Table of Content

01 October 2024, Volume 45 Issue 10

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Articles

Analytical modeling of piezoelectric meta-beams with unidirectional circuit for broadband vibration attenuation

Jiawei MAO, Hao GAO, Junzhe ZHU, Penglin GAO, Yegao QU

2024, 45(10):  1665-1684.  doi:10.1007/s10483-024-3155-9

Abstract ( 205 )   HTML ( 22)   PDF (10252KB) ( 181 )  

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Broadband vibration attenuation is a challenging task in engineering since it is difficult to achieve low-frequency and broadband vibration control simultaneously. To solve this problem, this paper designs a piezoelectric meta-beam with unidirectional electric circuits, exhibiting promising broadband attenuation capabilities. An analytical model in a closed form for achieving the solution of unidirectional vibration transmission of the designed meta-beam is developed based on the state-space transfer function method. The method can analyze the forward and backward vibration transmission of the piezoelectric meta-beam in a unified manner, providing reliable dynamics solutions of the beam. The analytical results indicate that the meta-beam effectively reduces the unidirectional vibration across a broad low-frequency range, which is also verified by the solutions obtained from finite element analyses. The designed meta-beam and the proposed analytical method facilitate a comprehensive investigation into the distinctive unidirectional transmission behavior and superb broadband vibration attenuation performance.

A transfer learning enhanced physics-informed neural network for parameter identification in soft materials

Jing'ang ZHU, Yiheng XUE, Zishun LIU

2024, 45(10):  1685-1704.  doi:10.1007/s10483-024-3178-9

Abstract ( 185 )   HTML ( 7)   PDF (11313KB) ( 202 )  

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Soft materials, with the sensitivity to various external stimuli, exhibit high flexibility and stretchability. Accurate prediction of their mechanical behaviors requires advanced hyperelastic constitutive models incorporating multiple parameters. However, identifying multiple parameters under complex deformations remains a challenge, especially with limited observed data. In this study, we develop a physics-informed neural network (PINN) framework to identify material parameters and predict mechanical fields, focusing on compressible Neo-Hookean materials and hydrogels. To improve accuracy, we utilize scaling techniques to normalize network outputs and material parameters. This framework effectively solves forward and inverse problems, extrapolating continuous mechanical fields from sparse boundary data and identifying unknown mechanical properties. We explore different approaches for imposing boundary conditions (BCs) to assess their impacts on accuracy. To enhance efficiency and generalization, we propose a transfer learning enhanced PINN (TL-PINN), allowing pre-trained networks to quickly adapt to new scenarios. The TL-PINN significantly reduces computational costs while maintaining accuracy. This work holds promise in addressing practical challenges in soft material science, and provides insights into soft material mechanics with state-of-the-art experimental methods.

Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Jiangcheng CAI, Mingxi DENG

2024, 45(10):  1705-1716.  doi:10.1007/s10483-024-3176-7

Abstract ( 146 )   HTML ( 4)   PDF (506KB) ( 102 )  

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Acoustic nonlinearity holds potential as a method for assessing material stress. Analogous to the acoustoelastic effect, where the velocity of elastic waves is influenced by third-order elastic constants, the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants. Despite this, there has been a notable absence of research exploring this phenomenon. Consequently, this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials. It delves into the impact of pre-stress on higher-order material parameters, and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress. This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.

A physics-informed neural network for simulation of finite deformation in hyperelastic-magnetic coupling problems

Lei WANG, Zikun LUO, Mengkai LU, Minghai TANG

2024, 45(10):  1717-1732.  doi:10.1007/s10483-024-3174-9

Abstract ( 179 )   HTML ( 3)   PDF (7702KB) ( 129 )  

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Recently, numerous studies have demonstrated that the physics-informed neural network (PINN) can effectively and accurately resolve hyperelastic finite deformation problems. In this paper, a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed. Since the solution space consists of two-phase domains, two separate networks are constructed to independently predict the solution for each phase region. In addition, a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients. With the developed framework, the magnetic fields and deformation fields of magnetorheological elastomers (MREs) are solved under the control of hyperelastic-magnetic coupling equations. Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework. Moreover, the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated, particularly in handling small data sets, as well as its ability in swiftly and precisely forecasting magnetostrictive motion.

A human-sensitive frequency band vibration isolator for heavy-duty truck seats

Qingqing LIU, Shenlong WANG, Ge YAN, Hu DING, Haihua WANG, Qiang SHI, Xiaohong DING, Huijie YU

2024, 45(10):  1733-1748.  doi:10.1007/s10483-024-3177-8

Abstract ( 176 )   HTML ( 2)   PDF (11903KB) ( 92 )  

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In this study, a human-sensitive frequency band vibration isolator (HFBVI) with quasi-zero stiffness (QZS) characteristics for heavy-duty truck seats is designed to improve the comfort of heavy-duty truck drivers on uneven roads. First, the analytical expressions for the force and displacement of the HFBVI are derived with the Lagrange equation and d'Alembert's principle, and are validated through the prototype restoring force testing. Second, the harmonic balance method (HBM) is used to obtain the dynamic responses under harmonic excitation, and further the influence of pre-stretching on the dynamic characteristics and transmissibility is discussed. Finally, the experimental prototype of the HFBVI is fabricated, and vibration experiments are conducted under harmonic excitation to verify the vibration isolation performance (VIP) of the proposed vibration isolator. The experimental results indicate that the HFBVI can effectively suppress the frequency band (4-8 Hz) to which the human body is sensitive to vertical vibration. In addition, under real random road spectrum excitation, the HFBVI can achieve low-frequency vibration isolation close to 2 Hz, providing new prospects for ensuring the health of heavy-duty truck drivers.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

Peng SHENG, Xin FANG, Dianlong YU, Jihong WEN

2024, 45(10):  1749-1772.  doi:10.1007/s10483-024-3165-7

Abstract ( 161 )   HTML ( 1)   PDF (16294KB) ( 87 )  

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The violent vibration of supersonic wings threatens aircraft safety. This paper proposes the strongly nonlinear acoustic metamaterial (NAM) method to mitigate aeroelastic vibration in supersonic wing plates. We employ the cantilever plate to simulate the practical behavior of a wing. An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory. The aerodynamic properties are systematically studied using both the time-domain integration and frequency-domain harmonic balance methods. While presenting the flutter and post-flutter behaviors of the NAM wing, we emphasize more on the pre-flutter broadband vibration that is prevalent in aircraft. The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%-90%, while the post-flutter vibration is reduced by over 95%, and the critical flutter velocity is also slightly delayed. As clarified, the significant reduction arises from the bandgap, chaotic band, and nonlinear resonances of the NAM plate. The reduction effect is robust across a broad range of parameters, with optimal performance achieved with only 10% attached mass. This work offers a novel approach for reducing aeroelastic vibration in aircraft, and it expands the study of nonlinear acoustic/elastic metamaterials.

Control and vibration analyses of a sandwich doubly curved micro-composite shell with honeycomb, truss, and corrugated cores based on the fourth-order shear deformation theory

F. SHIRDELAN, M. MOHAMMADIMEHR, F. BARGOZINI

2024, 45(10):  1773-1790.  doi:10.1007/s10483-024-3175-6

Abstract ( 148 )   HTML ( 2)   PDF (1250KB) ( 158 )  

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Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures, flexibility, and attractive appearance. However, the inability of controlling and regulating vibrations and destroying them afterward is a challenge to scientists. In this paper, the curve shell equations and a linear quadratic regulator are adopted for the state feedback design to manage the structure vibrations in state space forms. A five-layer sandwich doubly curved micro-composite shell, comprising two piezoelectric layers for the sensor and actuator, is modeled by the fourth-order shear deformation theory. The core (honeycomb, truss, and corrugated) is analyzed for the bearing of transverse shear forces. The results show that the honeycomb core has a greater effect on the vibrations. When the parameters related to the core and the weight percentage of graphene increase, the frequency increases. The uniform distribution of graphene platelets results in the lowest natural frequency while the natural frequency increases. Furthermore, without taking into account the piezoelectric layers, the third-order shear deformation theory (TSDT) and fourth-order shear deformation theory (FOSDT) align closely. However, when the piezoelectric layers are incorporated, these two theories diverge significantly, with the frequencies in the FOSDT being lower than those in the TSDT.

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

Jiajia MAO, Hong CHENG, Tianxue MA

2024, 45(10):  1791-1806.  doi:10.1007/s10483-024-3164-9

Abstract ( 153 )   HTML ( 1)   PDF (2165KB) ( 48 )  

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Curved-beams can be used to design modular multistable metamaterials (MMMs) with reprogrammable material properties, i. e., programmable curved-beam periodic structure (PCBPS), which is promising for controlling the elastic wave propagation. The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap, analyze the wave propagation mechanisms, and further form its geometrical and physical criteria for tuning the elastic wave propagation. With the equivalent model, we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability, and investigate the wave propagation characteristics through the PCBPS. To validate the equivalent system, the finite element method (FEM) is employed. It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics. The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

Bandgap adjustment of a sandwich-like acoustic metamaterial plate with a frequency-displacement feedback control method

Jianing LIU, Jinqiang LI, Ying WU

2024, 45(10):  1807-1820.  doi:10.1007/s10483-024-3167-8

Abstract ( 134 )   HTML ( 3)   PDF (6043KB) ( 40 )  

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Several types of acoustic metamaterials composed of resonant units have been developed to achieve low-frequency bandgaps. In most of these structures, bandgaps are determined by their geometric configurations and material properties. This paper presents a frequency-displacement feedback control method for vibration suppression in a sandwich-like acoustic metamaterial plate. The band structure is theoretically derived using the Hamilton principle and validated by comparing the theoretical calculation results with the finite element simulation results. In this method, the feedback voltage is related to the displacement of a resonator and the excitation frequency. By applying a feedback voltage on the piezoelectric fiber-reinforced composite (PFRC) layers attached to a cantilever-mass resonator, the natural frequency of the resonator can be adjusted. It ensures that the bandgap moves in a frequency-dependent manner to keep the excitation frequency within the bandgap. Based on this frequency-displacement feedback control strategy, the bandgap of the metamaterial plate can be effectively adjusted, and the vibration of the metamaterial plate can be significantly suppressed.

Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes

Donghai HAN, Qi JIA, Yuanyu GAO, Qiduo JIN, Xin FANG, Jihong WEN, Dianlong YU

2024, 45(10):  1821-1840.  doi:10.1007/s10483-024-3166-8

Abstract ( 165 )   HTML ( 2)   PDF (39247KB) ( 60 )  

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To solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes, a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed. First, an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes, and a novel periodic structure unit model is constructed for vibration reduction. Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure, the material parameters, structural parameters, and the arrangement interval of the periodic structure unit are optimized. The finite element method (FEM) is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure. Then, the wave/spectrum element method (WSEM) and experimental test are used to verify the calculated results above. Lastly, the vibration attenuation characteristics of the structure under different conditions, such as rubber material parameters, mass ring material, and fluid-structure coupling effect, are analyzed. The results show that the structure can produce a complete bandgap of 46 Hz-75 Hz in the low-frequency band below 100 Hz, which can effectively suppress the low broadband vibration of the fluid-conveying pipe. In addition, a high damping rubber material is used in the design of the periodic structure unit, which realizes the effective suppression of each formant peak of the pipe, and improves the vibration reduction effect of the fluid-conveying pipe. Meanwhile, the structure has the effect of suppressing both bending vibration and longitudinal vibration, and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe. The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

Xingjian DONG, Shuo WANG, Anshuai WANG, Liang WANG, Zhaozhan ZHANG, Yuanhao TIE, Qingyu LIN, Yongtao SUN

2024, 45(10):  1841-1856.  doi:10.1007/s10483-024-3168-7

Abstract ( 161 )   HTML ( 3)   PDF (8866KB) ( 127 )  

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The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch's theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169. 57 Hz to 216. 42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure's two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i. e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure's excellent low-frequency vibration suppression capability.