固定在长度有限的刚性支撑元件上的平面杆在自由端施加横向外力作用下的强制弯曲振动

IF 1.5 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Mechanics of Composite Materials Pub Date : 2024-07-02 DOI:10.1007/s11029-024-10206-1
V. N. Paimushin, V. M. Shishkin, S. F. Chumakova
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引用次数: 0

摘要

研究解决了具有有限长度紧固截面的平面杆在自由端横向外力作用下的受迫弯曲振动问题。采用经典几何非线性近似的基尔霍夫-洛夫模型来描述杆自由部分的变形过程。其固定部分的变形由 Timoshenko 精炼剪切模型描述,该模型考虑了横向应变。制定了杆的自由部分和固定部分的运动共轭条件。利用汉密尔顿-奥斯特罗格拉茨基变分原理获得了运动方程、相应的边界条件以及杆件共轭的受力条件。推导出了杆的未紧固部分自由端在谐波横向力作用下的受迫振动问题的精确解析解。通过数值实验研究了单向纤维复合材料杆的共振振动。结果表明,由于固定部分的横向收缩,所研究杆件悬臂部分末端的横向振动幅度明显增大。考虑到横向收缩,硬铝杆固定部分的最大横向剪应力几乎降低了两倍。
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Forced Bending Vibrations of a Plane Rod Fixed on a Rigid Support Element of Finite Length Under the Action of an External Transverse Force Aplied to Its Free End

The problem of forced bending vibrations of a plane rod with a finite-length fastening section under the action of an external transverse force at its free end was solved. The classical Kirchhoff–Love model in the classical geometrically nonlinear approximation was used to describe the deformation process of the free part of the rod. The deformation of its fixed part was described by the Timoshenko refined shear model that takes into account transverse strains. The conditions of kinematic conjugation of the free and fixed parts of the rod were formulated. The equations of motion, the corresponding boundary conditions, and the force conditions of conjugation of the rod parts were obtained using the Hamilton–Ostrogradsky variational principle. An exact analytical solution of the problem of forced vibrations of a rod under the action of a harmonic transverse force at the free end of the unfastened part of the rod was deduced. Numerical experiments were carried out to study the resonant vibrations of rods made of unidirectional fiber composite. The effect of a noticeable increase of the amplitudes of transverse vibrations of the ends of the cantilever parts of the rods studied due to transverse contraction of the fixed section was revealed. Taking into account the transverse contraction caused an almost twofold reduction of the maximum transverse shear stresses in the fixed part of the duralumin rod.

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来源期刊
Mechanics of Composite Materials
Mechanics of Composite Materials 工程技术-材料科学:复合
CiteScore
2.90
自引率
17.60%
发文量
73
审稿时长
12 months
期刊介绍: Mechanics of Composite Materials is a peer-reviewed international journal that encourages publication of original experimental and theoretical research on the mechanical properties of composite materials and their constituents including, but not limited to: damage, failure, fatigue, and long-term strength; methods of optimum design of materials and structures; prediction of long-term properties and aging problems; nondestructive testing; mechanical aspects of technology; mechanics of nanocomposites; mechanics of biocomposites; composites in aerospace and wind-power engineering; composites in civil engineering and infrastructure and other composites applications.
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