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2023年 第44卷 第5期    刊出日期：2023-05-01

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论文

A modified single edge V-notched beam method for evaluating surface fracture toughness of thermal barrier coatings

Haoran BAI, Zhanyu WANG, Sangyu LUO, Zhaoliang QU, Daining FANG

2023, 44(5):  693-710.  doi:10.1007/s10483-023-3001-6

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The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed (APS) thermal barrier coatings (TBCs). As APS TBCs are typical multilayer porous ceramic materials, the direct applications of the traditional single edge notched beam (SENB) method that ignores those typical structural characters may cause errors. To measure the surface fracture toughness more accurately, the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered. In this paper, a modified single edge V-notched beam (MSEVNB) method with typical structural characters is developed. According to the finite element analysis (FEA), the geometry factor of the multilayer structure is recalculated. Owing to the narrower V-notches, a more accurate critical fracture stress is obtained. Based on the Griffith energy balance, the reduction of the crack surface caused by micro-defects is corrected. The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.



Fractional nonlinear energy sinks

Shengtao ZHANG, Jiaxi ZHOU, Hu DING, Kai WANG, Daolin XU

2023, 44(5):  711-726.  doi:10.1007/s10483-023-2984-9

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The cubic or third-power (TP) nonlinear energy sink (NES) has been proven to be an effective method for vibration suppression, owing to the occurrence of targeted energy transfer (TET). However, TET is unable to be triggered by the low initial energy input, and thus the TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type of NES with fractional nonlinearity, e.g., one-third-power (OTP) nonlinearity, is proposed. The dynamic behaviors of a linear oscillator (LO) with an OTP NES are investigated numerically, and then both the TET feature and the vibration attenuation performance are evaluated. Moreover, an analogy circuit is established, and the circuit simulations are carried out to verify the design concept of the OTP NES. It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES. The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system. Additionally, significant energy transfer is usually accompanied with efficient energy dissipation. Consequently, the OTP NES can realize TET under low initial input energy, which should be a promising approach for micro-vibration suppression.

Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states

Jian'en CHEN, Jianling LI, Minghui YAO, Jun LIU, Jianhua ZHANG, Min SUN

2023, 44(5):  727-744.  doi:10.1007/s10483-023-2987-9

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The nonreciprocity of energy transfer is constructed in a nonlinear asymmetric oscillator system that comprises two nonlinear oscillators with different parameters placed between two identical linear oscillators. The slow-flow equation of the system is derived by the complexification-averaging method. The semi-analytical solutions to this equation are obtained by the least squares method, which are compared with the numerical solutions obtained by the Runge-Kutta method. The distribution of the average energy in the system is studied under periodic and chaotic vibration states, and the energy transfer along two opposite directions is compared. The effect of the excitation amplitude on the nonreciprocity of the system producing the periodic responses is analyzed, where a three-stage energy transfer phenomenon is observed. In the first stage, the energy transfer along the two opposite directions is approximately equal, whereas in the second stage, the asymmetric energy transfer is observed. The energy transfer is also asymmetric in the third stage, but the direction is reversed compared with the second stage. Moreover, the excitation amplitude for exciting the bifurcation also shows an asymmetric characteristic. Chaotic vibrations are generated around the resonant frequency, irrespective of which linear oscillator is excited. The excitation threshold of these chaotic vibrations is dependent on the linear oscillator that is being excited. In addition, the difference between the energy transfer in the two opposite directions is used to further analyze the nonreciprocity in the system. The results show that the nonreciprocity significantly depends on the excitation frequency and the excitation amplitude.

Symplectic analysis for regulating wave propagation in a one-dimensional nonlinear graded metamaterial

Yunping ZHAO, Xiuhui HOU, Kai ZHANG, Zichen DENG

2023, 44(5):  745-758.  doi:10.1007/s10483-023-2985-6

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An analytical method, called the symplectic mathematical method, is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs. Combined with the linearized perturbation approach, the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived, which only relies on the state vector. The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory. It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase. Subsequently, the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied. The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies. For small excitation frequencies, the gradient parameter plays a dominant role compared with the nonlinearity. The reason is that the gradient tuning aims at the gradient arrangement of local resonators, which is limited by the critical value of the local resonator mass. In contrast, for larger excitation frequencies, the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.

Vibration isolation performance analysis of a bilateral supported bio-inspired anti-vibration control system

Shihua ZHOU, Dongsheng ZHANG, Bowen HOU, Zhaohui REN

2023, 44(5):  759-772.  doi:10.1007/s10483-023-2988-6

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To achieve better anti-vibration performance in a low frequency region and expand the range of vibration isolation, a bilateral supported bio-inspired anti-vibration (BBAV) structure composed of purely linear elements is proposed, inspired by the motion form of bird legs and the nonlinear extension and compression of muscles and tendons. The kinematic relations and nonlinear dynamic model considering vertical and rotational vibrations are established. The loading capacity and equivalent stiffness are investigated with key parameters. The amplitude-frequency characteristics and force transmissibility are used to evaluate the stability and anti-vibration performance with the effects of the excitation amplitude, rod length, installation angle, and spring stiffness. The results show that the loading requirements and resonant characteristics of the BBAV structure are adjustable, and superior vibration isolation performance can be achieved readily by tuning the parameters. The X-shaped vibration structure is sensitive to the spring stiffness, which exhibits a wider vibration isolation bandwidth with smaller spring stiffness. Besides, depending on the parameters, the nonlinear behavior of the BBAV system can be interconverted between the softening type and the hardening type. The theoretical analysis in this study demonstrates the advantages and effectiveness of the vibration isolation structure.

Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment

Hai QING, Huidiao SONG

2023, 44(5):  773-786.  doi:10.1007/s10483-023-2981-7

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An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model, and is utilized to investigate the free damping vibration analysis of the viscoelastic Bernoulli-Euler microbeams in thermal environment. Hamilton's principle is used to derive the differential governing equations and corresponding boundary conditions. The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints. The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly. The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment. Considering the boundary conditions and constitutive constraints, one can get a nonlinear equation with complex coefficients, from which the complex characteristic frequency can be determined. A two-step numerical method is proposed to solve the elastic vibration frequency and the damping ratio. The effects of length scale parameters, viscous coefficient, thermal stress, vibration order on the vibration frequencies, and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.

The quaternion beam model for hard-magnetic flexible cantilevers

Wei CHEN, Guozhen WANG, Yiqun LI, Lin WANG, Zhouping YIN

2023, 44(5):  787-808.  doi:10.1007/s10483-023-2983-8

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The recently developed hard-magnetic soft (HMS) materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields, e.g., soft robotics, flexible electronics, and biomedicine. Theoretical investigations on large deformations of HMS structures are significant foundations of their applications. This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams. A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact (GE) beam model. The singularity-free governing equations for the three-dimensional (3D) large deformations of an HMS beam are first derived, and then solved with the Galerkin discretization method and the trust-region-dogleg iterative algorithm. The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones. The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples. It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field. The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.

Anti-plane pull-out of a rigid line inclusion from an elastic medium

Yansong WANG, Baolin WANG, Youjiang CUI, Kaifa WANG

2023, 44(5):  809-822.  doi:10.1007/s10483-023-2980-6

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The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied. The singular integral equation method is used to solve the stress field. Under the static load, the stress intensity factor (SIF) at the inclusion tips increases with the medium length. The problem becomes equivalent to an inclusion in a medium with an infinite length when the length of the medium is 3.5 times longer than that of the inclusion. However, under the transient load, the maximum value of the SIF occurs when the medium length is about two times the inclusion length. Besides, the relation between the pull-out force and the anti-plane displacement is given. The conclusions are useful in guiding the design of fiber reinforced composite materials.

Revealing the contribution of basilar membrane's biological activity to the mechanism of the cochlear phonosensitive amplification

J.Y. LIANG, Wenjuan YAO

2023, 44(5):  823-840.  doi:10.1007/s10483-023-2986-7

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Explaining the mechanism of the cochlear active phonosensitive amplification has been a major problem in medicine. The basilar membrane (BM) is the key infrastructure. In 1960, Nobel Laureate von Békésy first discovered BM's traveling wave motion. Since that time, BM's models only have considered the traveling wave but not the biological activity. Therefore, a new model considering changes of BM's stiffness in space and time is established based on the immersed boundary method to describe its biological activity. It not only reproduces the results of traveling wave motion but also explains the mechanization on the generation of traveling wave. An important discovery is that changes of BM's stiffness in space and time will cause the unstable global resonance, which will induce amplification of sounds in cochlea. An important inference is that biological activity shall be included in the application of mechanical principles to the analysis of life, which is the essential difference between biomechanics and general mechanics.

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

Huayang DANG, Dongpei QI, Minghao ZHAO, Cuiying FAN, C.S. LU

2023, 44(5):  841-856.  doi:10.1007/s10483-023-2989-7

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In this paper, we investigate the interfacial behavior of a thin one-dimensional (1D) hexagonal quasicrystal (QC) film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation. The contact interface is assumed to be non-slipping, with both perfectly bonded and debonded boundary conditions. The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress, which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials. The expressions are explicitly obtained for the phonon interfacial shear stress, internal normal stress, and stress intensity factors (SIFs). Finally, based on numerical calculations, we briefly discuss the effects of the material mismatch, the geometry of the QC film, and the debonded length and location on stresses and SIFs.