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An application of Rayleigh quotient for crack detection in simply supported beam 瑞利商在简支梁裂纹检测中的应用
Pub Date : 2023-03-31 DOI: 10.15625/0866-7136/18182
Duong The Hung
An explicit expression of natural frequencies through crack parameters is derived for multiple cracked beams with simply supported boundaries using the Rayleigh quotient. The obtained expression provides not only a simple tool for calculating natural frequencies of multiple cracked beams, but also allows employing the so-called crack scanning method for detecting multiple cracks in simply supported beams from measured natural frequencies. A numerical example demonstrates that the crack scanning method, in combination with the Rayleigh quotient, enables consistent identification of cracks with 1% relative depth.
利用瑞利商导出了具有简支边界的多裂纹梁的固有频率随裂纹参数的显式表达式。所得到的表达式不仅为计算多裂纹梁的固有频率提供了一个简单的工具,而且还允许采用所谓的裂纹扫描方法从测量的固有频率中检测简支梁的多裂纹。数值算例表明,裂纹扫描方法与瑞利商相结合,可以对相对深度为1%的裂纹进行一致的识别。
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引用次数: 0
Dynamic response of arbitrary double-curved shells by meridian curve digitalization 子午曲线数字化的任意双弯曲壳的动力响应
Pub Date : 2023-03-31 DOI: 10.15625/0866-7136/17305
N. D. Bich, Nguyen Hoang Tung, Le Xuan Tung
For the resulting equation of double-curved shells, which is formed by revolution of an arbitrary in-plane meridian curve and cannot be represented analytically, there exists no analytical approach to problem setting and solution. This paper presents the digitalization of the meridian curve in the polar coordinate system, which forms double number series. The double number series then can be approximated by an interpolation function so that calculations can be performed in a similar methodology for an explicit function. Digitalization enables the input parameters in the form of interpolation functions. Procedures for the proposed selection of solution forms, formation of the kinetic equation, and computation of coefficients for the kinetic equation from on the interpolation and explicit functions are presented in the paper. The final solution is obtained by using the program Mathematica 7.0 to solve the system of nonlinear differential equations. Assessment of the dynamic response of the double-curved shell, especially responses with chaotic motion, is also presented in the paper.
双弯曲壳的结果方程是由任意平面内子午线的旋转形成的,不能解析表示,因此没有解析的方法来设置和求解问题。本文介绍了在极坐标系下子午线曲线的数字化,它形成双数列。然后可以用插值函数来近似双数级数,这样就可以用类似的方法对显式函数进行计算。数字化使输入参数以插值函数的形式出现。本文给出了基于插值函数和显式函数的解形式的选择、动力学方程的形成和动力学方程系数的计算过程。最后利用Mathematica 7.0程序对非线性微分方程组进行求解,得到了最终的解。本文还对双弯曲壳的动力响应,特别是混沌运动下的响应进行了分析。
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引用次数: 0
Buckling analysis of laminated composite thin-walled I-beam under mechanical and thermal loads 层合薄壁工字梁在力学和热载荷作用下的屈曲分析
Pub Date : 2023-03-20 DOI: 10.15625/0866-7136/17956
Xuan-Bach Bui, Anh-Cao Nguyen, Ngoc-Duong Nguyen, T. Do, T. Nguyen
Despite the extensive use of thin-walled structures, the studies on their behaviours when exposed to extreme thermal environment are relatively scarce. Therefore, this paper aims to present the buckling analysis of thin-walled composite I-beams under thermo-mechanical loads. The thermal effects are investigated for the case of studied beams undergoing a uniform temperature rise through their thickness. The theory is based on the first-order shear deformation thin-walled beam theory with linear variation of displacements in the wall thickness. The governing equations of motion are derived from Hamilton's principle and are solved by series-type solutions with hybrid shape functions. Numerical results are presented to investigate the effects of fibre angle, material distribution, span-to-height's ratio and shear deformation on the critical buckling load and temperature rise. These results for several cases are verified with available references to demonstrate the present beam model’s accuracy.
尽管薄壁结构被广泛使用,但对其在极端热环境下的行为研究相对较少。因此,本文旨在对薄壁复合工字梁在热载荷作用下的屈曲进行分析。研究了梁在厚度上均匀升温的情况下的热效应。该理论基于位移随壁厚线性变化的一阶剪切变形薄壁梁理论。运动控制方程由哈密顿原理导出,用混合形函数的级数解求解。给出了纤维角度、材料分布、跨高比和剪切变形对临界屈曲载荷和温升的影响。这些结果与现有的参考文献进行了验证,证明了该梁模型的准确性。
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引用次数: 0
Static and vibration analysis of functionally graded microplate with porosities based on higher-order shear deformation and modified strain gradient theory 基于高阶剪切变形和修正应变梯度理论的多孔功能梯度微孔板静振动分析
Pub Date : 2023-03-01 DOI: 10.15625/0866-7136/17552
Van-Thien Tran, V. Nguyen, T. Nguyen, T. Vo
Based on fundamental equations of the elasticity theory, a unified higher-order shear deformation theory is developed for bending and free vibration analysis of functionally graded (FG) microplates with porosities. The modified strain gradient theory is employed to capture the size effects. Bi-directional series with hybrid shape functions are used to solve the problems. Several important effects including thickness-to-material length scale parameters, side-to-thickness ratio, and boundary conditions on the deflections and natural frequencies of FG porous microplates are investigated.
在弹性理论基本方程的基础上,建立了具有孔隙的功能梯度微孔板弯曲和自由振动分析的统一的高阶剪切变形理论。采用修正应变梯度理论来捕捉尺寸效应。采用混合形状函数的双向级数来解决这一问题。研究了厚度-材料长度尺度参数、边厚比和边界条件对FG多孔微孔板挠度和固有频率的影响。
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引用次数: 0
Dynamic modelling and singularity-free simulation of closed loop multibody system driven by electric motors 电机驱动闭环多体系统动力学建模与无奇点仿真
Pub Date : 2023-01-02 DOI: 10.15625/0866-7136/16977
N. Hoang, Vu Duc Vuong, Dinh Van Phong, Nguyen Tung Lam
This paper presents the dynamic model and singularity-free simulation of electromechanical systems including closed loop multibody systems, massless gear transmission and electric motors. The dynamic model of these systems is established in matrix form and written in a Differential-Algebraic Equations form by applying the Lagrangian equation with multipliers and substructure method. Moreover, this paper deals with two difficult issues in the simulation of closed-loop multibody systems which are to overcome smoothly the singular configurations and to stabilize the constrained equations due to accumulated errors. The singularity-free simulation is solved by using null-space of Jacobian matrix to eliminate the constraint forces – Lagrangian multipliers in equations of motion. The drift in the constraint equation during simulation is restricted by a combination of Baumgarte’s stabilization and post-adjusting technique. Some numerical experiments are carried out to the planar 3RRR parallel manipulator driven by electric motors. Simulation results confirm the effectiveness of the proposed approach in overcoming the singular configurations and in stabilization of the constraint.
本文介绍了闭环多体系统、无质量齿轮传动和电动机等机电系统的动力学模型和无奇点仿真。利用拉格朗日乘子方程和子结构法,建立了系统的矩阵形式的动力学模型,并将其写成微分代数方程形式。此外,本文还讨论了闭环多体系统仿真中的两个难点问题:平滑克服奇异构型和由于累积误差而使约束方程稳定。利用雅可比矩阵的零空间消除运动方程中的拉格朗日乘子的约束,求解无奇点仿真。通过结合鲍姆加特稳定化和后置调整技术来抑制仿真过程中约束方程的漂移。对电机驱动的平面3RRR并联机器人进行了数值实验。仿真结果验证了该方法在克服奇异构型和稳定约束方面的有效性。
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引用次数: 0
Dynamic buckling analysis of reinforced composite plate subjected to harmonic loads 加筋复合材料板在谐波荷载作用下的动力屈曲分析
Pub Date : 2023-01-02 DOI: 10.15625/0866-7136/17938
P. Dat, Le Pham Binh
Composite plates are high-tech structures used in many areas of modern engineering, like building, space travel, ships, etc. In practice, these structures are often used in their thin form, typically a reinforced composite plate subjected to dynamic loads. Therefore, when subjected to loads, the plate may be instability. The article presents the element model, finite element algorithm, and buckling analysis results of reinforced composite plates subjected to dynamic loads in order to determine the buckling domain. Furthermore, the influence of some factors such as geometric parameters, reinforcing stiffeners, and material characteristics on the buckling domain of the plate is studied in detail.
复合板是一种高科技结构,应用于现代工程的许多领域,如建筑、太空旅行、船舶等。在实践中,这些结构通常以薄的形式使用,通常是受动载荷的增强复合板。因此,当受到载荷时,板可能会失稳。本文介绍了加筋复合材料板在动载作用下的单元模型、有限元算法和屈曲分析结果,以确定其屈曲区域。此外,还详细研究了几何参数、加强筋和材料特性等因素对板的屈曲域的影响。
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引用次数: 0
Nonlinear buckling and post-buckling of imperfect FG porous sandwich cylindrical panels subjected to axial loading on elastic foundation 弹性基础上不完全FG多孔夹层圆柱板在轴向载荷作用下的非线性屈曲和后屈曲
Pub Date : 2022-12-31 DOI: 10.15625/0866-7136/17980
Pham Van Hoan, Dao Nhu Mai, K. V. Phu, L. K. Hoa
This paper deals with the nonlinear buckling and post-buckling of sandwich cylindrical panels with non-uniform porous core and functionally graded face sheets. The imperfect sandwich cylindrical panels are subjected to axial loading on elastic foundation. Based on the Donnell shell theory, with von Kármán geometrical nonlinearity, the governing equations are derived. The effects of elastic foundation, various panel geometrical characteristics, porosity parameters, and the thickness of the porous core are investigated. The effects of foundation parameters, porosity parameters, the thickness of the porous core, and material parameters are investigated.
本文研究了具有非均匀多孔芯和功能梯度面板的夹层圆柱板的非线性屈曲和后屈曲问题。不完全夹层圆柱板在弹性基础上承受轴向载荷。基于Donnell壳理论,结合von Kármán几何非线性,推导了控制方程。研究了弹性地基、不同面板几何特性、孔隙率参数和多孔岩心厚度等因素的影响。研究了地基参数、孔隙率参数、多孔岩心厚度、材料参数等因素的影响。
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引用次数: 1
Machine learning for predicting mechanical behavior of concrete beams with 3D printed TPMS 用3D打印TPMS预测混凝土梁力学行为的机器学习
Pub Date : 2022-12-31 DOI: 10.15625/0866-7136/17999
Kim Tran-Quoc, Lieu B. Nguyen, V. Luong, H. Nguyen-Xuan
Bioinspired structures are remarkable porous structures with great strength-to-weight ratios. Hence, they have been applied in various fields including biomedical, transportation, and aerospace materials, etc. Recent studies have shown the significant impact of the plastic 3D printed triply periodic minimal surfaces (TPMS) structure on the cement beam including increasing the peak load, reducing the deflection, and improving the ductility. In this study, a machine learning (ML) surrogate model has been conducted to predict the beam behavior under static bending load. At first, various combinations of plastic volume fractions and numbers of core layers have been adopted to reinforce the constituent beam. The finite element method (FEM) was implemented to investigate the influences of these reinforcement strategies. Next, the above data were employed to create the ML model. A three-process assessment was proposed to achieve the most suitable model for the present problem, these processes were the model hyperparameter tuning, the performance assessment, and the handling overfitting with deep learning (DL) techniques. Consequently, both beam peak loads and maximum deflections were proportional to the volume fraction. The increment in TPMS layers could lead to the enhancement in both traits but with a nonlinear relationship. Furthermore, each trait may be a ceiling value that could not be exceeded with a specific volume fraction despite any number of layers. This conclusion was indicated by the surrogate model predictions. The final model in this study could deal with noisy data from FEM and with the support of a new early stopping condition, excellent performance could be found on both train and test data. The maximum deviations of 2.5% and 3.5% for peak loads and maximum midpoint displacements, respectively, have verified the robustness of the present surrogate model.    
仿生结构是一种显著的多孔结构,具有很高的强度与重量比。因此,它们已被应用于生物医学、交通运输和航空航天材料等各个领域。最近的研究表明,塑料3D打印三周期最小表面(TPMS)结构对水泥梁有显著的影响,包括增加峰值载荷,减少挠度,提高延性。在这项研究中,机器学习(ML)代理模型已被用于预测静态弯曲荷载下的梁的行为。首先,采用塑性体积分数和核心层数的不同组合对构件梁进行加固。采用有限元方法分析了不同加固策略对结构的影响。接下来,利用上述数据创建ML模型。为了获得最适合当前问题的模型,提出了三个过程的评估,即模型超参数调整、性能评估和使用深度学习技术处理过拟合。因此,梁的峰值载荷和最大挠度都与体积分数成正比。TPMS层数的增加会导致两种性状的增强,但呈非线性关系。此外,无论层数多少,每个性状都可能是一个特定体积分数不能超过的上限值。这一结论得到了代理模型预测的证实。本研究最终建立的模型能够处理有限元数据中的噪声,并且在新的早停条件的支持下,对列车和试验数据都具有良好的性能。峰值荷载和最大中点位移的最大偏差分别为2.5%和3.5%,验证了该替代模型的鲁棒性。
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引用次数: 1
Multi-objective optimization of magnetorheological clutch with stationary housing 固定式壳体磁流变离合器的多目标优化
Pub Date : 2022-12-31 DOI: 10.15625/0866-7136/17979
B. Huy, L. Thang, D. B. Tri, Nguyen Ngoc Diep, Nguyen Quoc Hung
This study focuses on the development of magnetorheological fluid (MRF) based clutch systems for speed control of a rotary load. A new configuration for speed control of a rotary shaft using a magnetorheological clutch (MRC) with stationary winding housing and its mathematical model are proposed based on the Bingham plastic model of MRF. Multi-objective design optimization for MRCs simultaneously considering power consumption, transmitting torque, and rotating mass is then studied based on the derived mathematical model and electromagnetic finite element analysis (FEA) of the MRC. Subsequently, an optimal configuration of the proposed MRC is manufactured and experimentally investigated.
本研究的重点是开发基于磁流变液(MRF)的离合器系统,用于旋转负载的速度控制。基于Bingham磁流变离合器的塑性模型,提出了一种采用固定绕组壳磁流变离合器控制转轴速度的新结构,并建立了其数学模型。基于推导的MRC数学模型和电磁有限元分析,研究了同时考虑功耗、传递转矩和旋转质量的MRC多目标优化设计。随后,制造了所提出的MRC的最佳配置并进行了实验研究。
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引用次数: 0
Limit state analysis of asymmetrical microstructures based on yield design computational homogenization approach 基于屈服设计计算均匀化方法的非对称微结构极限状态分析
Pub Date : 2022-12-31 DOI: 10.15625/0866-7136/17985
Phuc L. H. Ho, C. Le, P. H. Nguyen, Chanh T. Ngo
This paper presents a novel formulation for the computational homogenization analysis of materials at the limit state. The polynomial interpolations are employed to impose the periodic boundary conditions for the fluctuating term of the displacement field when using arbitrary finite element meshes. Second-order cone programming provides an efficient solution to solve the resulting optimization problems, and accurate load multipliers can be obtained with the minimum computational cost. Several asymmetrical material models are investigated to perform the efficiency of the proposed method. The collapse mechanisms of the representative volume elements are also presented.
本文提出了一种计算材料极限状态均质化分析的新公式。采用多项式插值法对任意有限元网格的位移场波动项施加周期边界条件。二阶锥规划提供了求解优化问题的有效方法,并能以最小的计算代价得到精确的负载乘法器。对几种非对称材料模型进行了研究,验证了该方法的有效性。给出了具有代表性的体元的坍缩机理。
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引用次数: 0
期刊
Vietnam Journal of Mechanics
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