turbine tower on the monopile foundation assembled with rotating blades in the complex ocean environment. Several environment factors like wind, wave, current, and soil resistance are taken into account. The proposed model is analytically solved with the Galerkin method. Based on the numerical results, the effects of various structure parameters including the taper angle, the height and thickness of the tower, the depth, and the diameter and the cement filler of the monopile on the fundamental natural frequency of the wind turbine tower system are investigated in detail. It is found that the fundamental natural frequency decreases with the increase in the taper angle and the height and thickness of the tower, and increases with the increase in the diameter of the monopile. Moreover, filling cement into the monopile can effectively improve the fundamental natural frequency of the wind turbine tower system, but there is a critical value of the amount of cement maximizing the property of the monopile. This research may be helpful in the design and safety evaluation of offshore wind turbines.

Influence of elastic foundations and carbon nanotube reinforcement on the hydrostatic buckling pressure of truncated conical shells

A. H. SOFIYEV, I. T. PIRMAMEDOV, N. KURUOGLU

2020, 41(7):  1011-1026.  doi:10.1007/s10483-020-2631-7

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In this study, the effects of elastic foundations (EFs) and carbon nanotube (CNT) reinforcement on the hydrostatic buckling pressure (HBP) of truncated conical shells (TCSs) are investigated. The first order shear deformation theory (FOSDT) is generalized to the buckling problem of TCSs reinforced with CNTs resting on the EFs for the first time. The material properties of composite TCSs reinforced with CNTs are graded linearly according to the thickness coordinate. The Winkler elastic foundation (W-EF) and Pasternak elastic foundation (P-EF) are considered as the EF. The basic relations and equations of TCSs reinforced with CNTs on the EFs are obtained in the framework of the FOSDT and solved using the Galerkin method. One of the innovations in this study is to obtain a closed-form solution for the HBP of TCSs reinforced with CNTs on the EFs. Finally, the effects of the EFs and various types CNT reinforcements on the HBP are investigated simultaneously. The obtained results are compared with the results in the literature, and the accuracy of results is confirmed.

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets

A. AMIRI, M. MOHAMMADIMEHR, M. ANVARI

2020, 41(7):  1027-1038.  doi:10.1007/s10483-020-2627-7

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In this paper, the stresses and buckling behaviors of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets are considered based on the high-order shear deformation theory (HSDT) and the modified couple stress theory (MCST). The governing equations of equilibrium are obtained based on the total potential energy principle. The effects of various parameters such as the aspect ratio, elastic foundation, temperature changes, and volume fraction of the canbon nanotubes (CNTs) on the critical buckling loads, normal stress, shear stress, and deflection of the thick-walled micro cylindrical sandwich panel considering different distributions of CNTs are examined. The results are compared and validated with other studies, and showing an excellent compatibility. CNTs have become very useful and common candidates in sandwich structures, and they have been extensively used in many applications including nanotechnology, aerospace, and micro-structures. This paper also extends further applications of reinforced sandwich panels by providing the modified equations and formulae.

An analytical study on the Rayleigh wave generation in a stratified structure

A. MANDI, S. KUNDU, P. PATI, P. C. PAL

2020, 41(7):  1039-1054.  doi:10.1007/s10483-020-2625-9

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In this paper, an analytical method is used to investigate the Rayleigh wave generation in a stratified structure and the wave generation in a dry sandy layer constrained between the couple stress and inhomogeneous orthotropic half-spaces. This study is devoted to analyzing the impact of various effective parameters associated with the media on the phase velocities of the wave. The displacement components for each medium are derived by implementing the separable variable method. The frequency equation is secured by using the displacement components in the boundary conditions, imposed at the interfaces between the layer and half-spaces. Moreover, the secured equation is the relation between the phase velocity and the wave number. Numerical computations are performed, and graphical representations are demonstrated between the phase velocity and the wave number for both phase velocities with different values of the parameters. The comparison between the phase velocities is observed for the same value of each parameter.

A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate

Zhiwei LI, Guohua NIE

2020, 41(7):  1055-1068.  doi:10.1007/s10483-020-2626-6

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A procedure of the method of reverberation ray matrix (MRRM) is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners. A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading. Specifically, the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans, while the constraint condition of two remaining edges may be in any combination of free, simply-supported, and clamped boundary conditions. Furthermore, based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions, some recursive equations (REs) for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases, which promotes the computation efficiency. Several numerical examples are given, and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis.

Motion through spherical droplet with non-homogenous porous layer in spherical container

P. K. YADAV, A. TIWARI, P. SINGH

2020, 41(7):  1069-1082.  doi:10.1007/s10483-020-2628-8

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The problem of the creeping flow through a spherical droplet with a nonhomogenous porous layer in a spherical container has been studied analytically. Darcy's model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow. The drag force is exerted on the porous spherical particles enclosing a cavity, and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is calculated. Emphasis is placed on the spatially varying permeability of a porous medium, which is not covered in all the previous works related to spherical containers. The variation of hydrodynamic permeability and the wall effect with respect to various flow parameters are presented and discussed graphically. The streamlines are presented to discuss the kinematics of the flow. Some previous results for hydrodynamic permeability and drag forces have been verified as special limiting cases.

Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

A. HAFEEZ, M. KHAN, A. AHMED, J. AHMED

2020, 41(7):  1083-1094.  doi:10.1007/s10483-020-2629-9

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A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von Kármán similarity functions are utilized to convert the partial differential equations (PDEs) into ordinary differential equations (ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.

An Uzawa-type algorithm for the coupled Stokes equations

Pengzhan HUANG, Yinnian HE

2020, 41(7):  1095-1104.  doi:10.1007/s10483-020-2623-7

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An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided.

Scattering of Tollmien-Schlichting waves by localized roughness in transonic boundary layers

Ming DONG

2020, 41(7):  1105-1124.  doi:10.1007/s10483-020-2622-6

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The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional (2D) roughness element on the oncoming Tollmien-Schlichting (T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers (WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition:transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68-108 (2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue; while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the largeReynolds-number asymptotic theory, the Kármán-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out, and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the Kármán-Guderley parameter is provided.