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2019年 第40卷 第12期    刊出日期：2019-12-03

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论文

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

Lu LU, Li ZHU, Xingming GUO, Jianzhong ZHAO, Guanzhong LIU

2019, 40(12):  1695-1722.  doi:10.1007/s10483-019-2549-7

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In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton's principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.



An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

Z. SHARIFI, R. KHORDAD, A. GHARAATI, G. FOROZANI

2019, 40(12):  1723-1740.  doi:10.1007/s10483-019-2545-8

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In this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton's principle and derive the governing differential equations. Then, we use Navier's solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the lengthto-thickness ratio, and the nanoplate shape on natural frequencies are investigated.

Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method

Sha WEI, Shiqian CHEN, Zhike PENG, Xingjian DONG, Wenming ZHANG

2019, 40(12):  1741-1758.  doi:10.1007/s10483-019-2547-9

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Modal parameter identification is a mature technology. However, there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination. This paper proposes a new time-frequency method based on intrinsic chirp component decomposition (ICCD) to address these issues. In this method, a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction. The effectiveness and accuracy of the proposed method are illustrated using three examples:a cantilever beam structure with intensive noise contamination or environmental interference, a fourdegree-of-freedom structure with two closely spaced modes, and an impact test on a cantilever rectangular plate. By comparison with the identification method based on the empirical wavelet transform (EWT), it is shown that the presented method is effective, even in a high-noise environment, and the dynamic characteristics of closely spaced modes are accurately determined.

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

Lincong CHEN, Haisheng ZHU, J. Q. SUN

2019, 40(12):  1759-1776.  doi:10.1007/s10483-019-2543-5

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The vibroimpact systems with bilateral barriers are often encountered in practice. However, the dynamics of the vibroimpact system with bilateral barriers is full of challenges. Few closed-form solutions were obtained. In this paper, we propose a novel method for random vibration analysis of single-degree-of-freedom (SDOF) vibroimpact systems with bilateral barriers under Gaussian white noise excitations. A periodic approximate transformation is employed to convert the equations of the motion to a continuous form. The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov (FPK) equation. The closed-form stationary probability density function (PDF) of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow. Finally, the versatility of the proposed approach is demonstrated by its application to two typical examples. Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

Low-frequency and broadband vibration energy harvester driven by mechanical impact based on layer-separated piezoelectric beam

Dongxing CAO, Wei XIA, Wenhua HU

2019, 40(12):  1777-1790.  doi:10.1007/s10483-019-2542-5

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Vibration energy harvesting is to transform the ambient mechanical energy to electricity. How to reduce the resonance frequency and improve the conversion efficiency is very important. In this paper, a layer-separated piezoelectric cantilever beam is proposed for the vibration energy harvester (VEH) for low-frequency and wide-bandwidth operation, which can transform the mechanical impact energy to electric energy. First, the electromechanical coupling equation is obtained by the Euler-Bernoulli beam theory. Based on the average method, the approximate analytical solution is derived and the voltage response is obtained. Furthermore, the physical prototype is fabricated, and the vibration experiment is conducted to validate the theoretical principle. The experimental results show that the maximum power of 0.445 μW of the layer-separated VEH is about 3.11 times higher than that of the non-impact harvester when the excitation acceleration is 0.2 g. The operating frequency bandwidth can be widened by increasing the stiffness of the fundamental layer and decreasing the gap distance of the system. But the increasing of operating frequency bandwidth comes at the cost of reducing peak voltage. The theoretical simulation and the experimental results demonstrate good agreement which indicates that the proposed impact-driving VEH device has advantages for low-frequency and wide-bandwidth. The high performance provides great prospect to scavenge the vibration energy in environment.

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

Yewei ZHANG, Kefan XU, Jian ZANG, Zhiyu NI, Yunpeng ZHU, Liqun CHEN

2019, 40(12):  1791-1804.  doi:10.1007/s10483-019-2548-9

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A novel vibration isolation device called the nonlinear energy sink (NES) with NiTiNOL-steel wire ropes (NiTi-ST) is applied to a whole-spacecraft system. The NiTi-ST is used to describe the damping of the NES, which is coupled with the modified Bouc-Wen model of hysteresis. The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer (TET) to concentrate the energy locally on the nonlinear oscillator, and then dissipates it through damping in the NES with NiTi-ST. The generalized vibration transmissibility, obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions (NOFRFs), is first used as the evaluation index to analyze the whole-spacecraft system in the future. An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs. Finally, the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption. The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system, without changing its natural frequency. Moreover, the NES with NiTi-ST can be directly used in practical engineering applications.

Deformable micro-continua in which quantum mysteries reside

Heng XIAO

2019, 40(12):  1805-1830.  doi:10.1007/s10483-019-2546-6

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Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic scale. At every instant, the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass, the velocity, the internal stress, and the intrinsic angular momentum. The deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density field. It is shown that these microcontinua are endowed with the following unique response features:(i) the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable; (ii) this fundamental dynamic equation and this complex field variable are just the Schrödinger equation and the complex wave function in quantum theory; and, accordingly, (iii) the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered, thus following objective and deterministic response patterns for quantum entities, in which the physical origins and meanings of the wave function and the Schrödinger equation become self-evident and, in particular, any probabilistic indeterminacy becomes irrelevant.

Third-order elastic, piezoelectric, and dielectric constants

Yanming ZHANG, Jun JIN, Hongping HU

2019, 40(12):  1831-1846.  doi:10.1007/s10483-019-2550-7

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The definitions of the third-order elastic, piezoelectric, and dielectric constants and the properties of the associated tensors are discussed. Based on the energy conservation and coordinate transformation, the relations among the third-order constants are obtained. Furthermore, the relations among the third-order elastic, piezoelectric, and dielectric constants of the seven crystal systems and isotropic materials are listed in detail. These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials. It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups, while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material. The reason is that some of the point groups are centrally symmetric, and the other point groups are high symmetry. These results provide the foundation to measure these constants, to choose material, and to research nonlinear problems. Moreover, these results are helpful not only for the study of nonlinear elastic and piezoelectric problems, but also for the research on flexoelectric effects and size effects.

Morphology of cylindrical cell sheets with embedded contractile ring

Nan NAN, Guohui HU

2019, 40(12):  1847-1860.  doi:10.1007/s10483-019-2544-8

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The behavior of large deformations of cellular tissues is usually affected by the local properties of cells and their interactions, resulting in folding which acts as an important role in the embryonic development, as well as growing and spreading of a tumor, which can rapidly promote the stereo complexity of the architecture of the tissues. In the present study, a cylindrical vertex model is constructed to explore the morphology of the tubular cell sheets subject to an embedded contractile ring. It is found that an inner region of the contractile ring in equilibrium will protrude from the tube wall, and it will suddenly collapse when the contractile strength exceeds a threshold, indicating the occurrence of a bifurcation. These results on the effect of embedded contraction in the tubular shell are quite different from the planar cases, which can reveal the importance of the interaction between the geometric and material non-linearity in cylindrical geometry. The dependence of the large deformation on the bending modulus parameters and contraction strength is also analyzed for the cylindrical cell shell.

Double stratified radiative flow of an Oldroyd-B nanofluid with nonlinear convection

T. HAYAT, M. Z. KIYANI, I. AHMAD, A. ALSAEDI

2019, 40(12):  1861-1878.  doi:10.1007/s10483-019-2251-6

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The nonlinear convective flow of an Oldroyd-B fluid due to a nonlinear stretching sheet with varying thickness is examined. The salient features of the random movement and thermophoresis are described. Formulation is made with the nonlinear thermal radiation and heat generation/absorption. Further, the convective conditions and double stratification are taken into account. The resulting flow problems are tackled by the optimal homotopy analysis method (OHAM). The resulting nonlinear problems are solved for the velocity, temperature, and concentration fields. The temperature and concentration gradients are numerically discussed. The total residual error is calculated. The Nusselt number is an increasing function of the radiation parameter. The Sherwood number increases with the increase in the solutal stratification or the Schmidt number. The main outcomes are presented in conclusions. This study has a wide range of applications such as thermal stratification of oceans, reservoirs, and rivers, density stratification of atmosphere, hydraulic lifts, and polymer processing.