点阵芯复合材料矩形夹层板的非线性强迫振动与共振分析

IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL
Alireza Moradi, Alireza Shaterzadeh
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引用次数: 0

摘要

本研究引入了两个全新的晶格核模型(模型(a)和(c)),首次给出了它们的刚度矩阵,为今后的研究奠定了基础。此外,本文还首次对具有不同格芯几何图案的复合材料矩形夹层板在均匀压缩载荷作用下的非线性强迫振动行为进行了分析评估。该板由一个中心格芯和对称的均匀面板组成。利用一阶剪切变形理论,根据Hamilton原理和von Kármán的非线性应变-位移关系推导出了运动的偏微分方程。然后用伽辽金方法将这些方程化为随时间变化的非线性常微分方程。采用多尺度方法对主共振和次共振进行了分析。用龙格-库塔数值方法对解析得到的非线性主共振进行了验证,证明了很好的一致性。二次共振,包括超谐波和亚谐波类型,引入新的动态响应频率的倍数或分数的主要频率,也进行了研究。这些共振对夹层板的稳定性和动力性能有显著影响,对夹层板的优化设计起着关键作用。本研究进一步考察了肋厚、芯高和加劲角等关键参数对振动幅值和频率响应曲线的影响。通过与现有文献和ABAQUS有限元分析的比较,这些发现得到了验证,突出了这些因素对动力行为的关键影响,并为具有点阵芯的夹层板的设计考虑提供了有价值的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlinear forced vibration and resonance analysis of composite rectangular sandwich plates with lattice cores

This study introduces two entirely new lattice core models (models (a) and (c)), presenting their stiffness matrices for the first time, which serve as a foundation for future research. Additionally, it provides the first analytical assessment of the nonlinear forced vibration behavior of composite rectangular sandwich plates with various lattice core geometric patterns under uniform compressive loading. The plate consists of a central lattice core and symmetric homogeneous face plates. Using the first-order shear deformation theory, the partial differential equations of motion are derived via Hamilton’s principle and von Kármán’s nonlinear strain–displacement relations. These equations are then reduced to time-dependent nonlinear ordinary differential equations using the Galerkin method. Primary and secondary resonances are analyzed using the method of multiple scales. The analytically obtained nonlinear primary resonances are validated against the Runge–Kutta numerical method, demonstrating excellent agreement. Secondary resonances, including superharmonic and subharmonic types that introduce new dynamic response frequencies as multiples or fractions of the primary frequencies, are also investigated. These resonances significantly influence the stability and dynamic performance of sandwich plates and play a key role in optimizing their design. This study further examines the effects of key parameters, including rib thickness, core height, and stiffener angles, on vibration amplitude and frequency response curves. The findings, validated through comparisons with existing literature and finite element analysis in ABAQUS, highlight the critical impact of these factors on dynamic behavior and provide valuable insights into design considerations for sandwich plates with lattice cores.

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来源期刊
International Journal of Mechanics and Materials in Design
International Journal of Mechanics and Materials in Design ENGINEERING, MECHANICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY
CiteScore
6.00
自引率
5.40%
发文量
41
审稿时长
>12 weeks
期刊介绍: It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design. Analytical synopsis of contents: The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design: Intelligent Design: Nano-engineering and Nano-science in Design; Smart Materials and Adaptive Structures in Design; Mechanism(s) Design; Design against Failure; Design for Manufacturing; Design of Ultralight Structures; Design for a Clean Environment; Impact and Crashworthiness; Microelectronic Packaging Systems. Advanced Materials in Design: Newly Engineered Materials; Smart Materials and Adaptive Structures; Micromechanical Modelling of Composites; Damage Characterisation of Advanced/Traditional Materials; Alternative Use of Traditional Materials in Design; Functionally Graded Materials; Failure Analysis: Fatigue and Fracture; Multiscale Modelling Concepts and Methodology; Interfaces, interfacial properties and characterisation. Design Analysis and Optimisation: Shape and Topology Optimisation; Structural Optimisation; Optimisation Algorithms in Design; Nonlinear Mechanics in Design; Novel Numerical Tools in Design; Geometric Modelling and CAD Tools in Design; FEM, BEM and Hybrid Methods; Integrated Computer Aided Design; Computational Failure Analysis; Coupled Thermo-Electro-Mechanical Designs.
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