【新文速递】2024年6月6日固体力学SCI期刊最新文章

 

今日更新：Journal of the Mechanics and Physics of Solids 3 篇，Mechanics of Materials 1 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 7 篇

Journal of the Mechanics and Physics of Solids

Origami of multi-layered spaced sheets

Guowei Wayne Tu, Evgueni T. Filipov

doi:10.1016/j.jmps.2024.105730

多层间隔纸的折纸

Two-dimensional (2D) origami tessellations such as the Miura-ori are often generalized to build three-dimensional (3D) architected materials with sandwich or cellular structures. However, such 3D blocks are densely packed with continuity of the internal material, while for many engineering structures with multi-physical functionality, it is necessary to have thin sheets that are separately spaced and sparsely connected. This work presents a framework for the design and analysis of multi-layered spaced origami, which provides an origami solution for 3D structures where multiple flat sheets are intentionally spaced apart. We connect Miura-ori sheets with sparsely installed thin-sheet parallelogram-like linkages. To explore how this connectivity approach affects the behavior of the origami system, we model the rigid-folding kinematics using analytic trigonometry and rigid-body transformations, and we characterize the elastic-folding mechanics by generalizing a reduced order bar and hinge model for these 3D assemblies. The orientation of the linkages in the multi-layered spaced origami determines which of three folding paths the system will follow including a flat foldable type, a self-locking type, and a double-branch type. When the origami is flat foldable, a maximized packing ratio and a uniform in-plane shear stiffness can be achieved by strategically choosing the link orientation. We show possible applications by demonstrating how the multi-layered spaced origami can be used to build deployable acoustic cloaks and heat shields.

二维(2D)折纸镶嵌，如Miura-ori，通常被推广到构建具有三明治或细胞结构的三维(3D)建筑材料。然而，这种3D块体内部材料的连续性密集堆积，而对于许多具有多物理功能的工程结构来说，必须有单独间隔和稀疏连接的薄片。这项工作提出了一个设计和分析多层间隔折纸的框架，它提供了一个三维结构的折纸解决方案，其中多个平面被故意分开。我们用稀疏安装的薄片状平行四边形连接三浦ori板。为了探索这种连接方法如何影响折纸系统的行为，我们使用解析三角学和刚体变换对刚性折叠运动学进行建模，并通过推广这些3D组件的降阶杆和铰链模型来表征弹性折叠力学。多层间隔折纸中连杆的方向决定了系统将遵循的三种折叠路径中的哪一种，包括平面可折叠型、自锁型和双分支型。当折纸可平折时，通过对连杆方向的策略选择，可以获得最大的填充比和均匀的面内剪切刚度。我们通过展示多层间隔折纸如何用于建造可展开的声学斗篷和隔热罩来展示可能的应用。

A discrete dislocation analysis of size-dependent plasticity in torsion

A. Cruzado, M.P. Ariza, A. Needleman, M. Ortiz, A.A. Benzerga

doi:10.1016/j.jmps.2024.105709

扭转中尺寸相关塑性的离散位错分析

A method for solving three dimensional discrete dislocation plasticity boundary-value problems using a monopole representation of the dislocations is presented. At each time step, the displacement, strain and stress fields in a finite body are obtained by superposition of infinite body dislocation fields and an image field that enforces the boundary conditions. The three dimensional infinite body fields are obtained by representing dislocations as being comprised of points, termed monopoles, that carry dislocation line and Burgers vector information. The image fields are obtained from a three dimensional linear elastic finite element calculation. The implementation of the coupling of the monopole representation with the finite element method, including the interaction of curved dislocations with free surfaces, is presented in some detail because it differs significantly from an implementation with a line based dislocation representation. Numerical convergence and the modeling of dislocation loop nucleation for large scale computations are investigated. The monopole discrete dislocation plasticity framework is used to investigate the effect of size and initial dislocation density on the torsion of wires with diameters varying over three orders of magnitude. Depending on the initial dislocation source density and the wire diameter, three regimes of torsion-twist response are obtained: (i) for wires with a sufficiently small diameter, plastic deformation is nucleation controlled and is strongly size dependent; (ii) for wires with larger diameters dislocation plasticity is dislocation interaction controlled, with the emergence of geometrically necessary dislocations and dislocation pile-ups playing a key role, and is strongly size dependent; and (iii) for wires with sufficiently large diameters plastic deformation becomes less heterogeneous and the dependence on size is greatly diminished.

提出了一种用位错单极子表示来求解三维离散位错塑性边值问题的方法。在每个时间步，通过将无限体 位错场与强制边界条件的图像场叠加得到有限体的位移场、应变场和应力场。三维无限体场通过将位错表示为由携带位错线和伯格矢量信息的单极子组成的点来获得。图像场是通过三维线弹性有限元计算得到的。单极子表示与有限元方法耦合的实现，包括弯曲位错与自由表面的相互作用，由于它与基于线的位错表示的实现有很大的不同，因此给出了一些细节。研究了大规模计算中位错环形核的数值收敛和模拟。采用单极离散位错塑性框架研究了尺寸和初始位错密度对直径变化超过3个数量级的金属丝扭转的影响。根据初始位错源密度和线材直径的不同，可以得到三种扭扭响应模式:(i)对于直径足够小的线材，塑性变形受形核控制，且与尺寸密切相关;(ii)对于直径较大的金属丝，位错塑性受位错相互作用的控制，几何上必要的位错和位错堆积的出现起着关键作用，并且与尺寸密切相关;(3)对于直径足够大的线材，塑性变形的不均匀性降低，对尺寸的依赖性大大降低。

Exploiting dynamic bifurcation in elastic ribbons for mode skipping and selection

Weicheng Huang, Tian Yu, Dominic Vella, K. Jimmy Hsia, Mingchao Liu

doi:10.1016/j.jmps.2024.105721

利用弹性带的动态分岔进行模式跳转和选择

In this paper, we systematically study the dynamic snap-through behavior of a pre-deformed elastic ribbon by combining theoretical analysis, discrete numerical simulations, and experiments. By rotating one of its clamped ends with controlled angular speed, we observe two snap-through transition paths among the multiple stable configurations of a ribbon in three-dimensional (3D) space, which is different from the classical snap-through of a two-dimensional (2D) bistable beam. Our theoretical model for the static bifurcation analysis is derived based on the Kirchhoff equations, and dynamical numerical simulations are conducted using the Discrete Elastic Rods (DER) algorithm. The planar beam model is also employed for the asymptotic analysis of dynamic snap-through behaviors. The results show that, since the snap-through processes of both planar beams and 3D ribbons are governed by the saddle–node bifurcation, the same scaling law for the delay applies. We further demonstrate that, in elastic ribbons, by controlling the rotating velocity at the end, distinct snap-through pathways can be realized by selectively skipping specific modes, moreover, particular final modes can be strategically achieved. Through a parametric study using numerical simulations, we construct general phase diagrams for both mode skipping and selection of snapping ribbons. The work serves as a benchmark for future investigations on dynamic snap-through of thin elastic structures and provides guidelines for the novel design of intelligent mechanical systems.

本文采用理论分析、离散数值模拟和实验相结合的方法，系统地研究了预变形弹性带的动态通断行为。通过以控制的角速度旋转其夹紧的一端，我们观察到三维(3D)空间中条带的多个稳定构型之间有两条卡通过渡路径，这与传统的二维(2D)双稳光束的卡通不同。基于Kirchhoff方程推导了静态分岔分析的理论模型，并采用离散弹性杆(DER)算法进行了动态数值模拟。平面梁模型也被用于动态卡通行为的渐近分析。结果表明，由于平面梁和三维带的穿透过程都受鞍节点分岔的支配，因此时延的标度规律是相同的。我们进一步证明，在弹性带中，通过控制末端的旋转速度，可以通过选择性地跳过特定模式来实现不同的snap-through路径，并且可以策略性地实现特定的最终模式。通过数值模拟的参数化研究，我们构造了模跳变和夹带选择的一般相图。该研究为今后薄弹性结构的动态贯通研究提供了一个基准，并为智能机械系统的新型设计提供了指导。

Mechanics of Materials

A multiscale model for the multiaxial anisotropic damage of double-network gels

Lionel Ogouari, Qiang Guo, Fahmi Zaïri, Thanh-Tam Mai, Jian Ping Gong, Kenji Urayama

doi:10.1016/j.mechmat.2024.105058

双网凝胶多轴各向异性损伤的多尺度模型

Double-network (DN) gels possess exceptional mechanical properties and hold great promise as innovative soft materials due to their peculiar inherent structure made of a first highly cross-linked brittle short-chain network and a second flexible loosely cross-linked long-chain network. The stretch-induced molecular ordering in DN gels causes anisotropic effects along with complex interactions between the two networks. This paper attempts to contribute to the understanding of the history-dependent anisotropic multiaxial damage behavior of DN gels. A multiscale model is formulated for the constitutive description of the internal network physics in DN gels, such as the stretch-induced molecular ordering and damage, in connection to their multiaxial mechanics. The scission mechanism in the short-chain network is considered at the chain-scale using statistical mechanics by treating the breakage of internal molecular bonds as an energy activation process related to the thermal oscillation and stimulated by the chain stretch. The transition scale microsphere-based method is employed to realize the transition from the short-chain scale to the network scale while considering the statistical variability in chain lengths and their evolution due to the chain rearrangement consecutive to the progressive chain scission events. A two-phase microstructure representation allows accounting for the presence of the superimposed long-chain network along with the effective coupling due to mutual interpenetration of the two networks. The model capabilities to capture the biaxial behavior of gel material systems are critically evaluated by comparing the model outputs with a few available experimental observations under various loading modes highlighting both internal network coupling and anisotropic damage. The relevance of the proposed approach is highlighted by the favorable alignment of the model simulations with experimental observations of gel systems subjected to uniaxial stretching along orthogonal directions and exhibiting history-dependent anisotropic features induced by prior biaxial loading. The damage and rearrangement micro-mechanisms are discussed with respect to the model in connection to loading history.

双网(DN)凝胶具有优异的力学性能，由于其独特的固有结构，第一高度交联的脆性短链网络和第二柔性松散交联的长链网络。拉伸诱导的DN凝胶中的分子排序导致各向异性效应以及两个网络之间复杂的相互作用。本文试图对DN凝胶的各向异性多轴损伤行为的历史相关的理解作出贡献。建立了一个多尺度模型，用于描述DN凝胶内部网络物理的本构描述，例如拉伸诱导的分子有序和损伤，以及与它们的多轴力学有关的本构描述。利用统计力学的方法在链尺度上考虑短链网络的断裂机理，将分子内部键的断裂视为与热振荡有关的能量激活过程，并受到链拉伸的刺 激。采用基于微球的过渡尺度方法，在考虑连续的链断裂事件导致的链重排和链长演化的统计变异性的同时，实现了从短链尺度向网络尺度的过渡。两相微观结构表示允许考虑重叠长链网络的存在以及由于两个网络相互渗透而产生的有效耦合。通过将模型输出与几种不同加载模式下的实验观察结果进行比较，重点分析了内部网络耦合和各向异性损伤，对模型捕捉凝胶材料体系双轴行为的能力进行了严格评估。所提出的方法的相关性突出了模型模拟与实验观察的良好一致性，凝胶体系受到沿正交方向的单轴拉伸，并表现出由先前的双轴加载引起的历史相关的各向异性特征。结合加载历史，讨论了该模型的损伤和重排微观机制。

International Journal of Plasticity

Pseudo-twin boundary improves flow stress and cyclic stability of TiAl single crystal

Yiqi Zhu, Min Yi, Wanlin Guo

doi:10.1016/j.ijplas.2024.104021

伪孪晶界改善了TiAl单晶的流动应力和循环稳定性

Polysynthetically twinned (PST) TiAl single crystal with lamellar structures exhibits great mechanical properties at room temperature. Therein twin boundaries (TBs) are important for achieving optimized ductile and fatigue performance of PST TiAl, but their role and the associated mechanism are elusive. Herein, we decipher the role of true TB (TTB) and pseudo TB (PTB) by a combined atomistic simulation and mesoscopic modeling, and find that PTB could remarkably improve room-temperature flow stress and cyclic stability of TiAl single crystal. It is revealed that dislocations pile up at PTB while unobstructedly traverse TTB. The emergency of back stress and the movement of dislocations along PTB contribute to the strengthening mechanism. The flow stress of TiAl single crystal with PTB is 34% higher than that with TTB. It is further found that as the twin thickness decreases, the flow stress of TiAl single crystal with TTB initially increases and then decreases (i.e., inverse Hall–Petch like behavior), whereas that with PTB always increases owing to the extra back stress (i.e., Hall–Petch like behavior). Atomistic-informed mesoscopic theoretical models are then proposed to describe the flow stress as a function of twin thickness. Under cyclic loading, PTB is found to facilitate strain delocalization of TiAl single crystal during plastic deformation and thus noticeably improve the cyclic stability. These findings should shed light on achieving strong TiAl alloys with enhanced fatigue performance by the introduction and design of PTB.

具有片层结构的PST TiAl单晶在室温下表现出良好的力学性能。其中，孪晶界对优化PST TiAl的延性和疲劳性能具有重要意义，但其作用机制尚不明确。本文通过原子模拟和介观模拟相结合的方法分析了真TB (TTB)和伪TB (PTB)的作用，发现PTB可以显著改善TiAl单晶的室温流变应力和循环稳定性。揭示了位错在无阻碍地穿过TTB时在PTB处堆积。背应力的出现和位错沿PTB的移动有助于加强机制。添加PTB后TiAl单晶的流变应力比添加TTB时高34%。进一步发现，随着孪晶厚度的减小，加入TTB的TiAl单晶的流动应力先增大后减小(即逆Hall-Petch行为)，而加入PTB的TiAl单晶由于额外的背应力(即Hall-Petch行为)而始终增大。然后提出了原子信息介观理论模型来描述流动应力作为孪晶厚度的函数。在循环加载下，PTB可促进TiAl单晶在塑性变形过程中的应变离域，从而显著提高循环稳定性。这些发现将有助于通过引入和设计PTB来获得具有增强疲劳性能的强TiAl合金。

Thin-Walled Structures

Strength-induced peridynamic model for the dynamic failure of porous materials

JiuYi Li, Yong Mei, JingHui Peng, YunHou Sun

doi:10.1016/j.tws.2024.112064

多孔材料动态破坏的强度诱导周动力模型

Predicting the dynamic failure process of porous materials is a challenging task due to their complex structure. To minimize the use of time-consuming peridynamic (PD) models and to avoid surface effect issues in the dynamic failure of complex porous materials, this paper proposes a strength-induced PD model. The paper first presents the dynamic formula and relevant finite element discrete equation of the coupled PD and classical continuum mechanics (PD-CCM) model based on the Morphing method. The Morphing function is implemented to control the material parameters and enable the free transformation of PD and CCM models. Based on the coupled PD-CCM model, the strength-induced PD model is established to adaptively expand the PD subdomain in porous materials by controlling the Morphing function value through the strength state of the structure. This model enables the PD subdomain to appear automatically when the porous materials reach the critical stress state. The proposed model accurately predicts the location of crack initiation and path while minimizing computational costs and improving efficiency. Three two-dimensional numerical examples are used to verify the effectiveness, efficiency, and accuracy of the model. The results of the simulation suggest that the location where the crack initiates in the porous materials is strongly influenced by the amplitude of the dynamic load. Cracking is dependent on the pores and typically occurs through them.

由于多孔材料结构复杂，对其动态破坏过程进行预测是一项具有挑战性的任务。为了最大限度地减少使用耗时的周动力学(PD)模型，并避免复杂多孔材料动态破坏中的表面效应问题，本文提出了一种强度诱导PD模型。本文首先给出了基于Morphing方法的PD- ccm与经典连续介质力学(PD- ccm)耦合模型的动力学公式和相关的有限元离散方程。实现了对材料参数的控制，实现了PD和CCM模型的自由转换。在耦合PD- ccm模型的基础上，建立了强度诱导PD模型，通过结构的强度状态控制Morphing函数值，自适应扩展多孔材料的PD子域。该模型能够使多孔材料达到临界应力状态时，PD子域自动出现。该模型准确地预测了裂纹起裂位置和路径，降低了计算成本，提高了计算效率。通过三个二维数值算例验证了该模型的有效性、高效性和准确性。模拟结果表明，动载荷的幅值对多孔材料中裂纹的起始位置有很大影响。裂缝依赖于孔隙，通常通过它们发生。

Foreign Object Damage Characteristics of a Thin Nickel-based Superalloy Plate at Room and High temperatures

Weizhu Yang, Haowei Yang, Jianjun Liu, Yan Zeng, Xinmei Wang, Lei Li

doi:10.1016/j.tws.2024.112065

室温和高温下镍基高温合金薄板的异物损伤特性

Turbine blades with thin-walled structures usually works in harsh environments, and foreign object damage (FOD) is one of the conditions of special concern. In this paper, the FOD characteristics of thin nickel-based superalloy plates are studied by a combination of experimental, numerical and analytical methods, considering room and high temperatures, different impact conditions and plate thicknesses. An easy-to-use test system is developed to realize high speed impact of the thin nickel-based superalloy plate under elevated temperature. Crater morphologies, internal microstructure, and residual stress are analyzed after impact with different conditions. Numerical simulation of the impact process is performed by using Johnson-Cook (J-C) constitutive model. Based on Hertz theory, an analytical method for calculating the crater length and depth is proposed considering the deformation of the impact steel sphere. Results shows that the FOD characteristics at high temperature is significantly different from that at room temperature. The crater has lager dimensions under high speed and elevated temperature. Moreover, significant grain refinement is obvious and the dislocation layer is also thicker at higher speed and higher temperature. Due to the effect of high temperature softening, hardness and residual stress after impact with elevated temperature is lower than that at room temperature. Besides, non-normal impact mainly influences Goss texture and distribution of residual stress after high temperature impact. In addition, it is found that thickness have a significant effect on the FOD characteristics especially when the plate is thinner. The validity of the numerical model and analytical method is proved by comparing with the experimental results. The present study can provide data foundation and numerical analysis support for the damage assessment and maintenance of turbine blades.

具有薄壁结构的涡轮叶片通常工作在恶劣的环境中，异物损伤(FOD)是人们特别关注的条件之一。本文采用实验、数值和分析相结合的方法，考虑室温和高温、不同冲击条件和板材厚度，研究了镍基高温合金薄板的FOD特性。为实现镍基高温合金薄板在高温下的高速冲击，研制了一种易于操作的测试系统。分析了不同条件下撞击后的弹坑形貌、内部微观结构和残余应力。采用Johnson-Cook (J-C)本构模型对冲击过程进行了数值模拟。基于赫兹理论，提出了一种考虑冲击钢球变形的弹坑长度和深度的解析计算方法。结果表明，高温下的FOD特性与室温下的FOD特性有显著差异。在高速和高温下，陨石坑的尺寸更大。在较高的速度和温度下，晶粒细化明显，位错层也变厚。由于高温软化的作用，高温冲击后的硬度和残余应力均低于常温冲击。非正态冲击主要影响高温冲击后的高斯织构和残余应力分布。此外，发现厚度对FOD特性有显著影响，特别是当板较薄时。通过与实验结果的比较，验证了数值模型和分析方法的有效性。本研究可为涡轮叶片损伤评估和维修提供数据基础和数值分析支持。

Low-frequency and broadband vibration absorption of a metamaterial plate with Acoustic Black Hole resonators

Siting Hao, Hui Sheng, Xusheng Liu, Haiqin Li, Shaohua Li, Qian Ding

doi:10.1016/j.tws.2024.112073

具有声学黑洞谐振器的超材料板的低频和宽带振动吸收

Acoustic metamaterials with bandgap properties can lead to effective vibration attenuation in a targeted frequency range. In this paper, a novel locally resonant metamaterial plate is proposed, connected with acoustic black hole (ABH) resonators. The structure is shown to achieve low-frequency and broadband vibration absorption. The proposed microunit design consists of three parts: the ABH resonator, supporting beams as the connector, and the frame (FC-ABH). The modal characteristics of the microunit and the dispersion relation of the infinite periodic FC-ABH structure are calculated by both of Gaussian expansion method and finite element method. By the effects of flexural wave absorption of ABH coupled with the local resonance mechanism, a low-frequency and broad vibration attenuation band can be generated. When the damping of materials is included, the attenuation band can be further widened, with relative bandwidth measured by the experiment up to 0.93. The results of numerical simulations and experimental tests demonstrate that the finite periodic FC-ABH can act as an effective vibration absorber and isolator. The proposed structure may provide new ideas for the design and application of broadband vibration mitigation metadevices.

具有带隙特性的声学超材料可以在目标频率范围内实现有效的振动衰减。本文提出了一种与声黑洞(ABH)谐振腔相连接的新型局部谐振超材料板。该结构可以实现低频和宽带的吸振。提出的微芯片设计由三部分组成:ABH谐振器、作为连接器的支撑梁和框架(FC-ABH)。采用高斯展开法和有限元法计算了无限周期FC-ABH结构的模态特性和色散关系。利用ABH的弯波吸收作用和局部共振机制，可以产生低频宽的减振带。当考虑材料的阻尼时，衰减带可以进一步加宽，实验测得的相对带宽可达0.93。数值模拟和试验结果表明，有限周期FC-ABH具有有效的吸振和隔振作用。该结构可为宽频带减振元器件的设计和应用提供新的思路。

Optically-responsive liquid crystal elastomer thin film motors in linear/nonlinear optical fields

Lin Zhou, Haiming Chen, Kai Li

doi:10.1016/j.tws.2024.112082

线性/非线性光场中的光响应液晶弹性体薄膜电机

Currently, there is significant interest in photo-excited self-oscillation systems utilizing a thin film of liquid crystal elastomer. However, studying their complex dynamic behaviors is challenging due to the inhomogeneity of the optically driven deformations. In this paper, we derive the asymptotic relationship of the thin film motor module in the inhomogeneous light fields by establishing a theoretical framework for the module. Subsequently, the asymptotic relationship of the module is applied to investigate the liquid crystal elastomer thin film-mass systems in both linear and nonlinear light fields. Through the use of asymptotic relationship, three dynamic behaviors of the system are discovered, namely, damper, spring and motor, each characterized by different effective viscoelasticity coefficients. In particular, the liquid crystal elastomer motor can operate more efficiently in the linear optical field, requiring less energy to generate the same amplitude of self-oscillation as in the nonlinear field. The proposed asymptotic relationship of the optical thin film motors under both linear and nonlinear optical fields can be readily referenced in other research, offering convenience and guidance for soft robotic motors, energy harvesters, and micro-machines.

目前，人们对利用液晶弹性体薄膜的光激发自振荡系统非常感兴趣。然而，由于光驱动变形的不均匀性，研究其复杂的动力学行为是具有挑战性的。本文通过建立薄膜电机模块的理论框架，推导出薄膜电机模块在非均匀光场下的渐近关系。随后，应用模量渐近关系研究了液晶弹性体薄膜-质量系统在线性光场和非线性光场下的特性。通过使用渐近关系，发现了系统的三种动态特性，即阻尼器、弹簧和电机，每种特性都具有不同的有效粘弹性系数。特别是液晶弹性体电机可以在线性光场中更有效地工作，产生与非线性光场相同振幅的自振荡所需的能量更少。所提出的光学薄膜电机在线性和非线性光场下的渐近关系可为其他研究提供参考，为软机器人电机、能量采集器和微型机械提供方便和指导。

Mode transition of bistable composite panels induced by centrifugal environments

Pengpeng Liu, Yang Guo, Jie Tang, Yinghui Li

doi:10.1016/j.tws.2024.112087

离心环境下双稳态复合板的模态转换

In this paper, the dynamic characteristics of bistable composite panels in centrifugal environments are studied, and both the deformation of static configuration and the influence of centrifugal field are considered. To achieve this, the classical laminate theory (CLT) is employed, combining with first-order shear deformation theory and von-Kármán geometric nonlinearity. The principle of minimum potential energy is used to determine the static configuration of bistable composite panels under the combined influence of centrifugal field and thermal effect, with residual thermal stress introduced in the constitutive relationship. Meanwhile, Hamilton's principle and Rayleigh-Ritz method were employed for dynamic analysis to identify the natural frequencies and modes of panels. Results show that centrifugal environments generate significant alterations in both the static configurations and dynamic characteristics of bistable composite panels. Centrifugal environments not only lead to discrepancies between the natural frequencies of the upper and lower stable states but also contribute to the loss of bistable characteristics in composite panels, induce mode transitions in bistable composite panels. Adjusting the installation angle, and rotational hub can alter the critical angular velocity at which this transition occurs. This work provides an important foundation for calculating and understanding the complex dynamic behaviors of structures under complex conditions.

本文研究了双稳态复合材料板在离心环境下的动态特性，同时考虑了静态变形和离心力场的影响。为此，将经典层合理论(CLT)与一阶剪切变形理论和von-Kármán几何非线性相结合。利用最小势能原理，在本构关系中引入残余热应力，确定了离心场和热效应共同作用下双稳态复合板的静态构型。同时，采用Hamilton原理和Rayleigh-Ritz方法进行动力分析，识别板的固有频率和振型。结果表明，离心环境对双稳态复合材料板的静态结构和动态特性都产生了显著的影响。离心环境不仅会导致上下稳定态固有频率的差异，而且会导致复合材料板双稳态特性的丧失，引起双稳态复合材料板的模态跃迁。调整安装角度和转动轮毂可以改变发生这种转变的临界角速度。这项工作为计算和理解复杂条件下结构的复杂动力行为提供了重要的基础。

Thermoelastic damping in symmetrical three-layer piezoelectric microbeam resonators

Ningning Liu, Wanli Zuo, Xuan Liu

doi:10.1016/j.tws.2024.112088

对称三层压电微束谐振器的热弹性阻尼

Thermoelastic damping (TED) plays a crucial role in the design of multilayer micro-resonators, especially in the investigation of coupled multi-physical fields. An analytical model for TED in a symmetrical three-layer piezoelectric microresonator was proposed with electric-mechanical-thermal coupling. The three-layer microbeam consists of piezoelectric ceramic layers covering the upper and lower surfaces of a silicon-based layer, and the beam undergoes forced vibration due to electrical excitation. This model can be verified by comparing experimental data and simplifying to previous models. It is observed that with an increase in the proportion of the piezoelectric layers, there are unimodal-bimodal-unimodal variations. Two-dimensional heat conduction is considered in this model, which makes the peak damping value decrease slightly with the increases of the thickness, length and mode. The presence of piezoelectric layers and a high electromechanical coupling coefficient have inhibitory effects on TED. The simplification of the piezoelectric material into isotropic and a reduced residual polarization intensity all induce an increase in thermal stress modulus, which further amplifies differences in Zener modulus among different materials, thereby accelerating double peak formation and enhancing the contribution of the piezoelectric layers to TED. What's more, increasing the beam thickness, proportion of piezoelectric layers, and decreasing excitation voltage amplitude all contribute to decreasing the beam displacement amplitude.

热弹性阻尼(TED)在多层微谐振器的设计中起着至关重要的作用，特别是在耦合多物理场的研究中。建立了具有电-机-热耦合的对称三层压电微谐振器中TED的解析模型。三层微梁由覆盖在硅基层上下表面的压电陶瓷层组成，并且由于电激励，梁承受强制振动。通过对实验数据的比较和对以往模型的简化，可以验证该模型的正确性。随着压电层比例的增加，存在单峰-双峰-单峰的变化。该模型考虑了二维热传导，使得峰值阻尼值随着厚度、长度和模态的增加而略有减小。压电层和高机电耦合系数的存在对TED有抑制作用。压电材料简化为各向同性以及残余极化强度的降低都会引起热应力模量的增加，这进一步放大了不同材料之间齐纳模量的差异，从而加速双峰的形成，增强了压电层对TED的贡献。增加梁的厚度、增加压电层的比例、减小激励电压幅值都有助于减小梁的位移幅值。

Study on the attributes of transverse surface waves in a layered piezoelectric semi-space with surface elasticity theory and Extended Stroh formalism

Xuan Wang, Jiashun Zhou, Qiang Chen, Kefu Huang, Yahui Xue

doi:10.1016/j.tws.2024.112084

应用表面弹性理论和扩展Stroh形式论研究层状压电半空间中横表面波的特性

Previous works on surface acoustic wave sensors have shown great limitations in selecting piezoelectric materials and the wave propagation direction. To eliminate such limitations in the technological revolution of SAW sensors, the current paper's main purpose is to explore how wave propagation orientation affects the performance of SAW macro- and nano-sensors. Based on Extended Stroh formalism, the theoretical forms are derived and exploited to present the wavenumber of transverse waves in an arbitrary direction of the piezoelectric medium. Furthermore, we consider surface elasticity theory to acquire the phase velocity equation on the basis of the expression of the wavenumber. More intuitively, a physical model is set up to obtain the horizontal shear stiffness of the surface and bulk layers. Then, the numerical case is carried out to determine the relationship between phase velocity and wave propagation orientation. By comparing the numerical study and the physical model, it can be found that the empirical formula of shear stiffness for bulk and surface layers offers a helpful route to precisely predict the mechanical attributes of SAW macro- and nano-sensors, respectively. The summaries of the current theoretical work benefit the manufacturing of surface acoustic wave sensors with improved performance.

以往的表面声波传感器在压电材料的选择和波的传播方向上存在很大的局限性。为了消除SAW传感器技术革命中的这些限制，本文的主要目的是探索波的传播方向如何影响SAW宏观和纳米传感器的性能。基于扩展的Stroh形式，导出了压电介质任意方向横波波数的理论表达式。在波数表达式的基础上，利用表面弹性理论推导出相速度方程。更直观的方法是建立物理模型，得到表层和块体层的水平剪切刚度。然后，通过数值算例确定了相速度与波传播方向的关系。通过数值研究与物理模型的对比，可以发现体层和面层剪切刚度经验公式分别为精确预测SAW宏观和纳米传感器的力学属性提供了有益的途径。总结了目前的理论工作，有助于制造性能更好的表面声波传感器。