Equivalent spring-like system for two nonlinear springs in series: application in metastructure units design

IF 2.3 3区 工程技术 Q2 MECHANICS Acta Mechanica Pub Date : 2024-10-19 DOI:10.1007/s00707-024-04055-1
L. Cveticanin
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Abstract

The paper deals with the problem of design of unit in auxetic metastructure. The unit is modeled as a two-part spring-like system where each part is with individual stiffness. To overcome the problem of analyzing of each of parts separately, the equivalent spring is suggested to be introduced. In the paper, a method for obtaining the equivalent elastic force of the unit is developed. The method is the generalization of the procedure suggested for substitution of a hard and a soft spring in series with an equivalent one. The nonlinearity of original springs is of quadratic order. As a results, it is obtained that the equivalent elastic force for two equal springs remains of the same type as of the original springs (soft or hard). For two opposite type springs in series with equal coefficients, the equivalent force is soft. The method is applicable for any hard and soft nonlinear springs or spring-like systems. Thus the hexagonal auxetic unit which contains a soft and a hard part in series is analyzed. In the paper, a new analytic method for determination of the frequency of vibration for the unit under action of a constant compression force acting along the unit axis is introduced. The method is applied for units which contain two parts: hard–hard, soft–soft, hard–linear, soft–linear and opposite. The obtained approximate vibration results are compared with numerically obtained ones and show good agreement. The advantage of the method is its simplicity as it does not require the nonlinear equation of motion to be solved.

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两个非线性串联弹簧的等效弹簧系统:在结构单元设计中的应用
本文论述了辅助结构中的单元设计问题。该单元被模拟为一个由两部分组成的弹簧系统,其中每个部分都具有独立的刚度。为了克服单独分析每个部分的问题,建议引入等效弹簧。本文提出了一种获得该装置等效弹力的方法。该方法是对用等效弹簧替代串联的硬弹簧和软弹簧的程序的推广。原始弹簧的非线性为二次阶。因此,两个等效弹簧的等效弹力与原始弹簧(软弹簧或硬弹簧)的类型相同。对于系数相等的两个相反类型的串联弹簧,等效应力是软的。该方法适用于任何软硬非线性弹簧或类似弹簧的系统。因此,本文分析了包含一软一硬串联部分的六边形辅助单元。文中介绍了一种新的分析方法,用于确定在沿单元轴线作用的恒定压缩力作用下单元的振动频率。该方法适用于包含两部分的单元:硬-硬、软-软、硬-线性、软-线性和相反。所获得的近似振动结果与数值结果进行了比较,结果表明两者具有良好的一致性。该方法的优点是简单,不需要求解非线性运动方程。
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来源期刊
Acta Mechanica
Acta Mechanica 物理-力学
CiteScore
4.30
自引率
14.80%
发文量
292
审稿时长
6.9 months
期刊介绍: Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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