Transformational deformation models of continuous thin‐walled structural elements with support elements of finite sizes: Theoretical foundations, computational, and physical experiments

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-11-03 DOI:10.1002/zamm.202300214
Vitaly Nikolaevich Paimushin, Vyacheslav Anatolievich Firsov, Viktor Mikhailovich Shishkin, Ruslan Kamilevich Gazizullin
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Abstract

Abstract A method of experimental study of forced bending vibrations of unfixed spans of continuous thin‐walled structural element fixed on rigid support elements of finite dimensions has been developed using instrumental means for registration of vibration acceleration amplitudes. The technique is realized on beams with different types of their fixing under the loading of one of the beam section with an external force that varies in time according to a harmonic law. Experimental dependences of amplitude values of vibration accelerations in specific points of certain spans of the beam on the frequency of external load have been obtained. These results indicate the passage of vibrations through the fixed sections due to the transformation of bending vibration modes of the loaded section into longitudinal transverse‐shift vibrations of the fixed sections during the transition across the boundary from the unfixed section to the fixed one (from the fixed to the unfixed section). For the theoretical study of the described phenomenon a transformational model of the flat beam deformation is constructed on the basis of the refined Timoshenko model with additional account of the deformability of the section with fixation to a rigid support element of finite length on one of its face surfaces. The corresponding equations of motion of the unfixed and fixed sections are derived. The corresponding kinematic and force conditions of their conjugation are formulated. On their basis, analytical solutions of two specific problems are found in the linear approximation. One‐dimensional finite elements for modeling the dynamic response of continuous beam of the considered class are also constructed. Numerical experiments have been carried out for a flat beam made of aluminum alloys D16AT, AMg‐6 and unidirectional fiber reinforced plastic. The presence of a significant transformation of the stress‐strain state parameters of the considered beams at the transition across the boundary from unfixed to fixed sections and a significant increase in the level of transverse tangential stresses on the fixed section of the beam in the vicinity of the interface of the unfixed section with the fixed one have been revealed.
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具有有限尺寸支撑元件的连续薄壁结构元件的转换变形模型:理论基础,计算和物理实验
摘要:本文提出了一种用仪器记录振动加速度幅值的方法,对固定在有限尺寸刚性支撑单元上的连续薄壁构件的非固定跨强迫弯曲振动进行实验研究。该技术是在具有不同固定形式的梁上实现的,在一个梁段的载荷下,根据一个随时间变化的调和律施加外力。得到了梁的某些跨度的特定点的振动加速度幅值与外荷载频率的实验关系。这些结果表明,在从非固定截面过渡到固定截面(从固定截面到非固定截面)的过程中,由于加载截面的弯曲振动模式转变为固定截面的纵向横向位移振动,振动通过固定截面。为了对所描述的现象进行理论研究,在改进的Timoshenko模型的基础上建立了扁梁变形的转换模型,并附加考虑了固定在其一个表面上的有限长度刚性支撑单元的截面的变形能力。推导了非固定和固定截面的相应运动方程。给出了其共轭的运动学条件和受力条件。在此基础上,给出了线性近似中两个具体问题的解析解。建立了一类连续梁动力响应的一维有限元模型。对D16AT铝合金、AMg‐6铝合金和单向纤维增强塑料制成的平板梁进行了数值实验。所考虑的梁在从非固定截面过渡到固定截面时,应力应变状态参数发生了显著的转变,并且在非固定截面与固定截面的界面附近,梁的固定截面上的横向切向应力水平显著增加。
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来源期刊
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
期刊最新文献
A closed form solution for uniformly loaded rectangular plates with adjacent edges clamped and the two others simply supported (CCSS) Wave analysis in porous thermoelastic plate with microtemperature Transformational deformation models of continuous thin‐walled structural elements with support elements of finite sizes: Theoretical foundations, computational, and physical experiments On the exact controllability of a Galerkin scheme for 3D viscoelastic fluids with fractional Laplacian viscosity and anisotropic filtering An accurate and parameter‐free analysis for the converse Poynting effect in large constrained torsion of highly elastic soft tubes
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