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    03 February 2025, Volume 46 Issue 2
    Recent advancements of nonlinear dynamics in mode coupled microresonators: a review
    Xuefeng WANG, Zhan SHI, Qiqi YANG, Yuzhi CHEN, Xueyong WEI, Ronghua HUAN
    2025, 46(2):  209-232.  doi:10.1007/s10483-025-3211-6
    Abstract ( 189 )   HTML ( 7)   PDF (9217KB) ( 74 )  
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    Due to scale effects, micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications. This review focuses on mode-coupled micromechanical resonators, highlighting the latest advancements in four key areas: internal resonance, synchronization, frequency combs, and mode localization. The origin, development, and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated, with the goal of inspiring new ideas and directions for researchers in this field.

    Continuously adjustable mechanical metamaterial based on planetary gear trains and external meshing gears
    Shuai MO, Xu TANG, Keren CHEN, H. HOUJOH, Wei ZHANG
    2025, 46(2):  233-252.  doi:10.1007/s10483-025-3219-6
    Abstract ( 189 )   HTML ( 11)   PDF (39046KB) ( 102 )  
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    The metamaterial based on external meshing gears (MEG) is designed based on the principle of external meshing gear transmission. Based on the meshing transmission principle of external meshing gears and planetary gear trains, the internal and external gear rings are designed. Based on the internal and external gear rings, the metamaterial based on inner and outer planetary gear trains (MIP) is designed to study the shear modulus, Young's modulus, and amplitude-frequency characteristics of the metamaterial based on gears at different angles. The effects of the number of planetary gears on the physical characteristics of the MIP are studied. The results show that the MEG can be continuously adjusted by adjusting the shear modulus and Young's modulus due to its meshing characteristics. With the same number of gears, the adjustment range of the MIP is larger than the adjustment range of the MEG. When the number of planetary gears increases, the adjustment range of the MIP decreases. Moreover, when the metamaterial based on gears rotates, the harmonic response changes with the change of the angle.

    Light-powered self-rolling of a liquid crystal elastomer-based dicycle
    Kai LI, Chongfeng ZHAO, Yunlong QIU, Yuntong DAI
    2025, 46(2):  253-268.  doi:10.1007/s10483-025-3221-8
    Abstract ( 166 )   HTML ( 3)   PDF (3454KB) ( 11 )  
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    Conventional liquid crystal elastomer (LCE)-based robots are limited by the need for complex controllers and bulky power supplies, restricting their use in microrobots and soft robots. This paper introduces a novel light-powered dicycle that uses an LCE rod, enabling self-rolling by harvesting energy from the environment. The LCE rod serves as the driving force, with energy being supplied by a line light source. Employing a dynamic LCE model, we calculate the transverse curvature of the LCE rod after deformation, as well as the driving moment generated by the shift in a rod’s center of gravity, which allows the dicycle to roll on its own. Through extensive numerical simulations, we identify the correlations between the angular velocity of the dicycle and the key system parameters, specifically the light intensity, LCE rod length, light penetration depth, overall mass of the dicycle, rolling friction coefficient, and wheel radius. Further, the experimental verification is the same as the theoretical result. This proposed light-powered self-rolling dicycle comes with the benefits of the simple structure, the convenient control, the stationary light source, and the small luminous area of the light source. It not only demonstrates self-sustaining oscillations based on active materials, but also highlights the great potential of light-responsive LCE rods in applications such as robotics, aerospace, healthcare, and automation.

    Concurrent generation and amplification of longitudinal and bending waves using defective phononic crystals
    S. H. JO
    2025, 46(2):  269-288.  doi:10.1007/s10483-025-3212-7
    Abstract ( 183 )   HTML ( 5)   PDF (812KB) ( 22 )  
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    Defective phononic crystals (PnCs) have enabled spatial localization and quantitative amplification of elastic wave energy. Most previous research has focused on applications such as narrow-bandpass filters, ultrasonic sensors, and piezoelectric energy harvesters, typically operating under the assumption of an external elastic wave incidence. Recently, a novel approach that uses defective PnCs as ultrasonic actuators to generate amplified waves has emerged. However, the existing studies are limited to the generation of either longitudinal or bending waves, with no research addressing the concurrent generation of both. Hence, this paper proposes a straightforward methodology for the concurrent generation and amplification of both wave types utilizing defect modes at independent defect-band frequencies. Bimorph piezoelectric elements are attached to the defect, with each element connected to independent external voltage sources. By precisely adjusting the magnitude and temporal phase differences between the voltage sources, concurrently amplified wave generation is achieved. The paper highlights the advantages of the proposed analytical model. This model is both computationally time-efficient and accurate, in comparison with the COMSOL simulation results. For instance, in case studies, the analytical model reduces the computational time from one hour to mere seconds, while maintaining acceptable error rates of 1% in peak frequencies. This concurrent wave-generation methodology opens new avenues for applications in rotating machinery fault diagnosis, structural health monitoring, and medical imaging.

    On the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film based on the beam theory
    Wenkai ZHANG, C. S. LU, Minghao ZHAO, Cuiying FAN, Huayang DANG
    2025, 46(2):  289-304.  doi:10.1007/s10483-025-3214-9
    Abstract ( 175 )   HTML ( 7)   PDF (1548KB) ( 40 )  
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    In this paper, the mechanical response of a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) thin film is analyzed under electric and temperature loads. Based on the Euler-Bernoulli beam theory, a theoretical model is proposed, resulting in coupled governing integral equations that account for interfacial normal and shear stresses. To numerically solve these integral equations, an expansion method using orthogonal Chebyshev polynomials is employed. The results provide insights into the interfacial stresses, axial force, as well as axial and vertical deformations of the PQC film. Additionally, fracture criteria, including stress intensity factors, mode angles, and the J-integral, are evaluated. The solution is compared with the membrane theory, neglecting the normal stress and bending deformation. Finally, the effects of stiffness and aspect ratio on the PQC film are thoroughly discussed. This study serves as a valuable guide for controlling the mechanical response and conducting safety assessments of PQC film systems.

    Active traveling wave vibration control of elastic supported conical shells with smart micro fiber composites based on the differential quadrature method
    Yuxin HAO, Lei SUN, Wei ZHANG, Han LI
    2025, 46(2):  305-322.  doi:10.1007/s10483-025-3216-7
    Abstract ( 146 )   HTML ( 4)   PDF (6103KB) ( 39 )  
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    This paper investigates the active traveling wave vibration control of an elastic supported rotating porous aluminium conical shell (CS) under impact loading. Piezoelectric smart materials in the form of micro fiber composites (MFCs) are used as actuators and sensors. To this end, a metal pore truncated CS with MFCs attached to its surface is considered. Adding artificial virtual springs at two edges of the truncated CS achieves various elastic supported boundaries by changing the spring stiffness. Based on the first-order shear deformation theory (FSDT), minimum energy principle, and artificial virtual spring technology, the theoretical formulations considering the electromechanical coupling are derived. The comparison of the natural frequency of the present results with the natural frequencies reported in previous literature evaluates the accuracy of the present approach. To study the vibration control, the integral quadrature method in conjunction with the differential quadrature approximation in the length direction is used to discretize the partial differential dynamical system to form a set of ordinary differential equations. With the aid of the velocity negative feedback method, both the time history and the input control voltage on the actuator are demonstrated to present the effects of velocity feedback gain, pore distribution type, semi-vertex angle, impact loading, and rotational angular velocity on the traveling wave vibration control.

    Distributed stochastic model predictive control for energy dispatch with distributionally robust optimization
    Mengting LIN, Bin LI, C. CECATI
    2025, 46(2):  323-340.  doi:10.1007/s10483-025-3215-6
    Abstract ( 161 )   HTML ( 7)   PDF (547KB) ( 31 )  
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    A chance-constrained energy dispatch model based on the distributed stochastic model predictive control (DSMPC) approach for an islanded multi-microgrid system is proposed. An ambiguity set considering the inherent uncertainties of renewable energy sources (RESs) is constructed without requiring the full distribution knowledge of the uncertainties. The power balance chance constraint is reformulated within the framework of the distributionally robust optimization (DRO) approach. With the exchange of information and energy flow, each microgrid can achieve its local supply-demand balance. Furthermore, the closed-loop stability and recursive feasibility of the proposed algorithm are proved. The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.

    Prediction of velocity and pressure of gas-liquid flow using spectrum-based physics-informed neural networks
    Nanxi DING, Hengzhen FENG, H. Z. LOU, Shenghua FU, Chenglong LI, Zihao ZHANG, Wenlong MA, Zhengqian ZHANG
    2025, 46(2):  341-356.  doi:10.1007/s10483-025-3217-8
    Abstract ( 164 )   HTML ( 3)   PDF (7336KB) ( 82 )  
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    This research introduces a spectrum-based physics-informed neural network (SP-PINN) model to significantly improve the accuracy of calculation of two-phase flow parameters, surpassing existing methods that have limitations in global and continuous data sampling. SP-PINNs address the challenges of traditional methods in terms of continuous sampling by integrating the spectral analysis and pressure correction into the Navier-Stokes (N-S) equations, enhancing the predictive accuracy especially in critical regions like gas-phase boundaries and velocity peaks. The novel introduction of a pressure-correction module within SP-PINNs mitigates prediction errors, achieving a substantial reduction to 1‰ compared with the conventional physics-informed neural network (PINN) approaches. Experimental applications validate the model’s ability to accurately and rapidly predict flow parameters with different sampling time intervals, with the computation time of predicting unsampled data less than 0.01 s. Such advancements signify a 100-fold improvement over traditional DNS calculations, underscoring the model’s potential in the real-time calculation and analysis of multiphase flow dynamics.

    Analysis of convective-radiative heat transfer in dovetail longitudinal fins with shape-dependent hybrid nanofluids: a study using the Hermite wavelet method
    C. G. PAVITHRA, B. J. GIREESHA, S. SUSHMA, K. J. GOWTHAM
    2025, 46(2):  357-372.  doi:10.1007/s10483-025-3218-9
    Abstract ( 154 )   HTML ( 5)   PDF (3249KB) ( 20 )  
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    A distinguished category of operational fluids, known as hybrid nanofluids, occupies a prominent role among various fluid types owing to its superior heat transfer properties. By employing a dovetail fin profile, this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties, flowing uniformly at a velocity U. The analysis focuses on four distinct types of nanoparticles, i.e., Al2O3, Ag, carbon nanotube (CNT), and graphene. Specifically, two of these particles exhibit a spherical shape, one possesses a cylindrical form, and the final type adopts a platelet morphology. The investigation delves into the pairing of these nanoparticles. The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid. The fin design, under the specified circumstances, gives rise to the derivation of a differential equation. The given equation is then transformed into a dimensionless form. Notably, the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features. To validate the credibility of this research, the results obtained in this study are systematically compared with the numerical simulations. The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.

    Research on the application of the parameter freezing precise exponential integrator in vehicle-road coupling vibration
    Yu ZHANG, Chao ZHANG, Shaohua LI, Shaopu YANG
    2025, 46(2):  373-390.  doi:10.1007/s10483-025-3220-7
    Abstract ( 151 )   HTML ( 2)   PDF (425KB) ( 44 )  
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    The vehicle-road coupling dynamics problem is a prominent issue in transportation, drawing significant attention in recent years. These dynamic equations are characterized by high-dimensionality, coupling, and time-varying dynamics, making the exact solutions challenging to obtain. As a result, numerical integration methods are typically employed. However, conventional methods often suffer from low computational efficiency. To address this, this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models. The model accounts for road roughness irregularities, incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector. The general construction process of the algorithm is detailed. The validity of numerical results is verified through approximate analytical solutions (AASs), and the advantages of this method over traditional numerical integration methods are demonstrated. Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework, with the fourth-order four-stage scheme identified as the optimal one. The study indicates that this method can quickly and accurately capture the dynamic system's vibration response, offering a new, efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.

    Applications of variable thermal features for the bioconvective flow of Jeffrey nanofluids due to stretching surface with masssuction effects: Cattaneo-Christov model
    S. U. KHAN, M. GARAYEV, ADNAN, K. RAMESH, M. EL MELIGY, D. ABDUVALIEVA, M. I. KHAN
    2025, 46(2):  391-402.  doi:10.1007/s10483-025-3213-8
    Abstract ( 160 )   HTML ( 7)   PDF (1631KB) ( 62 )  
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    The thermal nanofluids have garnered widespread attention for their use in multiple thermal systems, including heating processes, sustainable energy, and nuclear reactions. Research on nanofluids has revealed that the thermal efficiencies of such materials are adversely affected by various thermal features. The purpose of the current work is to demonstrate the thermal analysis of Jeffrey nanofluids with the suspension of microorganisms in the presence of variable thermal sources. The variable effects of thermal conductivity, Brownian diffusivity, and motile density are utilized. The investigated model also reveals the contributions of radiation phenomena and chemical reactions. A porous, saturated, moving surface with a suction phenomenon promotes flow. The modeling of the problem is based on the implementation of the Cattaneo-Christov approach. The convective thermal constraints are used to promote the heat transfer features. A simplified form of the governing model is treated with the assistance of a shooting technique. The physical effects of different parameters for the problem are presented. The current problem justifies its applications in heat transfer, coating processes, heat exchangers, cooling systems in microelectronics, solar systems, chemical processes, etc.

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