非线性自治包装系统动态响应研究

发布时间：2018-11-23 17:50

【摘要】：物流中,振动与冲击等恶劣环境会造成产品破损。在优化改进产品自身结构的同时,缓冲包装也是产品防护的重要组成部分,设计可靠的包装结构可以有效降低振动与冲击对产品的损坏。然而,目前物流中恶劣环境下产品防护动力学研究较为薄弱,产品的包装设计缺乏深入和有效的理论支持与指导。各种实际缓冲包装件可以统一抽象为缓冲包装系统,各种型式包装系统在各种典型激励下的动力学响应特性是缓冲包装设计的理论依据。缓冲系统的响应既取决于环境作用的力或运动,也取决于系统本身的力学特性,如刚度、粘性与惯性等。缓冲包装系统往往是非线性系统,典型的有三次型、正切型和双曲正切型等非线性系统。本课题主要以跌落冲击工况下单自由度非线性自治包装系统为研究对象,分别进行了三个阶段的研究:一般非线性保守系统自由振动动力学响应分析、一般非线性耗散系统自由振动动力学响应分析与一般非线性耗散系统跌落冲击动力学响应分析。本文首先介绍了最大—最小值法(MMA)与同伦分析法(HAM)并以算例形式阐述了两种方法的优缺点。对于典型的正切型与双曲正切型非线性自治系统,两种算法都需要对控制方程进行近似简化,近似控制方程大大增加了分析误差。对于这类更一般形式的二阶非线性微分方程,本文提出了一种新的算法,可以简单有效地求解此类自由振动响应求解问题。考虑线性阻尼的影响,本文介绍了纯非线性耗散系统响应的Ateb函数表达解,进而发展为三角函数的近似解析解。由于非线性的多样性,不同形式的非线性系统可能具有相同的运动特征,进行相同的运动。对于恢复力项更一般形式的耗散系统自由振动问题,提出了一般非线性微分方程的等效纯非线性方程。在此基础上,得到了非线性耗散系统自由振动的响应通解。结果与数值分析对比,准确度较高,方法简单有效。缓冲包装系统在跌落冲击与自由振动中具有相同的控制方程,但是初始条件的不同,运动特征有所区别。本文对三次型与正切型非线性包装系统在保守形式与耗散形式下的动态响应分别进行了分析,近似解析解与数值解非常接近。本文最后设计试验对理论计算进行验证,选取空气垫缓冲材料为试验样品,分别在不同跌落高度与不同静应力下进行重复试验。试验结果显示空气垫在不同条件下的冲击压缩过程中具有统一的力学行为规律,由此建立了动态本构关系,进一步得到空气垫作为缓冲材料时产品的动力学控制方程。采用本文理论分析阶段的算法得到了最大冲击加速度与静应力关系,由此绘制出在不同跌落高度下的动态缓冲曲线。理论值与实测值相当吻合,表明了理论分析结果的正确性。
[Abstract]:In logistics, adverse conditions such as vibration and shock can cause product breakage. Buffer packaging is also an important part of product protection while optimizing and improving the product structure. The design of reliable packaging structure can effectively reduce the vibration and impact damage to the product. However, at present, the research of product protection dynamics in the adverse environment of logistics is relatively weak, and the packaging design of products is lack of in-depth and effective theoretical support and guidance. All kinds of practical cushioning packages can be abstracted as cushioning packaging system. The dynamic response characteristics of various types of packaging systems under various typical excitations are the theoretical basis of cushioning packaging design. The response of the buffer system depends not only on the force or motion of the environment, but also on the mechanical properties of the system, such as stiffness, viscosity and inertia. Cushioning packaging systems are usually nonlinear systems, such as cubic, tangent and hyperbolic tangent. In this paper, the nonlinear autonomous packaging system with order degree of freedom under the condition of drop impact is studied in three stages: the dynamic response analysis of free vibration of general nonlinear conservative system. The dynamic response analysis of free vibration of general nonlinear dissipative system and drop shock of general nonlinear dissipative system. In this paper, the Max-Minimum method (MMA) and Homotopy Analysis method (HAM) are introduced, and the advantages and disadvantages of the two methods are illustrated by an example. For a typical nonlinear autonomous system of tangent and hyperbolic tangent, both algorithms need to simplify the control equation approximately, and the approximate control equation greatly increases the analysis error. For this kind of second order nonlinear differential equation, a new algorithm is proposed, which can solve the problem of free vibration response simply and effectively. Considering the influence of linear damping, this paper introduces the Ateb function expression solution of the response of pure nonlinear dissipative system, and then develops into the approximate analytic solution of trigonometric function. Because of the diversity of nonlinearity, different nonlinear systems may have the same motion characteristics and the same motion. For the problem of free vibration of dissipative systems with more general form of restoring force term, the equivalent pure nonlinear equations of general nonlinear differential equations are proposed. On this basis, a general solution to the free vibration of a nonlinear dissipative system is obtained. Results compared with numerical analysis, the accuracy is high and the method is simple and effective. The cushioning packaging system has the same governing equation in the drop shock and free vibration, but the motion characteristics are different with different initial conditions. In this paper, the dynamic responses of cubic and tangent nonlinear packaging systems in conservative form and dissipative form are analyzed, respectively. The approximate analytical solution is very close to the numerical solution. At the end of this paper, the theoretical calculation is verified by designing experiments. The air cushion material is selected as the test sample, and repeated tests are carried out under different drop heights and different static stresses respectively. The experimental results show that the air cushion has a uniform mechanical behavior in the process of impact compression under different conditions. The dynamic constitutive relation is established and the dynamic governing equation of the product when the air cushion is used as the buffer material is obtained. The relationship between the maximum impact acceleration and the static stress is obtained by using the algorithm of the theoretical analysis stage in this paper, and the dynamic buffering curves at different drop heights are drawn. The theoretical values are in good agreement with the measured values, which indicates the correctness of the theoretical analysis results.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB48

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