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    2017年 第38卷 第1期    刊出日期:2017-01-01
    论文
    Primary resonance of traveling viscoelastic beam under internal resonance
    Hu DING, Linglu HUANG, Xiaoye MAO, Liqun CHEN
    2017, 38(1):  1-14.  doi:10.1007/s10483-016-2152-6
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    Under the 3:1 internal resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the internal resonance, the energy transfer between the internal resonance modes and the saturation-like phenomena in the steady-state responses is presented.

    Determination of elastic moduli of composite medium containing bimaterial matrix and non-uniform inclusion concentrations
    Weitao SUN
    2017, 38(1):  15-28.  doi:10.1007/s10483-017-2157-6
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    Reservoir porous rocks usually consist of more than two types of matrix materials, forming a randomly heterogeneous material. The determination of the bulk modulus of such a medium is critical to the elastic wave dispersion and attenuation. The elastic moduli for a simple matrix-inclusion model are theoretically analyzed. Most of the efforts assume a uniform inclusion concentration throughout the whole single-material matrix. However, the assumption is too strict in real-world rocks. A model is developed to estimate the moduli of a heterogeneous bimaterial skeleton, i.e., the host matrix and the patchy matrix. The elastic moduli, density, and permeability of the patchy matrix differ from those of the surrounding host matrix material. Both the matrices contain dispersed particle inclusions with different concentrations. By setting the elastic constant and density of the particles to be zero, a double-porosity medium is obtained. The bulk moduli for the whole system are derived with a multi-level effective modulus method based on Hashin's work. The proposed model improves the elastic modulus calculation of reservoir rocks, and is used to predict the kerogen content based on the wave velocity measured in laboratory. The results show pretty good consistency between the inversed total organic carbon and the measured total organic carbon for two sets of rock samples.

    Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams
    Jiemin XIE, Yuantai HU
    2017, 38(1):  29-38.  doi:10.1007/s10483-017-2154-6
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    The electric admittance of a compound system composed of a thicknessshear mode (TSM) quartz crystal resonator (QCR) and an array of surface viscoelastic micro-beams (MBs) is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin (SU-8) MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak(s) and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

    Quantum enigma hidden in continuum mechanics
    Heng XIAO
    2017, 38(1):  39-56.  doi:10.1007/s10483-017-2151-6
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    It is reported that there exist deformable media which display quantum effects just as quantum entities do. As such, each quantum entity usually treated as a point particle may be represented by a deformable medium, the dynamic behavior of which is prescribed by four dynamic state variables, including mass density, velocity, internal pressure, and intrinsic angular momentum. In conjunction with the finding of the characteristic equation characterizing the physical nature of such media, it is found that a complex field quantity may be introduced to uncover a perhaps unexpected correlation, i.e., the governing dynamic equations for such media may be exactly reduced to the Schrödinger equation, from which the closed-form solutions for all the four dynamic state variables can be obtained. It turns out that this complex field quantity is just the wavefunction in the Schrödinger equation. Moreover, the dynamic effects peculiar to spin are derivable as direct consequences. It appears that these results provide a missing link in quantum theory, in the sense of disclosing the physical origin and nature of both the wavefunction and the wave equation. Now, the inherent indeterminacy in quantum theory may be rendered irrelevant. The consequences are explained for certain long-standing fundamental issues.

    Matrix description of differential relations of moment functions in structural reliability sensitivity analysis
    Tianxiao ZHANG
    2017, 38(1):  57-72.  doi:10.1007/s10483-017-2160-6
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    In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

    Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory
    D. V. DUNG, H. T. THIEM
    2017, 38(1):  73-98.  doi:10.1007/s10483-017-2159-6
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    The postbuckling of the eccentrically stiffened circular cylindrical shells made of functionally graded materials (FGMs), subjected to the axial compressive load and external uniform pressure and filled inside by the elastic foundations in the thermal environments, is investigated with an analytical method. The shells are reinforced by FGM stringers and rings. The thermal elements of the shells and stiffeners in the fundamental equations are considered. The equilibrium and nonlinear stability equations in terms of the displacement components for the stiffened shells are derived with the third-order shear deformation theory and Leckhniskii smeared stiffener technique. The closed-form expressions for determining the buckling load and postbuckling load-deflection curves are obtained with the Galerkin method. The effects of the stiffeners, the foundations, the material and dimensional parameters, and the pre-existent axial compressive and thermal load are considered.

    Peridynamic modelling of impact damage in three-point bending beam with offset notch
    Ning LIU, Dahsin LIU, Wu ZHOU
    2017, 38(1):  99-110.  doi:10.1007/s10483-017-2158-6
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    The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics. Based upon the integrodifferential equations, peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving, and arrest. In this paper, the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch, which is widely used to investigate the mixed I-II crack propagation in brittle materials. The predictions from the peridynamic analysis agree well with available experimental observations. The numerical results show that the dynamic fracture behaviors of the beam under the impact load, such as crack initiation, curving, and branching, rely on the location of the offset notch and the impact speed of the drop hammer.

    Research of influence of reduced-order boundary on accuracy and solution of interior points
    Yunlong LI, Wei CAO
    2017, 38(1):  111-124.  doi:10.1007/s10483-017-2153-6
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    The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately. However, there are two problems, i.e., the reduced-order boundary is inevitable and the order of the scheme at the discontinuous shock wave contained in the flow field as the supersonic flow field is low. It is questionable whether the reduced-order boundary and the low-order scheme at the shock wave have an effect on the numerical solution and accuracy of the flow field inside. In this paper, according to the actual situation of the direct numerical simulation of the flow field, two model equations with the exact solutions are solved, which are steady and unsteady, respectively, to study the question with a high order scheme at the interior of the domain and the reduced-order method at the boundary and center of the domain. Comparing with the exact solutions, it is found that the effect of reduced-order exists and cannot be ignored. In addition, the other two model equations with the exact solutions, which are often used in fluid mechanics, are also studied with the same process for the reduced-order problem.

    Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity
    Jing ZHU, Shengnan WANG, Liancun ZHENG, Xinxin ZHANG
    2017, 38(1):  125-136.  doi:10.1007/s10483-017-2155-6
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    The heat transfer of a magnetohydrodynamics nanofluid inside an annulus considering the second-order slip condition and nanoparticle migration is theoretically investigated. A second-order slip condition, which appropriately represents the non-equilibrium region near the interface, is prescribed rather than the no-slip condition and the linear Navier slip condition. To impose different temperature gradients, the outer wall is subjected to q2, the inner wall is subjected to q1, and q1>q2. A modified two-component four-equation non-homogeneous equilibrium model is employed for the nanofluid, which have been reduced to two-point ordinary boundary value differential equations in the consideration of the thermally and hydrodynamically fully developed flow. The homotopy analysis method (HAM) is employed to solve the equations, and the h-curves are plotted to verify the accuracy and efficiency of the solutions. Moreover, the effects of the physical factors on the flow and heat transfer are discussed in detail, and the semi-analytical relation between NuB and NBT is obtained.

    Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel
    I. M. ELDESOKY, S. I. ABDELSALAM, R. M. ABUMANDOUR, M. H. KAMEL, K. VAFAI
    2017, 38(1):  137-154.  doi:10.1007/s10483-017-2156-6
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    The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated. The momentum equations for the compressible flow are solved with a perturbation analysis. The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall. The zeroth-order terms yield the Poiseuille flow, and the first-order terms give the Orr-Sommerfeld equation. The explicit expression for the net axial velocity is derived. The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications. The features of the flow characteristics are analyzed and discussed in detail. The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm, whereas the particle diameter has been taken to be 8 μm. This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems, and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.

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