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An explicit nonlinear model for large spatial deflections of symmetric slender beams 对称细长梁大空间挠度的显式非线性模型
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-19 DOI: 10.1016/j.ijnonlinmec.2024.104910
Yuhan Chen , Shilong Yao , Li Liu , Max Q.-H. Meng
Flexible slender beams are commonly used in compliant mechanisms and continuum robots. However, the modeling of these beams can be complicated due to the geometric nonlinearity becoming significant at large elastic deflections. This paper presents an explicit nonlinear model for large spatial deflections of a slender beam with uniform, symmetrical sections subjected to general end-loading. The elongation, bending, torsion, and shear deformations of the beams are modeled based on Timoshenko’s assumptions and Cosserat rod theory. Subsequently, the nonlinear governing differential equations for the beam are derived from the quaternion representation of the rotation matrix. The explicit load–displacement relations of the beam are obtained using the improved Adomian decomposition method. This method is superior to the classical Adomian decomposition method in terms of convergence rate and domain. The convergence and superiority of the method are also rigorously demonstrated. Simulations are provided to verify the one-, two-, and three-dimensional deflections of beams. Real-world experiments have also been performed to validate our method’s effectiveness with two different beam configurations. The results indicate that the proposed method accurately estimates large spatial deflections of flexible beams.
柔性细长梁通常用于顺从机构和连续机器人。然而,由于几何非线性在大弹性挠度时变得非常明显,这些梁的建模可能会变得复杂。本文提出了一种显式非线性模型,用于计算具有均匀对称截面的细长梁在承受一般端面荷载时的大空间挠度。梁的伸长、弯曲、扭转和剪切变形是基于 Timoshenko 假设和 Cosserat 杆件理论建模的。随后,根据旋转矩阵的四元数表示法推导出梁的非线性控制微分方程。梁的显式载荷-位移关系是通过改进的阿多米分解法得到的。该方法在收敛速度和域方面优于经典的 Adomian 分解法。该方法的收敛性和优越性也得到了严格证明。模拟验证了梁的一维、二维和三维挠度。此外,还进行了实际实验,以验证我们的方法在两种不同梁配置下的有效性。结果表明,所提出的方法能准确估计柔性梁的大空间挠度。
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引用次数: 0
Modeling of residual stiffness phenomenon in modified Iwan model of bolted joints and its application 螺栓连接修正伊万模型中残余刚度现象的建模及其应用
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-19 DOI: 10.1016/j.ijnonlinmec.2024.104909
Hao Chen , Zhiming Hao , Jinxin Kuang , Yongjian Mao
Bolted joints have been widely used in various mechanical structures. Due to the presence of contact interfaces, the joints exhibit complex nonlinear behavior under dynamic loading. Effective prediction of the dynamic response of bolted structures requires the construction of appropriate dynamic models. This paper proposes a modified Iwan model which gives a more comprehensive description of joints than the previous Iwan models, especially for the phenomenon of residual stiffness in macro slip. The equations of the model's backbone curve, hysteresis curve, and energy dissipation are derived. The parameter identification procedure is also provided. Subsequently, connection elements based on the modified Iwan model are integrated into a single bolted joint and a thin-walled cylinder containing multiple bolted joints, the responses under quasi-static unidirectional loading, quasi-static cyclic loading and constant-frequency excitation are investigated. The physical interpretation of the parameters in the model is discussed, thus explaining the relationship between the bolted joint's physical parameters and some important variables. The results indicate that the model can effectively characterize the nonlinear mechanical behavior of the bolted joint for both micro and macro slip regime, with significant improvement in computational efficiency.
螺栓连接已广泛应用于各种机械结构中。由于接触界面的存在,接头在动态载荷下表现出复杂的非线性行为。要有效预测螺栓连接结构的动态响应,需要构建适当的动态模型。本文提出了一种改进的 Iwan 模型,与之前的 Iwan 模型相比,该模型能更全面地描述接头,尤其是宏观滑移中的残余刚度现象。推导了模型的骨干曲线、滞后曲线和能量耗散方程。同时还提供了参数识别程序。随后,将基于改进 Iwan 模型的连接元件集成到单个螺栓连接和包含多个螺栓连接的薄壁圆柱体中,研究了准静态单向载荷、准静态循环载荷和恒频激励下的响应。讨论了模型参数的物理解释,从而解释了螺栓连接的物理参数与一些重要变量之间的关系。结果表明,该模型能有效描述螺栓连接在微滑移和大滑移情况下的非线性力学行为,并显著提高了计算效率。
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引用次数: 0
Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation 允许压力平移的气体动力学方程的部分不变解与任意吹胀面
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-17 DOI: 10.1016/j.ijnonlinmec.2024.104904
Dilara Siraeva
We applied a method of symmetry reduction to the gas dynamics equations with a special form of the equation of state. This equation of state is a pressure represented as the sum of a density and an entropy functions. The symmetry Lie algebra of the system is 12-dimensional. One, two and three-dimensional subalgebras were considered. In this article, four-dimensional subalgebras are considered for the first time. Specifically, invariants are calculated for 50 four-dimensional subalgebras. Using invariants of one of the subalgebras, a symmetry reduction of the original system is calculated. The reduced system is a partially invariant submodel because one gas-dynamic function cannot be expressed in terms of the invariants. The submodel leads to two families of exact solutions, one of which describes the isochoric motion of the media, and the other solution specifies an arbitrary blow-up surface. For the first family of solutions, the particle trajectories are parabolas or rays; for the second family of solutions, the particles move along cubic parabolas or straight lines. From each point of the blow-up surface, particles fly out at different speeds and end up on a straight line at any other fixed moment in time. A description of the motion of particles for each family of solutions is given.
我们将对称性还原法应用于具有特殊形式状态方程的气体动力学方程。该状态方程是以密度函数和熵函数之和表示的压力。系统的对称李代数为 12 维。考虑了一维、二维和三维子代数。本文首次考虑了四维子代数。具体来说,计算了 50 个四维子代数的不变式。利用其中一个子代数的不变式,计算出原始系统的对称性还原。缩减后的系统是一个部分不变的子模型,因为一个气体动力函数无法用不变式来表示。子模型导致两个精确解系列,其中一个描述了介质的等速运动,另一个则指定了一个任意炸开面。对于第一个解系列,粒子轨迹是抛物线或射线;对于第二个解系列,粒子沿立方抛物线或直线运动。粒子从爆炸面上的每一点以不同的速度飞出,并在时间的任何其他固定时刻以一条直线结束。本文给出了每个解系的粒子运动描述。
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引用次数: 0
Impact of compliant electrodes on the dynamics of electromagnetoactive membranes 顺应性电极对电磁活动膜动力学的影响
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-17 DOI: 10.1016/j.ijnonlinmec.2024.104906
Asesh Kumar Patra , Aman Khurana , Deepak Kumar , Prashant Saxena
The dynamics of electromagnetoactive polymer (EMAP) membranes have attracted much attention recently because of their wide range of modern robotic applications. Such applications majorly centered on how the dynamics of this novel class of membranes are affected by the mechanical behavior of the compliant electrode. This article presents the dynamic modeling and analysis of EMAP membranes, examining how the inertia of the electrode, coupled with its inherent viscoelastic properties, impacts its dynamic performance. Both the compression and suspension stages of the membrane are covered here in broad terms. An Euler–Lagrange equation of motion is implemented to deduce the governing dynamic model equation of the membrane system. The findings of the model solutions provide preliminary insights to characterize the dynamic response, instability analysis, periodic behavior, and resonance properties across varying parameters such as inertia, electric field, magnetic field, and prestress. Moreover, the study also evaluates the periodicity and stability of the nonlinear oscillations using Poincaré maps and phase portraits, facilitating an assessment of quasi-periodic to periodic transitions.
最近,电磁活性聚合物(EMAP)膜的动力学因其在现代机器人领域的广泛应用而备受关注。这些应用主要集中在这类新型膜的动力学如何受到顺应电极机械行为的影响。本文介绍了 EMAP 膜的动态建模和分析,研究了电极的惯性及其固有的粘弹性如何影响其动态性能。这里大致涵盖了膜的压缩和悬浮阶段。采用欧拉-拉格朗日运动方程来推导膜系统的支配动态模型方程。模型求解的结果提供了初步的见解,说明了不同参数(如惯性、电场、磁场和预应力)下的动态响应、不稳定性分析、周期行为和共振特性。此外,该研究还利用波恩卡雷图和相位肖像评估了非线性振荡的周期性和稳定性,从而有助于评估从准周期到周期的转变。
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引用次数: 0
Nonlinear analysis of spatial trusses with different strain measures and compressible solid 采用不同应变措施和可压缩固体的空间桁架的非线性分析
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-13 DOI: 10.1016/j.ijnonlinmec.2024.104907
William T.M. Silva, Kamirã B. Ribeiro, A. Portela

This paper investigates the nonlinear behavior of spatial truss elements under finite deformations, focusing on the impact of various strain measures in compressible materials. We examine both Total Lagrangian (using engineering and Green–Lagrange strains) and Eulerian formulations (using natural, Biot, and Almansi strains). The analysis assumes a linear spatial hyperelastic material where Cauchy stress is proportional to axial natural strain via Young’s modulus. For infinitesimal strains, Young’s modulus remains consistent across different stress/strain pairs. In the finite strain regime, we derive a nonlinear secant modulus based on Young’s modulus. Internal force vectors and tangent stiffness matrices are computed using the direction cosines of the truss element in its deformed state. The paper demonstrates that for infinitesimal deformations, adjusting the modulus of elasticity when using different stress/strain pairs is unnecessary. However, for finite deformations, it is essential to adjust the modulus of elasticity. Numerical simulations validate the performance of the proposed 3D truss element against established formulations. This research offers critical insights into the nonlinear response of spatial trusses, guiding the selection of appropriate strain measures for enhanced accuracy in engineering applications. These findings contribute to more reliable and efficient structural designs, especially in scenarios involving finite deformations and compressible materials.

本文研究了空间桁架元素在有限变形下的非线性行为,重点是可压缩材料中各种应变措施的影响。我们对全拉格朗日应变(使用工程应变和格林-拉格朗日应变)和欧拉应变(使用自然应变、Biot 应变和 Almansi 应变)进行了研究。分析假定材料为线性空间超弹性材料,其中考氏应力通过杨氏模量与轴向自然应变成正比。对于无穷小应变,不同应力/应变对的杨氏模量保持一致。在有限应变机制中,我们根据杨氏模量推导出非线性正切模量。内力矢量和切线刚度矩阵是利用桁架元素在变形状态下的方向余弦计算得出的。论文证明,对于无限小变形,在使用不同应力/应变对时无需调整弹性模量。然而,对于有限变形,调整弹性模量是必要的。数值模拟验证了所提出的三维桁架元素的性能与已有公式的对比。这项研究为空间桁架的非线性响应提供了重要的见解,指导人们选择适当的应变测量方法,以提高工程应用的精确度。这些发现有助于提高结构设计的可靠性和效率,尤其是在涉及有限变形和可压缩材料的情况下。
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引用次数: 0
Cascaded robust fixed-time terminal sliding mode control for uncertain cartpole systems with incremental nonlinear dynamic inversion 带增量非线性动态反演的不确定车杆系统的级联鲁棒固定时间终端滑模控制
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-12 DOI: 10.1016/j.ijnonlinmec.2024.104900
Changyi Lei , Quanmin Zhu , Ruobing Li

This paper proposes a cascaded fixed-time terminal sliding mode controller (TSMC) for uncertain underactuated cartpole dynamics using incremental nonlinear dynamic inversion (INDI). Leveraging partial linearization and prioritizing pole dynamics for internal tracking, the proposed controller achieves efficient stabilization of the cart upon convergence of the pole. Stability analysis is carried out using Lyapunov stability theorem, proving that the proposed controller stabilizes the state variables to an arbitrarily small neighborhood of the equilibrium in fixed-time, along with the suboptimality (steady-state error), existence and uniqueness of the solutions. The INDI is also integrated into TSMC to further improve the robustness while suppressing the conservativeness of conventional TSMC. The stability of INDI is rigorously proved using sampling-based Lyapunov function under sampling-based control realm. The simulation results illustrate the superiority of the proposed method with comparison and ablation studies.

本文提出了一种级联固定时间终端滑动模式控制器(TSMC),利用增量非线性动态反演(INDI)来控制不确定的欠驱动小车极点动态。利用部分线性化和内部跟踪的极点动态优先权,所提出的控制器在极点收敛后实现了小车的高效稳定。利用 Lyapunov 稳定性定理进行了稳定性分析,证明了所提出的控制器能在固定时间内将状态变量稳定在平衡点的任意小邻域,同时还证明了解的次优性(稳态误差)、存在性和唯一性。INDI 还被集成到 TSMC 中,以进一步提高鲁棒性,同时抑制传统 TSMC 的保守性。在基于采样的控制境界下,使用基于采样的 Lyapunov 函数严格证明了 INDI 的稳定性。仿真结果通过对比和烧蚀研究说明了所提方法的优越性。
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引用次数: 0
Study on nonlinear relaxation properties of composite solid propellant 复合固体推进剂的非线性弛豫特性研究
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-12 DOI: 10.1016/j.ijnonlinmec.2024.104908
Xu Zhang , Jiangtao Wang , Xiangyang Liu , Yanqing Wu , Ningfei Wang , Xiao Hou

Under large deformations, the nonlinear relaxation properties of composite solid propellants result in significant prediction deviations. In this study, viscoelastic experiments of solid propellants at variable temperatures are conducted. A method for calculating the equal stress derivative in multi-step relaxation test results is proposed to calibrate the proportional relationship of nonlinear relaxation times. The relaxation times increase monotonically with deformation and exhibit a logarithmic evolution law. Under large deformations, the increase of relaxation times slows down. The nonlinear relaxation times are introduced into the thermo-hyper-viscoelastic constitutive model constructed by the generalized Maxwell model and the eight-chain tube model. After calibrating the constitutive model parameters based on experimental results, the accuracy of the constitutive model is verified through double-step relaxation tests on center-holed samples. The incorporation of the nonlinear relaxation times reduces the prediction deviations of composite solid propellants from 11% to 5%. The nonlinear relaxation properties of solid propellants originate from the nonlinearity of moduli and viscosities. The moduli and viscosities exhibit a pattern of initially increasing and then dropping with deformation. The microscopic mechanism involves the time consumption of rearrangement due to heightened friction following deformation, as well as the fracture of the molecular chain under large deformation. The temperatures reduce relaxation times and viscosities by increasing the extensibility of molecular chains.

在大变形情况下,复合固体推进剂的非线性松弛特性会导致预测结果出现重大偏差。本研究对不同温度下的固体推进剂进行了粘弹性实验。提出了计算多步松弛试验结果中等应力导数的方法,以校准非线性松弛时间的比例关系。弛豫时间随变形单调增加,并呈现对数演化规律。在大变形情况下,松弛时间的增长速度减慢。非线性弛豫时间被引入到由广义麦克斯韦模型和八链管模型构建的热超粘弹性构成模型中。在根据实验结果校准构成模型参数后,通过对中心孔样品进行双步松弛试验验证了构成模型的准确性。加入非线性弛豫时间后,复合固体推进剂的预测偏差从 11% 降至 5%。固体推进剂的非线性松弛特性源于模量和粘度的非线性。模量和粘度随着变形呈现出先增大后减小的模式。微观机理包括变形后摩擦力增大导致的重排时间消耗,以及大变形下分子链的断裂。温度通过增加分子链的延展性来缩短弛豫时间和降低粘度。
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引用次数: 0
Neural networks based surrogate modeling for efficient uncertainty quantification and calibration of MEMS accelerometers 基于神经网络的代用建模,用于 MEMS 加速计的高效不确定性量化和校准
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-12 DOI: 10.1016/j.ijnonlinmec.2024.104902
Filippo Zacchei , Francesco Rizzini , Gabriele Gattere , Attilio Frangi , Andrea Manzoni

This paper addresses the computational challenges inherent in the stochastic characterization and uncertainty quantification of Micro-Electro-Mechanical Systems (MEMS) capacitive accelerometers. Traditional methods, such as Markov Chain Monte Carlo (MCMC) algorithms, are often constrained by the computational intensity required for high-fidelity (e.g., finite element) simulations. To overcome these limitations, we propose to use supervised learning-based surrogate models, specifically artificial neural networks, to effectively approximate the response of MEMS capacitive accelerometers. Our approach involves training the surrogate models with data derived from initial high-fidelity finite element analyses (FEA), providing rich datasets to be generated in an offline phase. The surrogate models replicate the FEA accuracy in predicting the behavior of the accelerometer under a wide range of fabrication parameters, thereby reducing the online computational cost without compromising accuracy. This enables extensive and efficient stochastic analyses of complex MEMS devices, offering a flexible framework for their characterization. A key application of our framework is demonstrated in estimating the sensitivity of an accelerometer, accounting for unknown mechanical offsets, over-etching, and thickness variations. We employ an MCMC approach to estimate the posterior distribution of the device’s unknown fabrication parameters, informed by its response to transient voltage signals. The integration of surrogate models for mapping fabrication parameters to device responses, and subsequently to sensitivity measures, greatly enhances both backward and forward uncertainty quantification, yielding accurate results while significantly improving the efficiency and effectiveness of the characterization process. This process allows for the reconstruction of device sensitivity using only voltage signals, without the need for direct mechanical acceleration stimuli.

本文探讨了微机电系统(MEMS)电容式加速度计的随机表征和不确定性量化所固有的计算挑战。马尔可夫链蒙特卡罗 (MCMC) 算法等传统方法往往受到高保真(如有限元)模拟所需的计算强度的限制。为了克服这些限制,我们建议使用基于监督学习的代理模型,特别是人工神经网络,来有效地近似 MEMS 电容式加速度计的响应。我们的方法包括利用从初始高保真有限元分析 (FEA) 中获得的数据来训练代用模型,从而在离线阶段生成丰富的数据集。代用模型复制了有限元分析在各种制造参数下预测加速度计行为的精度,从而在不影响精度的情况下降低了在线计算成本。这样就能对复杂的 MEMS 设备进行广泛而高效的随机分析,为其特性分析提供灵活的框架。在估算加速度计的灵敏度时,我们展示了该框架的一个关键应用,其中考虑到了未知的机械偏移、过蚀和厚度变化。我们采用 MCMC 方法,根据器件对瞬态电压信号的响应,估计器件未知制造参数的后验分布。代用模型可将制造参数映射到器件响应,进而映射到灵敏度测量,这种集成极大地增强了后向和前向不确定性量化,在获得精确结果的同时,显著提高了表征过程的效率和有效性。这一过程允许仅使用电压信号重建器件灵敏度,而无需直接的机械加速度刺激。
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引用次数: 0
Static analysis using flexibility disassembly perturbation for material nonlinear problem with uncertainty 利用柔性拆卸扰动对具有不确定性的材料非线性问题进行静态分析
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-11 DOI: 10.1016/j.ijnonlinmec.2024.104901
X. Peng , Q.W. Yang , H.F. Cao

Nonlinear finite element analysis of large-scale structures usually requires a lot of calculation cost, because it is necessary to repeatedly inverse the modified stiffness matrix caused by nonlinearity in the calculation process. When considering the uncertainty in materials, the calculation of the nonlinear analysis will be more unbearable. To improve the computational efficiency, this work develops a new method for nonlinear analysis with material uncertainty based on flexibility disassembly perturbation (FDP) approach. The FDP is an algorithm that can quickly calculate the inverse of a stiffness matrix. The basic idea of the proposed method is to introduce the FDP formula into Newton-Raphson iteration method to accelerate the nonlinear iterative calculation. Three numerical examples, one statically determinate structure and two statically indeterminate structures, are used to verify the accuracy and efficiency of the proposed method. The results show that the calculation time of the proposed method is far less than that of the existing complete analysis and combined approximation algorithms. In terms of computational accuracy, for statically determinate structures, the proposed algorithm can obtain exact solutions that are identical to the complete analysis results, while for statically indeterminate structures, the proposed algorithm can obtain approximate solutions that are very close to the complete analysis results.

大型结构的非线性有限元分析通常需要大量的计算费用,因为在计算过程中需要反复反演由非线性引起的修正刚度矩阵。如果考虑到材料的不确定性,非线性分析的计算将更加难以承受。为了提高计算效率,本研究基于柔性分解扰动(FDP)方法,开发了一种新的材料不确定性非线性分析方法。FDP 是一种可以快速计算刚度矩阵逆的算法。所提方法的基本思想是将 FDP 公式引入牛顿-拉夫逊迭代法,以加速非线性迭代计算。我们使用了三个数值实例(一个静定结构和两个静不定结构)来验证所提方法的准确性和效率。结果表明,建议方法的计算时间远远少于现有的完整分析和组合近似算法。在计算精度方面,对于静定结构,建议的算法可以获得与完整分析结果完全一致的精确解,而对于静不定结构,建议的算法可以获得与完整分析结果非常接近的近似解。
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引用次数: 0
Nonparametric identification of multi-degree-of-freedom nonlinear systems from partially measured responses under uncertain dynamic excitations 在不确定的动态激励下,根据部分测量响应对多自由度非线性系统进行非参数识别
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-10 DOI: 10.1016/j.ijnonlinmec.2024.104903
Ye Zhao , Bin Xu , Genda Chen

With the rapid advent of new materials and novel structures, it becomes difficult, if not impossible, to accurately model and simulate the nonlinear response of complex systems under uncertain dynamic excitations based on close-formed nonlinear functions and parametric identification. In this study, a two-step structural nonlinearity localization and identification approach for multi-degree-of-freedom (MDOF) nonlinear systems under uncertain dynamic excitations is developed by integrating an extended Kalman filter with unknown inputs into the equivalent linearized systems. In the first step, unmeasured responses and excitations are estimated as well as unknown structural parameters and nonlinearity locations are identified by fusing acceleration with displacement time histories at the observed degrees of freedom (DOFs). In the second step, the nonlinear restoring force of the detected nonlinear structural members is identified nonparametrically using three polynomial models, including a power series polynomial model (PSPM), a double Chebyshev polynomial model (DCPM), and a Legendre polynomial model (LPM). Linear multi-story shear frames controlled by nonlinear magnetorheological (MR) dampers are modelled computationally to demonstrate the generality of the proposed methodology. The multi-source uncertainties considered in these representative examples include the location and the type of nonlinearities represented by a Bingham model and a modified Dahl model of the dampers, the location of response measurements, the location and intensity of dynamic excitations, the level of measurement noise, and the initial assignment of structural parameters. The acceleration, velocity, and displacement time histories of structures can be evaluated accurately with a maximum error of 2.62% even with the presence of 8% measurement noise, while the external excitations can be estimated within an error of 1.77%. The location of nonlinear elements can be detected correctly. The structural parameters, the NRFs provided by MR dampers and the corresponding energy dissipation can be identified with a maximum error of 2.08%, 1.19% and 0.39%, respectively, even 8% measurement noise and very rough initial assignment of structure parameters (−70%) are considered. Moreover, the numerical results change little (<0.20%) even the initial assignment of structural parameters varies from 50% to 30% of their original values, no matter which nonparametric model is employed. Results indicate that the presented algorithm can effectively identify unmeasured dynamic responses, structural parameters, unknown excitations, nonlinear locations, and NRF of nonlinear elements in a nonparametric way.

随着新材料和新结构的快速出现,基于近似非线性函数和参数识别来精确建模和模拟复杂系统在不确定动态激励下的非线性响应变得十分困难,甚至是不可能。在本研究中,通过将带有未知输入的扩展卡尔曼滤波器集成到等效线性化系统中,开发了一种在不确定动态激励下多自由度(MDOF)非线性系统的两步结构非线性定位和识别方法。第一步,估算未测量的响应和激励,以及未知的结构参数,并通过融合加速度和观测自由度(DOF)的位移时间历程来确定非线性位置。第二步,使用三种多项式模型(包括幂级数多项式模型 (PSPM)、双切比雪夫多项式模型 (DCPM) 和勒让德多项式模型 (LPM))对检测到的非线性结构构件的非线性恢复力进行非参数识别。对由非线性磁流变(MR)阻尼器控制的线性多层剪力框架进行了计算建模,以证明所提方法的通用性。在这些具有代表性的例子中考虑的多源不确定性包括:由宾汉模型和改进的达尔模型所代表的阻尼器非线性的位置和类型、响应测量的位置、动态激励的位置和强度、测量噪声水平以及结构参数的初始分配。即使存在 8%的测量噪声,也能准确评估结构的加速度、速度和位移时间历程,最大误差为 2.62%,而外部激励的估计误差为 1.77%。非线性元素的位置可以正确检测。即使考虑 8%的测量噪声和非常粗糙的结构参数初始分配(-70%),结构参数、MR 阻尼器提供的 NRFs 和相应的能量耗散也能识别,最大误差分别为 2.08%、1.19% 和 0.39%。此外,无论采用哪种非参数模型,即使结构参数的初始分配从原始值的 50%到 30%不等,数值结果的变化也很小(<0.20%)。结果表明,所提出的算法能以非参数方式有效识别未测量的动态响应、结构参数、未知激励、非线性位置和非线性元素的 NRF。
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引用次数: 0
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International Journal of Non-Linear Mechanics
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