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摘要 ：
The volume fraction of the carbon nanotube (CNT) plays a key role in ensuring the performance of the CNT reinforced polymer composite, especially under the severe vibration, which leads to the resonance and failure of the composite structure. In this paper, a bottom-up multiscale method is adopted to study the effect of the CNT volume fractions on the nonlinear vibration of the poly (methyl methacrylate) (PMMA)/CNT composite. According to the molecular simulation, the longitudinal, transverse and shear moduli of the PMMA/CNT nanocomposites are found to increase with the increasing CNT volume fractions. Substituting the simulated moduli into the extended rule of mixtures (EROM), the efficiency parameters of the PMMA/CNT composite with various CNT volume fractions are derived based on a homogenization approach. The derived efficiency parameters are used in the functionally graded (FG)-based EROM to obtain the expressions of the longitudinal, transverse and shear moduli of the macroscopic composite plate, so as to obtain the constitutive equation for the nonlinear vibrations of the FG-based PMMA/CNT composite plate. The subsequent meshless simulation results demonstrate that the natural frequencies of the FG-based composite plate increase with the increasing volume fractions, whereas the ratios of the nonlinear to linear frequencies decrease. Using the bottom-up multiscale analysis, the macroscopic vibration responses are analyzed for the PMMA/CNT composites with the CNT volume fractions up to 9.0%, which provides a paradigm of the design of the PMMA/CNT composite by considering the CNT volume fraction effect.
关键词 ：
CNT composite CNT composite CNT volume fraction CNT volume fraction Meshless simulation Meshless simulation Molecular dynamics Molecular dynamics Nonlinear vibration Nonlinear vibration PMMA PMMA
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| GB/T 7714 | Wang, J. F. , Yang, J. P. , Tam, L-H et al. Effect of CNT volume fractions on nonlinear vibrations of PMMA/CNT composite plates: A multiscale simulation [J]. | THIN-WALLED STRUCTURES , 2022 , 170 . |
| MLA | Wang, J. F. et al. "Effect of CNT volume fractions on nonlinear vibrations of PMMA/CNT composite plates: A multiscale simulation" . | THIN-WALLED STRUCTURES 170 (2022) . |
| APA | Wang, J. F. , Yang, J. P. , Tam, L-H , Zhang, W. . Effect of CNT volume fractions on nonlinear vibrations of PMMA/CNT composite plates: A multiscale simulation . | THIN-WALLED STRUCTURES , 2022 , 170 . |
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摘要 ：
This paper analytically and numerically presents global dynamics of the generalized Boussinesq equation (GBE) with cubic nonlinearity and harmonic excitation. The effect of the damping coefficient on the dynamical responses of the generalized Boussinesq equation is clearly revealed. Using the reductive perturbation method, an equivalent wave equation is then derived from the complex nonlinear equation of the GBE. The persistent homoclinic orbit for the perturbed equation is located through the first and second measurements, and the breaking of the homoclinic structure will generate chaos in a Smale horseshoe sense for the GBE. Numerical examples are used to test the validity of the theoretical prediction. Both theoretical prediction and numerical simulations demonstrate the homoclinic chaos for the GBE.
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| GB/T 7714 | Li, Mingyuan , Zhang, Wei , Wu, Qiliang . Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation [J]. | MATHEMATICAL PROBLEMS IN ENGINEERING , 2021 , 2021 . |
| MLA | Li, Mingyuan et al. "Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation" . | MATHEMATICAL PROBLEMS IN ENGINEERING 2021 (2021) . |
| APA | Li, Mingyuan , Zhang, Wei , Wu, Qiliang . Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation . | MATHEMATICAL PROBLEMS IN ENGINEERING , 2021 , 2021 . |
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摘要 ：
In the current work, an accurate modified couple stress-based cylindrical micro-panel model is developed in the framework of sinusoidal shear deformation theory. The classical strain tensors and curvature tensor components in a modified couple stress-based model are given with consideration of the geometric curve of cylindrical panels. In conjunction with a general Lagrange procedure, the proposed model is implemented to derive a system of Mathieu-Hill equations of governing dynamic stability behaviors of the cylindrical micro-panels. The Navier-type solution and Bolotin's method are applied to predict the principle unstable regions of the micro-panels with simply-supported boundary condition. As an application of the proposed model, the size-dependent stability of a functionally graded graphene nanoplatelets reinforced composite (FG-GNPRC) cylindrical micro-panel under axial oscillation compression is investigated for the first time. It is assumed that the weight fraction of graphene nanoplatelets (GNPs) is graded in the panel thickness. The effective Young's modulus of FG-GNPRC is determined based on a modified Halpin-Tsai model, while the mixture rule used to evaluate the effective Poisson's ratio and the mass density. The parameter studies are performed to examine the effect of dimensionless length parameter, GPL distribution patterns, GPL size and shape, length-to-span ratio and radius-to-span ratio on the sizedependent dynamic stabilities of FG-GNPRC cylindrical micro-panels.
关键词 ：
Cylindrical micro-panel Cylindrical micro-panel Dynamic stability Dynamic stability Functionally graded graphene nanoplatelets reinforced composite Functionally graded graphene nanoplatelets reinforced composite Modified couple stress theory Modified couple stress theory Sinusoidal shear deformation theory Sinusoidal shear deformation theory
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| GB/T 7714 | Wang, Yuewu , Fu, Tairan , Zhang, Wei . An accurate size-dependent sinusoidal shear deformable framework for GNP-reinforced cylindrical panels: Applications to dynamic stability analysis [J]. | THIN-WALLED STRUCTURES , 2021 , 160 . |
| MLA | Wang, Yuewu et al. "An accurate size-dependent sinusoidal shear deformable framework for GNP-reinforced cylindrical panels: Applications to dynamic stability analysis" . | THIN-WALLED STRUCTURES 160 (2021) . |
| APA | Wang, Yuewu , Fu, Tairan , Zhang, Wei . An accurate size-dependent sinusoidal shear deformable framework for GNP-reinforced cylindrical panels: Applications to dynamic stability analysis . | THIN-WALLED STRUCTURES , 2021 , 160 . |
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摘要 ：
Regarding the dynamic behavior of the functionally graded materials (FGM) conical panels under the static and harmonic in-plane loading, most studies focus on parametric resonances and dynamic instability which determine the stability regions. Studies on the bursting oscillation of the conical panels under the lower frequency excitation are quite rare. In this paper, we present a novel nonautonomous system of the cantilever functionally graded materials sandwich conical panels with a slowly varying parametric excitation and study the bending-torsion coupling bursting oscillations. The face sheets and core layer are the metal ceramic composite layer and homogeneous metal layer, respectively. In two surfaces layers, the component materials are gradually changed in the transverse direction and the temperature dependent properties show the form of the power law distribution. The excitations in the meridional direction include the static preload and lower frequency harmonic excitation. The mode functions of the first-order bending mode and the first order torsion mode are obtained in terms of Chebyshev polynomials with the help of energy principle. The bending-torsion coupling nonautonomous nonlinear oscillation system is derived by Lagrange equations. Under the slowly varying in-plane load, the equilibrium solutions of the system are obtained by treating them as a generalized autonomous system and they will be no longer stable through the pitchfork bifurcation with the symmetry breaking. The bursting oscillations of the novel dynamic system are analyzed by numerical methods. It is interesting to find that the mechanisms of bursting oscillation are associated with the pitchfork bifurcation with the symmetry breaking. (C) 2020 Elsevier Ltd. All rights reserved.
关键词 ：
Bursting oscillation Bursting oscillation Conical panel Conical panel Functionally graded sandwich structures Functionally graded sandwich structures Pitchfork bifurcation Pitchfork bifurcation Slowly varying parametric excitation Slowly varying parametric excitation
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| GB/T 7714 | Hao, Y. X. , Wang, M. X. , Zhang, W. et al. Bending-torsion coupling bursting oscillation of a sandwich conical panel under parametric excitation [J]. | JOURNAL OF SOUND AND VIBRATION , 2021 , 495 . |
| MLA | Hao, Y. X. et al. "Bending-torsion coupling bursting oscillation of a sandwich conical panel under parametric excitation" . | JOURNAL OF SOUND AND VIBRATION 495 (2021) . |
| APA | Hao, Y. X. , Wang, M. X. , Zhang, W. , Yang, S. W. , Liu, L. T. , Qian, Y. H. . Bending-torsion coupling bursting oscillation of a sandwich conical panel under parametric excitation . | JOURNAL OF SOUND AND VIBRATION , 2021 , 495 . |
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摘要 ：
High-voltage transmission line possesses a typical suspended cable structure that produces ice in harsh weather. Moreover, transversely galloping will be excited due to the irregular structure resulting from the alternation of lift force and drag force. In this paper, the nonlinear dynamics and internal resonance of an iced cable under wind excitation are investigated. Considering the excitation caused by pulsed wind and the movement of the support, the nonlinear governing equations of motion of the iced cable are established using a three-degree-of-freedom model based on Hamilton's principle. By the Galerkin method, the partial differential equations are then discretized into ordinary differential equations. The method of multiple scales is then used to obtain the averaged equations of the iced cable, and the principal parametric resonance-1/2 subharmonic resonance and the 2:1 internal resonance are considered. The numerical simulations are performed to investigate the dynamic response of the iced cable. It is found that there exist periodic, multi-periodic, and chaotic motions of the iced cable subjected to wind excitation.
关键词 ：
chaotic motion chaotic motion galloping galloping iced cable iced cable wind excitation wind excitation
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| GB/T 7714 | Zhang, Wei , Li, Ming-Yuan , Wu, Qi-Liang et al. Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model* [J]. | CHINESE PHYSICS B , 2021 , 30 (9) . |
| MLA | Zhang, Wei et al. "Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model*" . | CHINESE PHYSICS B 30 . 9 (2021) . |
| APA | Zhang, Wei , Li, Ming-Yuan , Wu, Qi-Liang , Xi, An . Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model* . | CHINESE PHYSICS B , 2021 , 30 (9) . |
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摘要 ：
The radial propagation of the steady-state wave motion is studied for a pre-stressed cylindrical shell composed of the isotropic compressible neo-Hookean material. The radial static deformation of the cylindrical shell and radial wave motion of the pre-stressed cylindrical shell are investigated. The mathematical model is established as a class of boundary value problems of the second-order nonlinear ordinary differential equation (ODE). Based on the theory of the large elastic deformation superposed by the small harmonic deformation, a radial dynamic displacement is added to the pre-stressed cylindrical shell. The existence of the steady-state wave motion is conducted. Numerical solutions are obtained by using the multiple shooting method. In addition, the influences of the static load, material and structural parameters on the steady-state wave motion are discussed. Numerical results indicate that as the static load increases, the frequency of the steady-state wave motion increases and the amplitude decreases in the compressible hyperelastic cylindrical shell. The material parameter plays a significant role in the frequency and amplitude of the steady-state wave motion.
关键词 ：
compressible hyperelastic cylindrical shell compressible hyperelastic cylindrical shell large deformations superposed by small deformations large deformations superposed by small deformations multiple shooting method multiple shooting method pre-stress pre-stress Steady-state wave motion Steady-state wave motion
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| GB/T 7714 | Zhao, W. , Zhang, W. , Zhang, J. et al. Wave motion of pre-stressed compressible hyperelastic cylindrical shell under radial perturbation [J]. | WAVES IN RANDOM AND COMPLEX MEDIA , 2021 . |
| MLA | Zhao, W. et al. "Wave motion of pre-stressed compressible hyperelastic cylindrical shell under radial perturbation" . | WAVES IN RANDOM AND COMPLEX MEDIA (2021) . |
| APA | Zhao, W. , Zhang, W. , Zhang, J. , Yang, S. W. . Wave motion of pre-stressed compressible hyperelastic cylindrical shell under radial perturbation . | WAVES IN RANDOM AND COMPLEX MEDIA , 2021 . |
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摘要 ：
The eccentric rotating cylindrical shell structure has an important application prospect in aerospace engineering field, such as space annular antenna. In this paper, the dynamic model of an eccentric rotating functionally graded grapheme platelets reinforced composite (FG-GPLRC) cylindrical shell based on the first-order shear deformation theory is established. The free vibration and buckling analyses of the eccentric rotating FGGPLRC cylindrical shell under the axial excitation are presented. Taking into account the influences of the Coriolis force and centrifugal force caused by eccentric rotation. Considering five grapheme platelets (GPLs) distribution patterns of the FG-GPLRC cylindrical shell, and the modified Halpin-Tsai model is used to calculate the effective Young's modulus. By utilizing the Hamilton principle, the first-order shear deformation shell theory and the von-Karman type nonlinear geometric relationships, a system of the partial differential governing equations for the eccentric rotating FG-GPLRC cylindrical shell is derived. Then, the ordinary differential equations of the cylindrical shell are obtained according to Galerkin method. The influences of the GPLs distribution pattern, weight fraction, eccentric distance, ratio of radius to thickness, ratio of length to radius, as well as rotating speed of the eccentric rotating FG-GPLRC cylindrical shell on the buckling and free vibration behaviors are discussed.
关键词 ：
Buckling Buckling Cylindrical shell Cylindrical shell Eccentric rotating Eccentric rotating FG-GPLRC FG-GPLRC Free vibration Free vibration
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| GB/T 7714 | Yang, S. W. , Hao, Y. X. , Zhang, W. et al. Free vibration and buckling of eccentric rotating FG-GPLRC cylindrical shell using first-order shear deformation theory [J]. | COMPOSITE STRUCTURES , 2021 , 263 . |
| MLA | Yang, S. W. et al. "Free vibration and buckling of eccentric rotating FG-GPLRC cylindrical shell using first-order shear deformation theory" . | COMPOSITE STRUCTURES 263 (2021) . |
| APA | Yang, S. W. , Hao, Y. X. , Zhang, W. , Yang, L. , Liu, L. T. . Free vibration and buckling of eccentric rotating FG-GPLRC cylindrical shell using first-order shear deformation theory . | COMPOSITE STRUCTURES , 2021 , 263 . |
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摘要 ：
The occurrence conditions of the metastable chaotic vibrations are firstly studied in the bistable asymmetric composite laminated square shallow shell under the foundation excitation. The metastable chaos is observed in the vibration experiments of the bistable asymmetric composite laminated square shallow shell. Based on the dynamic model of the bistable asymmetric composite laminated square shallow shell, the critical instability condition of the zero equilibrium point is analyzed in the bistable asymmetric composite laminated square shallow shell by using Jacobian matrix and Routh-Hurwitz criterion. We perform numerical simulations based on Runge-Kutta algorithm and the vibration experiments. A sufficient condition is found for the existence of the metastable chaos in the bistable asymmetric composite laminated square shallow shell. It is found that the zero equilibrium point of the bistable asymmetric composite laminated square shallow shell is unstable when the parametric excitation exceeds a specific critical value. The numerical results verify the theoretical analyses of the metastable chaos. It is demonstrated that the increase of the parametric excitation leads to the easier occurrence of the metastable chaos through observing the characteristics of the nonlinear dynamic behaviors of the system. Moreover, the existence of the metastable chaotic vibrations is confirmed in the bistable asymmetric composite laminated square shallow shell under the foundation excitation by using the vibration experiments. The large parametric excitation subjecting to the bistable asymmetric composite laminated square shallow shell is a key factor for the existence of the metastable chaos in the bistable asymmetric composite laminated square shallow shell under the foundation excitation. © 2020 Elsevier Ltd
关键词 ：
Chaos theory Chaos theory Foundations Foundations Jacobian matrices Jacobian matrices Laminated composites Laminated composites Laminating Laminating Runge Kutta methods Runge Kutta methods Shells (structures) Shells (structures)
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| GB/T 7714 | Liu, T. , Zhang, W. , Wu, M.Q. et al. Metastable nonlinear vibrations: Third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation [J]. | Composite Structures , 2021 , 255 . |
| MLA | Liu, T. et al. "Metastable nonlinear vibrations: Third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation" . | Composite Structures 255 (2021) . |
| APA | Liu, T. , Zhang, W. , Wu, M.Q. , Zheng, Y. , Zhang, Y.F. . Metastable nonlinear vibrations: Third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation . | Composite Structures , 2021 , 255 . |
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摘要 ：
This paper experimentally and numerically investigates the nonlinear vibrations and dynamic snap-through behaviors of the bistable asymmetric carbon fiber-reinforced [90n/0n] composite laminated shallow shell. In the experimental research, in order to produce the dynamic snap-through phenomena, the center of a bistable asymmetric composite laminated shallow shell is clamped on an electromechanical shaker. The shaker provides the controlled frequency and amplitude of the foundation excitation. A laser displacement testing system collects the data of the vibration signals for the bistable asymmetric composite laminated shallow shell. A high-speed camera captures the steady-state vibrations of the bistable asymmetric composite laminated shallow shell. The experimental results demonstrate the influence of the structural parameters on the dynamic snap-through phenomena and nonlinear vibrations of the bistable asymmetric composite laminated shallow shell. The amplitude-frequency response curves are obtained by the experimental results. The bifurcation diagrams, phase portraits, time histories, power spectrums, and Poincaré maps are obtained to experimentally and numerically illustrate the single-well periodic, chaotic and double-well chaotic vibrations of the bistable asymmetric composite laminated shallow shell under the center foundation excitation. In numerical research, ABAQUS/CAE is used to simulate the dynamic responses of the bistable asymmetric composite laminated shallow shell. The subspace iteration method is utilized to give the vibration modal analysis. The vibration modes in the experimental research are qualitatively consistent with the results of the ABAQUS numerical simulation. The phenomenon of the energy transfer from the high-order to low-order primary resonance is discovered. The results of the experiment and numerical simulation are well verified with each other. © 2021 Elsevier Masson SAS
关键词 ：
Beams and girders Beams and girders Composite structures Composite structures Energy transfer Energy transfer Frequency response Frequency response Graphite fibers Graphite fibers High speed cameras High speed cameras Iterative methods Iterative methods Laminated composites Laminated composites Laminating Laminating Modal analysis Modal analysis Numerical models Numerical models Shells (structures) Shells (structures) Vibration analysis Vibration analysis
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| GB/T 7714 | Wu, M.Q. , Zhang, W. , Niu, Y. . Experimental and numerical studies on nonlinear vibrations and dynamic snap-through phenomena of bistable asymmetric composite laminated shallow shell under center foundation excitation [J]. | Solids , 2021 , 89 . |
| MLA | Wu, M.Q. et al. "Experimental and numerical studies on nonlinear vibrations and dynamic snap-through phenomena of bistable asymmetric composite laminated shallow shell under center foundation excitation" . | Solids 89 (2021) . |
| APA | Wu, M.Q. , Zhang, W. , Niu, Y. . Experimental and numerical studies on nonlinear vibrations and dynamic snap-through phenomena of bistable asymmetric composite laminated shallow shell under center foundation excitation . | Solids , 2021 , 89 . |
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摘要 ：
In this study, the first-order shear deformation theory (FSDT) is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite (FG-GPLRC). The vibration analyses of the FG-GPLRC truncated conical shell are presented. Considering the graphene platelets (GPLs) of the FG-GPLRC truncated conical shell with three different distribution patterns, the modified Halpin-Tsai model is used to calculate the effective Young's modulus. Hamilton's principle, the FSDT, and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell. The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell. Then, the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method. The effects of the weight fraction and distribution pattern of the GPLs, the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed. This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.
关键词 ：
chaos chaos functionally graded graphene platelet-reinforced composite (FG-GPLRC) functionally graded graphene platelet-reinforced composite (FG-GPLRC) harmonic balance method harmonic balance method nonlinear free vibration nonlinear free vibration O322 O322 truncated conical shell truncated conical shell
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| GB/T 7714 | Yang, Shaowu , Hao, Yuxin , Zhang, Wei et al. Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory [J]. | APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION , 2021 , 42 (7) : 981-998 . |
| MLA | Yang, Shaowu et al. "Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory" . | APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION 42 . 7 (2021) : 981-998 . |
| APA | Yang, Shaowu , Hao, Yuxin , Zhang, Wei , Yang, Li , Liu, Lingtao . Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory . | APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION , 2021 , 42 (7) , 981-998 . |
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