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Prediction of nonlinear dynamic responses and generation of seismic fragility curves for steel moment frames using boosting machine learning techniques 利用提升机器学习技术预测钢弯矩框架的非线性动态响应并生成地震脆性曲线
IF 4.7 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-19 DOI: 10.1016/j.compstruc.2024.107580
Farzaneh Zareian, Mehdi Banazadeh, Mohammad Sajjad Zareian
The main objective of this paper is to develop machine learning (ML) models for predicting the seismic responses of steel moment frames. For this purpose, four boosting ML techniques-gradient boosting, XGBoost, LightGBM, and CatBoost-were developed in Python. To create an inclusive dataset, 92,400 nonlinear time-history analyses were performed on 1,848 steel moment frames under 50 earthquakes using OpenSeesPy. Geometric configurations, structural properties, and ground motion intensity measures were considered as the inputs for the models. The outputs included maximum global drift ratio (MGDR), maximum interstory drift ratio (MIDR), base shear coefficient (BSC), and maximum floor acceleration (MFA). The study also investigated the effectiveness of the ML models in estimating fragility curves for an 8-story steel frame at different performance levels. Finally, a web application was developed to facilitate the estimation of the peak dynamic responses for steel moment frames. The results show that the LightGBM and CatBoost models demonstrate superior predictive performance, with coefficient of determinations (R2) higher than 0.925. Furthermore, the LightGBM models can estimate the fragility curves with minimal errors (e.g., the relative errors in the median values of the predicted curves are less than 10%).
本文的主要目的是开发用于预测钢矩形框架地震响应的机器学习(ML)模型。为此,使用 Python 开发了四种增强 ML 技术--梯度增强、XGBoost、LightGBM 和 CatBoost。为了创建一个包容性数据集,我们使用 OpenSeesPy 对 50 次地震中的 1848 个钢弯矩框架进行了 92400 次非线性时史分析。几何配置、结构属性和地动强度测量值被视为模型的输入。输出结果包括最大总体漂移比 (MGDR)、最大层间漂移比 (MIDR)、基底剪切系数 (BSC) 和最大楼层加速度 (MFA)。研究还调查了 ML 模型在估算不同性能等级的 8 层钢结构框架脆性曲线时的有效性。最后,还开发了一个网络应用程序,以方便估算钢矩形框架的峰值动态响应。结果表明,LightGBM 和 CatBoost 模型的预测性能优越,确定系数 (R2) 高于 0.925。此外,LightGBM 模型能以最小的误差估算脆性曲线(例如,预测曲线中值的相对误差小于 10%)。
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引用次数: 0
Bearing capacity analysis of RC slabs under cyclic loads: Dual numerical approaches 循环荷载下的钢筋混凝土板承载能力分析:双重数值方法
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-16 DOI: 10.1016/j.compstruc.2024.107585
Phuc L.H. Ho , Canh V. Le , Dung T. Tran , Phuong H. Nguyen , Jurng-Jae Yee
Shakedown analysis is a powerful and efficient tool for calculating the safety factors of structures under variable and repeated external quasi-static loads, that can prevent structures from incremental and alternative plasticity collapses. RC slabs in practical engineering applications are usually under long-tern variable and cyclic loads, but their fatigue behavior was rarely reported in the literature, particularly for those governed by the Nielsen yield condition. In this paper, dual static and kinematic shakedown formulations based on displacement-finite elements and conic programming are developed. The resulting optimization problems, characterized by a huge number of variables, are effectively solved. A wide range of practical RC slabs with diverse geometries, loading and boundary conditions are investigated, precisely capturing the collapse modes in terms localized plastic dissipation energy and presenting moment distribution at fatigue state. Strengthening strategies are performed in regions with localized plastic dissipation energy, showing that the load-bearing capacity of such slabs increases significantly while incremental and alternative collapse modes are prevented.
振动分析是一种强大而有效的工具,用于计算结构在可变和重复外部准静态荷载作用下的安全系数,可防止结构发生增量和替代塑性坍塌。实际工程应用中的钢筋混凝土板通常处于长期可变和循环荷载下,但其疲劳行为在文献中鲜有报道,尤其是受尼尔森屈服条件制约的疲劳行为。本文基于位移有限元和圆锥程序设计,提出了静态和运动学双重减震公式。由此产生的优化问题具有变量数量庞大的特点,但却能得到有效解决。研究了具有不同几何形状、荷载和边界条件的各种实用 RC 板,精确捕捉了局部塑性耗散能量的坍塌模式,并呈现了疲劳状态下的力矩分布。在具有局部塑性耗散能的区域实施了加固策略,结果表明,在防止增量和替代坍塌模式的同时,此类板的承载能力显著提高。
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引用次数: 0
Material parameter sensitivity analysis for intralaminar damage of laminated composites through direct differentiation 通过直接微分法分析层状复合材料层内损伤的材料参数敏感性
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-16 DOI: 10.1016/j.compstruc.2024.107584
P. Minigher , A. Arteiro , A. Turon , J. Fatemi , L. Barrière , P.P. Camanho
Understanding the effect of the material parameters variability on the mechanical response of laminated composites is of great importance for many engineering problems. Not only an accurate sensitivity analysis enables to estimate how much each parameter under consideration affects the response, but the linearization of the output provides also the possibility to, for example, use gradient-based optimization tools and to propagate in an inexpensive way the material uncertainties. In this paper, a material parameter sensitivity study is carried out in the context of continuum damage mechanics applied to predict intralaminar damage in laminated composites. The sensitivity w.r.t. the input material variables is estimated in a relatively inexpensive way from a single run of the Finite Element (FE) model. The results obtained provide a good understanding of the influence of the material parameters throughout the simulation.
了解材料参数变化对层压复合材料机械响应的影响对许多工程问题都非常重要。准确的灵敏度分析不仅可以估算出所考虑的每个参数对响应的影响程度,而且输出的线性化还为使用基于梯度的优化工具和以低成本的方式传播材料不确定性等提供了可能性。本文以连续损伤力学为背景,进行了材料参数敏感性研究,用于预测层状复合材料的层内损伤。通过有限元(FE)模型的一次运行,以相对低成本的方式估算了输入材料变量的敏感性。所获得的结果可以很好地理解材料参数在整个模拟过程中的影响。
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引用次数: 0
Theoretical study of multipoint ground motion characteristics under V-shaped site induced P1 wave V 形场地诱导 P1 波下多点地面运动特征的理论研究
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-15 DOI: 10.1016/j.compstruc.2024.107583
Feng Guang-rui, Xie Li-quan
An advanced analytical technique known as the Oblique Coordinate Wave Function Integral Method builds on Biot’s wave theory for saturated porous material, has been developed to address seismic wave scattering in irregular media. This method employs an integral representation of scattered waves, solved by using an oblique coordinate transformation within a rectangular coordinate system with wave function series expansion methods. The inverse transformation between rectangular and cylindrical coordinate systems frequently presents convergence issues, this method effectively resolves these issues. Moreover, using a Cartesian coordinate system to solve the scattered wave field, overcomes the limitations of earlier methods. Such as the large arc assumption in wave function series expansion, that often did not meet boundary conditions precisely. In addition, this method’s scattering analytical solutions are used to derive the coherence function of multi-point ground motion from the second-moment correlation function of a random process. Lastly, a sensitivity analysis of key parameters, such as canyon depth, incident frequency, and soil porosity, is performed to assess the robustness of the method.
以饱和多孔材料的 Biot 波理论为基础,开发了一种先进的分析技术,称为斜坐标波函数积分法,用于解决不规则介质中的地震波散射问题。该方法采用散射波积分表示法,通过矩形坐标系内的斜坐标变换和波函数级数展开方法求解。矩形坐标系和圆柱坐标系之间的逆变换经常出现收敛问题,该方法有效地解决了这些问题。此外,使用直角坐标系求解散射波场,克服了早期方法的局限性。比如波函数级数展开中的大弧度假设,这往往无法精确满足边界条件。此外,该方法的散射解析解还用于从随机过程的第二时刻相关函数推导出多点地面运动的相干函数。最后,对峡谷深度、入射频率和土壤孔隙度等关键参数进行了敏感性分析,以评估该方法的稳健性。
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引用次数: 0
Bridge roughness scanned by Dual-Wheeled 3D test vehicle and processed by augmented Kalman filter: Theory and application 用双轮 3D 测试车扫描桥梁粗糙度,并用增强卡尔曼滤波器进行处理:理论与应用
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-14 DOI: 10.1016/j.compstruc.2024.107581
Z. Li , Z. Liu , Z.L. Wang , W.Y. He , B.Q. Wang , Y. He , Y.B. Yang
A novel method is presented for estimating the bridge surface roughness scanned by a single-axle dual-wheeled 3D test vehicle and processed by an augmented Kalman filter (AKF). Two acceleration sensors are installed atop the axle near the two wheels of the vehicle to measure its vertical and rocking motions. Meanwhile, the Kalman filter algorithm is augmented specially for the vehicle-bridge interaction (VBI) system, allowing the bridge surface roughness to be treated as the only unknown in the state-space formulation. To meet the invertibility criterion for resolving the dynamic VBI problems using the AKF, the observation vector is restructured by consolidating the accelerations recorded for the two wheels and their derivative displacements. The effectiveness of the present method was validated by the finite element method and demonstrated in a parametric study encompassing various system properties. In addition, a self-made, single-axle, dual-wheeled test vehicle was adopted in the field test to verify the theory presented. The reliability of the present technique was confirmed by its application to a real three-span continuous concrete girder bridge. The results indicate that the present technique is suitable for detecting bridge surface roughness of all levels with low sensitivity to noise interference and vehicle damping. Moreover, the surface elevations identified along the traces of the left and right wheels of the moving vehicle are “spatial” in nature. For practical application, it is recommended that the vehicle operates at speeds not exceeding 12 m/s to keep errors below 2 %.
本文提出了一种新方法,用于估算单轴双轮三维测试车扫描的桥梁表面粗糙度,并通过增强卡尔曼滤波器(AKF)进行处理。两个加速度传感器安装在车辆两个车轮附近的车轴顶端,用于测量车辆的垂直运动和摇摆运动。同时,卡尔曼滤波算法专门针对车桥交互(VBI)系统进行了增强,允许将桥面粗糙度作为状态空间公式中唯一的未知数。为了满足使用 AKF 解决 VBI 动态问题的可逆性标准,通过合并两个车轮的加速度及其导数位移来重组观测向量。有限元法验证了本方法的有效性,并在包含各种系统属性的参数研究中得到了证明。此外,还在现场测试中采用了自制的单轴双轮测试车辆,以验证所提出的理论。本技术在实际三跨连续混凝土梁桥上的应用证实了其可靠性。结果表明,本技术适用于检测所有级别的桥梁表面粗糙度,对噪声干扰和车辆阻尼的灵敏度较低。此外,沿行驶车辆左右车轮痕迹识别的表面高程具有 "空间 "性质。在实际应用中,建议车辆运行速度不超过 12 米/秒,以将误差控制在 2% 以下。
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引用次数: 0
Static, free vibration, and buckling analysis of functionally graded plates using the dual mesh control domain method 使用双网格控制域法对功能分级板进行静态、自由振动和屈曲分析
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-12 DOI: 10.1016/j.compstruc.2024.107575
Zeyu Jiao , Tanmaye Heblekar , Guannan Wang , Rongqiao Xu , J.N. Reddy
In this paper, the Dual Mesh Control Domain Method (DMCDM) put forward by Reddy is applied to solve linear static, free vibration, and buckling problems of functionally graded plates modeled using the First-Order Shear Deformation Theory (FSDT). The material properties are assumed to vary continuously through the thickness of the plate according to a power-law. Formulations are presented for linear triangular (3-noded) and bilinear quadrilateral (4-noded) primal elements of arbitrary shape. The influence of the power-law exponents, length to thickness ratio, boundary conditions, and plate skewness on the numerical solution is systematically analyzed. Additionally, the numerical solutions using the DMCDM are compared against those from the Finite Element Method (FEM) to demonstrate the robustness of the DMCDM as a strong competitor to well-established numerical techniques such as the FEM.
本文采用 Reddy 提出的双网格控制域法(DMCDM)来求解采用一阶剪切变形理论(FSDT)建模的功能梯度板的线性静力、自由振动和屈曲问题。假定材料特性在板厚度范围内按幂律连续变化。计算公式适用于任意形状的线性三角形(3编码)和双线性四边形(4编码)基元。系统分析了幂律指数、长度与厚度比、边界条件和板偏斜对数值解的影响。此外,还将 DMCDM 的数值解与有限元方法 (FEM) 的数值解进行了比较,以证明 DMCDM 作为 FEM 等成熟数值技术的有力竞争者的稳健性。
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引用次数: 0
A computationally efficient method for evaluating impact sound insulation for custom concrete floor geometries 一种高效计算方法,用于评估定制混凝土地板几何形状的冲击隔音效果
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-12 DOI: 10.1016/j.compstruc.2024.107582
Jonathan M. Broyles , Micah R. Shepherd , Andrew R. Barnard , Nathan C. Brown
Advanced construction technologies are creating opportunities to design and fabricate non-traditional concrete structural geometries. While removing structurally unnecessary material can aid in sustainability efforts, it can also reduce a structure’s ability to attenuate impact sound. An assessment of the impact sound insulation performance of custom concrete floors has often been excluded from previous studies because of the large computational cost for simulating radiated sound at high frequencies. In response, this paper presents a hybrid, computationally efficient method to approximate the impact sound performance of floors by strategically using the air-hemisphere method for a subset of low frequencies, while relying on the structure’s radiation efficiency at higher frequencies. This method improves upon existing strategies to discretize the receiving side of the floor for impact sound performance. To demonstrate this method, six anthropometric walking paths are simulated on four non-traditional floor geometries and three conventional floor slabs. The simulated results are compared to experimentally obtained dynamic behavior for the custom slabs and full-scale tests of impact sound for the conventional slabs. The proposed method is much more efficient than maintaining high resolution discretization across all frequencies, leading to significant computational time savings. Efficient simulations for determining the impact sound insulation of non-traditional structures may further enable the design of novel floor geometries, potentially accelerating their implementation in buildings.
先进的建筑技术为设计和制造非传统的混凝土结构几何形状创造了机会。虽然去除结构上不必要的材料有助于可持续发展,但也会降低结构对冲击声的衰减能力。由于模拟高频辐射声的计算成本较高,对定制混凝土地板冲击声隔音性能的评估往往被排除在以往的研究之外。为此,本文提出了一种计算效率高的混合方法,通过对低频子集战略性地使用空气半球法来近似计算地板的冲击声性能,同时依靠结构在高频时的辐射效率。这种方法改进了现有的对地板接收端冲击声性能进行离散化的策略。为了演示这种方法,我们在四种非传统地板几何结构和三种传统楼板上模拟了六种人体行走路径。模拟结果与实验获得的定制楼板的动态行为以及传统楼板的全尺寸撞击声测试结果进行了比较。与保持所有频率的高分辨率离散化相比,所提出的方法更为有效,从而大大节省了计算时间。通过高效模拟来确定非传统结构的撞击声隔音效果,可进一步促进新型楼板几何结构的设计,从而加快其在建筑物中的应用。
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引用次数: 0
Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media 用于模拟流体饱和多孔介质断裂的具有 I-II 复合模式内聚区弹塑性的孔力学内聚界面元素
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-12 DOI: 10.1016/j.compstruc.2024.107554
Dafer K. Jadaan , Jessica Rimsza , Reese Jones , Richard A. Regueiro
A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. The CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.
为模拟流体饱和多孔介质中二维裂纹的成核和扩展,在 ABAQUS 用户单元 (UEL) 中制定并实施了一个 I-II 模式内聚区(CZ)弹塑性组合构成模型和一个二维(2D)内聚界面单元(CIE)。CZ 模型缓解了 ABAQUS 中全局牛顿-拉斐森求解器的收敛问题,与粘性稳定程序相结合,可在耦合孔力学有限元分析(如混凝土重力坝稳定性分析)的载荷控制下模拟峰值后响应。演示了验证实例,以及更复杂的石灰石-混凝土楔形断裂实验、水加压混凝土楔形实验和混凝土重力坝稳定性分析。在石灰石-混凝土楔形断裂过程中,演示了估算 CZ 参数的校准程序。在水压混凝土楔形断裂实验中,孔隙力学 CIE 分析的固有时间依赖性与不同裂口张开率下的力与位移实验结果非常吻合,但却忽略了裂口扩展前的孔隙水压力演变。这可能是由于实验中混凝土部分饱和,而有限元分析假定混凝土完全水饱和。混凝土重力坝分析表明,基底裂缝开裂和相关的水上浮压力会导致安全系数降低,这一点在单独的分析计算中得到了证实。
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引用次数: 0
Size, shape and topology optimization of truss structure via the finite particle method 通过有限粒子法优化桁架结构的尺寸、形状和拓扑结构
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-07 DOI: 10.1016/j.compstruc.2024.107570
Jinhang Zhou , Yan Zeng , Gang Li
The finite particle method (FPM), a novel numerical analysis approach for simulating structural statics and dynamics, is introduced into the field of structural optimization through the development of a new structural sensitivity analysis procedure. Using FPM, we can analyze static and dynamic structural responses, including typical nonlinear behaviors, based on a system composed of a finite number of particles. The new sensitivity analysis procedure integrates seamlessly with the general time-difference scheme of FPM. In the initial application of this sensitivity analysis procedure, we focus on the static optimization of truss structures. Optimization strategies tailored to truss structures are developed by predicting static responses via FPM. The positions of improperly placed particles are adjusted through particle fusion and projection strategies to achieve a reasonable configuration, enabling collaborative size, shape, and topology optimization. Various 2D and 3D numerical examples demonstrate the effectiveness and efficiency of the static optimization framework, made possible by the new sensitivity analysis procedure and FPM.
有限粒子法(FPM)是一种用于模拟结构静力学和动力学的新型数值分析方法,它通过开发一种新的结构灵敏度分析程序被引入结构优化领域。利用 FPM,我们可以根据由有限数量粒子组成的系统分析结构的静态和动态响应,包括典型的非线性行为。新的灵敏度分析程序与 FPM 的一般时差方案无缝集成。在该灵敏度分析程序的初步应用中,我们重点关注桁架结构的静态优化。通过 FPM 预测静态响应,为桁架结构量身定制了优化策略。通过粒子融合和投影策略来调整位置不当的粒子的位置,以达到合理的配置,从而实现尺寸、形状和拓扑结构的协同优化。各种二维和三维数值示例证明了静态优化框架的有效性和效率,新的灵敏度分析程序和 FPM 使之成为可能。
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引用次数: 0
Complete dispersion characteristics of elastic waves in periodically multilayered arbitrarily-anisotropic media 周期性多层任意各向异性介质中弹性波的完全弥散特性
IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-04 DOI: 10.1016/j.compstruc.2024.107573
Q.Q. Li, Y.Q. Guo, B.R. Peng
In the previous researches, the dispersion property of periodically layered media (PLM) is mainly represented by the frequency-wavenumber spectra. Here this paper studies the complete dispersion characteristics of elastic waves along arbitrary direction in space in periodically layered arbitrarily-anisotropic media (PLAM) by the comprehensive frequency-related dispersion surfaces and their profiles. The present model deems that the wave components in the thickness and layering directions are both variable quantities and considers their interrelation effect. For obtaining the general propagation characteristics of Floquet-Bloch waves, firstly the partial waves in the constituent layers of triclinic materials are described by the state-space formalism. Secondly, considering the traveling within the constituent layers, the multiple scattering at the interfaces and the periodicity across the unit cell of these partial waves, the dispersion equation is derived by the method of reverberation-ray matrix (MRRM), which is further solved by the golden section and bisection methods in combination. Finally, numerical examples are provided to verify the analysis method and to illustrate the comprehensive frequency-related dispersion surfaces and their profiles on four typical sections. On the basis of these numerical results, the general and complete band and dispersion characteristics of the Floquet-Bloch waves in general PLAM are summarized in detail. It is discovered that with respect to the thickness-directed components of wave quantities, the dispersion surfaces and curves reflect the band characteristic of Floquet-Bloch waves on the frequency axis due to the repeated configuration (periodic condition) along the thickness, and the wave repulsion between neighboring orders of modes and the wave coupling between different kinds of modes (Primary and Shear modes) generally contribute to the formation of frequency bands. It is also found that with respect to the layering-directed components of wave quantities, the dispersion surfaces and curves indicate the cutoff property and the continuously-propagating characteristic of Floquet-Bloch waves as the frequency below and above the cutoff frequencies, respectively, which are caused separately by the multiple scattering of waves at interfaces and by the wave conversion between neighboring orders of modes subjected to the Snell’s law due to infinitely expanding configuration along the layering.
在以往的研究中,周期层介质(PLM)的频散特性主要由频率-波数谱来表示。本文通过与频率相关的综合频散面及其剖面,研究了周期层状任意各向异性介质(PLAM)中弹性波沿空间任意方向的完整频散特性。本模型认为厚度方向和分层方向的波分量都是可变量,并考虑了它们之间的相互影响。为获得 Floquet-Bloch 波的一般传播特性,首先用状态空间形式主义描述了三菱材料组成层中的部分波。其次,考虑到这些分波在组成层内的传播、在界面上的多重散射以及在整个单元格内的周期性,通过混响射线矩阵(MRRM)方法推导出频散方程,并进一步结合黄金分割法和二分法进行求解。最后,提供了数值示例来验证分析方法,并说明了四个典型断面上与频率相关的综合频散面及其剖面。在这些数值结果的基础上,详细总结了一般 PLAM 中 Floquet-Bloch 波的一般完整频带和频散特性。研究发现,就波量的厚度方向分量而言,由于沿厚度方向的重复构造(周期条件),频散面和频散曲线反映了弗洛克-布洛赫波在频率轴上的频带特性,相邻阶次模态之间的波斥和不同种类模态(原生模态和剪切模态)之间的波耦合一般都有助于频带的形成。研究还发现,在波量的分层方向分量方面,频散面和频散曲线分别显示了 Floquet-Bloch 波在截止频率以下和截止频率以上的截止特性和连续传播特性,这分别是由界面上的多重散射和由于沿分层无限扩展配置而受斯奈尔定律影响的相邻阶次模态之间的波转换引起的。
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