非線性自治包裝系統(tǒng)動態(tài)響應(yīng)研究
發(fā)布時間：2018-11-23 17:50
【摘要】：物流中,振動與沖擊等惡劣環(huán)境會造成產(chǎn)品破損。在優(yōu)化改進(jìn)產(chǎn)品自身結(jié)構(gòu)的同時,緩沖包裝也是產(chǎn)品防護(hù)的重要組成部分,設(shè)計可靠的包裝結(jié)構(gòu)可以有效降低振動與沖擊對產(chǎn)品的損壞。然而,目前物流中惡劣環(huán)境下產(chǎn)品防護(hù)動力學(xué)研究較為薄弱,產(chǎn)品的包裝設(shè)計缺乏深入和有效的理論支持與指導(dǎo)。各種實際緩沖包裝件可以統(tǒng)一抽象為緩沖包裝系統(tǒng),各種型式包裝系統(tǒng)在各種典型激勵下的動力學(xué)響應(yīng)特性是緩沖包裝設(shè)計的理論依據(jù)。緩沖系統(tǒng)的響應(yīng)既取決于環(huán)境作用的力或運動,也取決于系統(tǒng)本身的力學(xué)特性,如剛度、粘性與慣性等。緩沖包裝系統(tǒng)往往是非線性系統(tǒng),典型的有三次型、正切型和雙曲正切型等非線性系統(tǒng)。本課題主要以跌落沖擊工況下單自由度非線性自治包裝系統(tǒng)為研究對象,分別進(jìn)行了三個階段的研究:一般非線性保守系統(tǒng)自由振動動力學(xué)響應(yīng)分析、一般非線性耗散系統(tǒng)自由振動動力學(xué)響應(yīng)分析與一般非線性耗散系統(tǒng)跌落沖擊動力學(xué)響應(yīng)分析。本文首先介紹了最大—最小值法(MMA)與同倫分析法(HAM)并以算例形式闡述了兩種方法的優(yōu)缺點。對于典型的正切型與雙曲正切型非線性自治系統(tǒng),兩種算法都需要對控制方程進(jìn)行近似簡化,近似控制方程大大增加了分析誤差。對于這類更一般形式的二階非線性微分方程,本文提出了一種新的算法,可以簡單有效地求解此類自由振動響應(yīng)求解問題�？紤]線性阻尼的影響,本文介紹了純非線性耗散系統(tǒng)響應(yīng)的Ateb函數(shù)表達(dá)解,進(jìn)而發(fā)展為三角函數(shù)的近似解析解。由于非線性的多樣性,不同形式的非線性系統(tǒng)可能具有相同的運動特征,進(jìn)行相同的運動。對于恢復(fù)力項更一般形式的耗散系統(tǒng)自由振動問題,提出了一般非線性微分方程的等效純非線性方程。在此基礎(chǔ)上,得到了非線性耗散系統(tǒng)自由振動的響應(yīng)通解。結(jié)果與數(shù)值分析對比,準(zhǔn)確度較高,方法簡單有效。緩沖包裝系統(tǒng)在跌落沖擊與自由振動中具有相同的控制方程,但是初始條件的不同,運動特征有所區(qū)別。本文對三次型與正切型非線性包裝系統(tǒng)在保守形式與耗散形式下的動態(tài)響應(yīng)分別進(jìn)行了分析,近似解析解與數(shù)值解非常接近。本文最后設(shè)計試驗對理論計算進(jìn)行驗證,選取空氣墊緩沖材料為試驗樣品,分別在不同跌落高度與不同靜應(yīng)力下進(jìn)行重復(fù)試驗。試驗結(jié)果顯示空氣墊在不同條件下的沖擊壓縮過程中具有統(tǒng)一的力學(xué)行為規(guī)律,由此建立了動態(tài)本構(gòu)關(guān)系,進(jìn)一步得到空氣墊作為緩沖材料時產(chǎn)品的動力學(xué)控制方程。采用本文理論分析階段的算法得到了最大沖擊加速度與靜應(yīng)力關(guān)系,由此繪制出在不同跌落高度下的動態(tài)緩沖曲線。理論值與實測值相當(dāng)吻合,表明了理論分析結(jié)果的正確性。
[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.
【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB48
本文編號：2352293
[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.
【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB48
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