Applied Mathematics and Mechanics (English Edition)

Nonlinear vibrations of a composite circular plate with a rigid body

Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN

2023, 44(6): 857-876. doi:10.1007/s10483-023-3005-8

摘要 ( 1095 )

HTML ( 273)

PDF (1023KB) ( 105 )

参考文献 | 相关文章 | 多维度评价

The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.

A novel way for vibration control of FGM fluid-conveying pipes via NiTiNOL-steel wire rope

Jian ZANG, Ronghuan XIAO, Yewei ZHANG, Liqun CHEN

2023, 44(6): 877-896. doi:10.1007/s10483-023-3008-7

摘要 ( 1081 )

HTML ( 240)

PDF (1179KB) ( 79 )

参考文献 | 相关文章 | 多维度评价

In this study, a coupling model of fluid-conveying pipes made of functionally graded materials (FGMs) with NiTiNOL-steel (NiTi-ST) for vibration absorption is investigated. The vibration responses of the FGM fluid-conveying pipe with NiTi-ST are studied by the Galerkin truncation method (GTM) and harmonic balance method (HBM). The harmonic balance solutions and the numerical results are consistent. Also, the linearized stability of the structure is determined. The effects of the structure parameters on the absorption performance are also studied. The results show that the NiTi-ST is an effective means of vibration absorption. Furthermore, in studying the effect of the NiTi-ST, a closed detached response (CDR) is first observed. It is noteworthy that the CDR may dramatically change the vibration amplitude and that the parameters of the NiTi-ST may determine the emergence or disappearance of the CDR. This vibration absorption device can be extended to offer more general vibration control in engineering applications.

Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment

Wenhao YUAN, Haitao LIAO, Ruxin GAO, Fenglian LI

2023, 44(6): 897-916. doi:10.1007/s10483-023-3004-7

摘要 ( 1110 )

HTML ( 236)

PDF (1290KB) ( 210 )

参考文献 | 相关文章 | 多维度评价

This study investigates the vibration and acoustic properties of porous foam functionally graded (FG) plates under the influence of the temperature field. The dynamics equations of the system are established based on Hamilton's principle by using the higher-order shear deformation theory under the linear displacement-strain assumption. The displacement shape function is assumed according to the four-sided simply-supported (SSSS) boundary condition, and the characteristic equations of the system are derived by combining the motion control equations. The theoretical model of vibro-acoustic coupling is established by using the acoustic theory and fluid-structure coupling solution method under the simple harmonic acoustic wave. The system's natural frequency and sound transmission loss (STL) are obtained through programming calculations and compared with the literature and COMSOL simulation to verify the validity and reliability of the theoretical model. The effects of various factors, such as temperature, porosity coefficients, gradient index, core thickness, width-to-thickness ratio on the vibration, and STL characteristics of the system, are discussed. The results provide a theoretical basis for the application of porous foam FG plates in engineering to optimize vibration and sound transmission properties.

Experimental and simulation studies on similitude design method for shock responses of beam-plate coupled structure

Lei LI, Zhong LUO, Fengxia HE, Jilai ZHOU, Hui MA, Hui LI

2023, 44(6): 917-930. doi:10.1007/s10483-023-3000-8

摘要 ( 1078 )

HTML ( 4)

PDF (1108KB) ( 110 )

参考文献 | 相关文章 | 多维度评价

The similitude theory helps to understand the physical behaviors of large structures through scaled models. Several papers have studied the similitude of shock issues. However, the dynamic similitude for shock responses of coupled structures is rarely incorporated in open studies. In this paper, scaling laws are derived for the shock responses and spectra of coupled structures. In the presented scaling laws, the geometric distortion and energy loss are considered. The ability of the proposed scaling laws is demonstrated in the simulation and experimental cases. In both cases, the similitude prediction for the prototype's time-domain waveform and spectrum is conducted with the scaled model and scaling laws. The simulation and experimental cases indicate that the predicted shock responses and spectra agree well with those of the prototype, which verifies the proposed scaling laws for predicting shock responses.

On fracture behavior of inner enamel: a numerical study

Siyong LIU, Yuanzhi XU, Richeng LIAO, Ge HE, Li DING, Bingbing AN, Dongsheng ZHANG

2023, 44(6): 931-940. doi:10.1007/s10483-023-3007-6

摘要 ( 1112 )

HTML ( 7)

PDF (596KB) ( 161 )

参考文献 | 相关文章 | 多维度评价

The ingenious hierarchical structure of enamel composed of rods and protein produces excellent fracture resistance. However, the fracture resistance mechanism in the inner enamel is unknown. The micromechanical models of enamel are constructed to numerically analyze the mechanical behaviors of the inner enamel with different decussation angles and different decussation planes. The results show that the manner of crack propagation in the inner enamel, including crack bridging, crack deflection, and crack bifurcation, is determined by both the rod decussation angle and the decussation plane. In the case of the strong decussation plane, the fracture strength and the required energy dissipation with the decussation angles of 15° and 30° are much higher than those without decussation, demonstrating that decussation is an important mechanism in improving the fracture resistance of enamel. The maximum tensile stress of enamel with the decussation angle of 15° is slightly higher than that of enamel with the decussation angle of 30°, illustrating that an optimal decussation angle exists which balances the strength and toughness. The synergetic mechanism of the decussation angle and the decussation plane on the crack propagation provides a new design hint for bionic composites.

High-order targeted essentially non-oscillatory scheme for two-fluid plasma model

Yuhang HOU, Ke JIN, Yongliang FENG, Xiaojing ZHENG

2023, 44(6): 941-960. doi:10.1007/s10483-023-3003-6

摘要 ( 1108 )

HTML ( 6)

PDF (931KB) ( 160 )

参考文献 | 相关文章 | 多维度评价

The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model, which cannot describe certain nonequilibrium phenomena by finite collisions of particles, decreasing the fidelity of the solution. Based on an alternative formulation of the targeted essentially non-oscillatory (TENO) scheme, a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems. The numerical flux is constructed by the TENO interpolation of the solution and its derivatives, instead of being reconstructed from the physical flux. The present scheme is used to solve the two sets of Euler equations coupled with Maxwell's equations. The numerical methods are verified by several classical plasma problems. The results show that compared with the original TENO scheme, the present scheme can suppress the non-physical oscillations and reduce the numerical dissipation.

Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

Lan JIANG, Jie WU, Liming YANG, Hao DONG

2023, 44(6): 961-980. doi:10.1007/s10483-023-3009-9

摘要 ( 1077 )

HTML ( 2)

PDF (1445KB) ( 149 )

参考文献 | 相关文章 | 多维度评价

A high-order gas kinetic flux solver (GKFS) is presented for simulating inviscid compressible flows. The weighted essentially non-oscillatory (WENO) scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS (C-GKFS) to capture more details of the flow fields with fewer grids. Different from most of the current GKFSs, which are constructed based on the Maxwellian distribution function or its equivalent form, the C-GKFS simplifies the Maxwellian distribution function into the circular function, which ensures that the Euler or Navier-Stokes equations can be recovered correctly. This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering. Several benchmark cases are simulated, and good agreement can be obtained in comparison with the references, which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

Lattice Boltzmann simulation of the effects of cavity structures and heater thermal conductivity on nucleate boiling heat transfer

Fanming CAI, Zhaomiao LIU, Nan ZHENG, Yanlin REN, Yan PANG

2023, 44(6): 981-996. doi:10.1007/s10483-023-2982-7

摘要 ( 1152 )

HTML ( 4)

PDF (1116KB) ( 107 )

参考文献 | 相关文章 | 多维度评价

The boiling heat transfer technology with cavity surfaces can provide higher heat flux under lower wall superheat, which is of great significance for the cooling of electronic chips and microelectromechanical devices. In this paper, the boiling characteristics of the cavity surfaces are investigated based on the lattice Boltzmann (LB) method, focusing on the effects of cavity shapes, sizes, and heater thermal conductivity on the heat transfer performance. The results show that the triangular cavity has the best boiling performance since it has less residual vapor and higher bubble departure frequency than those of the trapezoidal and rectangular cavities. As the cavity size increases, the enhancement of heat transfer by the cavity mouth is suppressed by the heat accumulation effect at the heater bottom. The liquid rewetting process during bubble departure is the reason for the fluctuation of the space-averaged heat flux, and the heater thermal conductivity determines the fluctuation amplitude. The evaporation of liquid in the cavity with high thermal conductivity walls is more intense, resulting in shorter waiting time and higher bubble departure frequency.

Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

C. Q. RU

2023, 44(6): 997-1006. doi:10.1007/s10483-023-3002-9

摘要 ( 1090 )

HTML ( 2)

PDF (200KB) ( 69 )

参考文献 | 相关文章 | 多维度评价

Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations. The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity. An explicit modified form of the Neumann equations is derived to determine the two contact angles, which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate. Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature, particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.

Analytical study of pulsatile mixed electroosmotic and shear-driven flow in a microchannel with a slip-dependent zeta potential

D. BANERJEE, S. PATI, P. BISWAS

2023, 44(6): 1007-1022. doi:10.1007/s10483-023-3010-6

摘要 ( 1068 )

HTML ( 4)

PDF (766KB) ( 143 )

参考文献 | 相关文章 | 多维度评价

The escalation of zeta potential by the influence of wall slip for the electrokinetically modulated flow through a microchannel motivates to consider the impact of hydrodynamic slippage upon the zeta or surface potential. The reported study undergoes an analytical exploration of the pulsatile electroosmosis and shear-actuated flow characteristics of a fluid with a Newtonian model through a microchannel with parallel plates by invoking the reliance of a zeta or surface potential on slippage. The linearized Poisson-Boltzmann and momentum equations are solved analytically to obtain the explicit expression of the electrical potential induced in the electrical double layer (EDL), the flow velocity field, and the volumetric flow rate for an extensive span of parameters. The velocity field proximal to the microchannel wall is observed to enhance by an apparent zeta potential, and is further escalated for a thinner EDL and an oscillating electric field with a higher amplitude. However, near the core region of the microchannel, the flow velocity becomes invariant with the EDL thickness. The result shows that the lower wall velocity contributes to the flow velocity along with the electroosmotic body force and the impact of the velocity of the wall underneath diminishes proximal to the upper wall. Moreover, the volumetric flow rate increases when the thickness of the EDL decreases, owing to the influence of the wall slip. However, for thinner EDLs and medium and higher oscillating Reynolds numbers, the volumetric flow rate varies non-monotonously, correlative to the slip-free and slip cases.

Linear analysis of the dynamic response of a riser subject to internal solitary waves

Dalin TAN, Xu WANG, Jinlong DUAN, Jifu ZHOU

2023, 44(6): 1023-1034. doi:10.1007/s10483-023-3006-9

摘要 ( 1109 )

HTML ( 5)

PDF (613KB) ( 85 )

参考文献 | 相关文章 | 多维度评价

The flow field induced by internal solitary waves (ISWs) is peculiar wherein water motion occurs in the whole water depth, and the strong shear near the pycnocline can be generated due to the opposite flow direction between the upper and lower layers, which is a potential threat to marine risers. In this paper, the flow field of ISWs is obtained with the Korteweg-de Vries (KdV) equation for a two-layer fluid system. Then, a linear analysis is performed for the dynamic response of a riser with its two ends simply supported under the action of ISWs. The explicit expressions of the deflection and the moment of the riser are deduced based on the modal superposition method. The applicable conditions of the theoretical expressions are discussed. Through comparisons with the finite element simulations for nonlinear dynamic responses, it is proved that the theoretical expressions can roughly reveal the nonlinear dynamic response of risers under ISWs when the approximation for the linear analysis is relaxed to some extent.

当期目录