矩形夹层板的非线性磁弹性随机振动

以表层较薄、夹心较软的四边简支矩形夹层板为研究对象,分析其在磁场环境中的非线性磁弹性随机振动问题。根据板壳磁弹性基本理论、夹层板的弯曲振动理论、连续体的随机振动理论,利用伽辽金积分法得到了在电磁场中受横向随机载荷作用时四边简支矩形夹层板的非线性磁弹性随机振动方程;并利用FPK方程法解出了四边简支矩形夹层板非线性随机振动位移响应和速度响应的方差、位移响应和速度响应的概率密度等多个数字特征。最后针对具体算例,通过数值模拟讨论了电磁参数、功率谱密度参数、板的几何尺寸的变化对各数字特征的影响。由数值模拟结果可知,调节随机激励、磁场强度、板的几何尺寸的大小能有效地控制结构随机振动产生振动位移的概率。     

硬夹心矩形夹层板的整体稳定性分析

摘要：本文在Reissner型理论给出的位移模式基础上,修正其软夹心假设,考虑夹心层面内刚度,给出了硬夹心夹层板的几何方程、物理方程,建立了硬夹心夹层板结构在面内纵向载荷作用下的平衡微分方程,并对方程进行了简化,通过理论计算得到了四边简支条件下硬夹心矩形夹层板整体失稳临界载荷的解析解,并分别计算了夹心层材料的弹性模量 、厚度 、泊松比 对硬夹心夹层板临界载荷的影响,结果证明,对于硬夹心夹层结构,夹心层面内刚度对硬夹心夹层板整体失稳临界载荷的影响较大,考虑其面内刚度是必要的。     

蜂窝层芯夹层板结构振动与传声特性研究

蜂窝层芯夹层板应用于飞行器、高速列车等交通工具的主体及底板结构时需要考虑其振动及隔声特性. 针对声压激励下的四边简支蜂窝层芯夹层板结构,应用基于Reissner夹层板理论的结构振动方程建立了的声振耦合理论模型(声压以简支模态双级数的形式引入振动控制方程),结合流固耦合条件求解了声振耦合系统控制方程,应用有限元模拟对理论预测进行了验证. 基于理论模型的数值计算结果,系统研究了蜂窝层芯夹层板结构的振动特性和传声特性,刻画了层芯厚度、蜂窝壁厚、夹层板面内尺寸和声压入射角度等关键系统参数对夹层板振动和传声特性的影响,为此类结构的工程优化设计提供了必要的理论参考.     

考虑芯层离散特性的方形蜂窝夹层板自由振动分析

针对方形蜂窝夹层板,考虑其离散的芯层结构形式,在经典夹层板理论的基础上,运用Hamilton变分原理导出了其离散结构形式的运动控制方程.该文以四边简支的方形蜂窝矩形夹层板为例,采用傅立叶级数和伽辽金法求解出夹层板固有频率的半解析解,并与有限元仿真结果进行了比较,两者吻合良好.该文还将夹层板与等质量的实体板固有频率进行了比较,讨论了夹层板芯层薄壁间距、厚度、高度以及面板厚度对其固有频率的影响.计算结果表明,夹层板相对实体板具有很大的刚度;芯层薄壁高度相对其它参数对夹层板固有频率的影响更大.     

四边固支蜂窝夹层板1:3内共振非线性动力学分析

基于经典叠层板理论和几何大变形理论,将铝基蜂窝芯层等效为一正交异性层,等效弹性参数由修正后的Gibson公式得出,对四边固支蜂窝夹层板非线性动力学特性进行了分析。考虑横向阻尼的影响,建立了四边固支蜂窝夹层板受横向激振力作用的受迫振动微分方程,通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程,利用同伦分析方法对双模态下蜂窝夹层板的动力学控制方程进行研究,得到了1:3内共振下的幅频特性曲线,研究了不同结构尺寸对动力学特性的影响以及蜂窝夹层板作稳态运动时的稳定性问题。本文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考。     

曲壁蜂窝夹层板的振动特性研究

曲壁蜂窝具有负刚度特性,可以在大变形过程中吸收能量、抗冲击,并且在冲击过后可以自我恢复而不像传统蜂窝被压溃。本文将曲梁构成的负刚度蜂窝作为芯层,建立夹层板的动力学模型;推导出了曲壁负刚度蜂窝胞元的等效弹性参数,将其周期性排列为蜂窝芯,应用Reddy高阶剪切变形理论、Von-Karman大变形关系和Hamilton原理推导了负刚度蜂窝夹层板的非线性动力学方程;应用Navier法计算了四边简支边界条件下的固有频率。并利用有限元软件ABAQUS建立模型,计算固有频率,与理论计算结果进行比较,结果显示二者的计算结果具有较好的一致性,验证了芯层等效弹性参数及模型的有效性。探讨了在蜂窝胞元具有较高吸能情形下,夹层板在不同芯层厚度、不同芯厚比以及不同胞元曲壁厚度时的固有频率的变化特性。     

考虑横向拉伸影响的FGM夹层板动不稳定性分析

以受多种形式面内载荷作用下的功能梯度夹层矩形板为研究对象,夹层板的功能梯度层组分材料沿厚度方向按幂律分布,考虑组分材料物性参数的温度相关性.研究中所用的位移场在Reddy高阶剪切变形理论基础上考虑了横向拉伸的影响.利用能量原理和Galerkin法得到四边简支功能梯度材料夹层矩形板的动力学模型.运用Bolotin法求得了...     

四边简支硬夹芯夹层板的弯曲问题研究

现有的夹层结构理论都是将夹芯视为软夹芯,忽略了其面内应力分量和弯曲刚度.该理论不能满足近年来出现的硬夹芯夹层结构.对此,考虑了以上被忽略的因素,修正了Reissner理论的软夹芯假设,提出了考虑夹芯面内应力分量和弯曲刚度的硬夹芯夹层板基本假设.根据最小势能原理得到了硬夹芯夹层板弯曲的基本方程和边界条件,给出了四边简支硬夹芯夹层板在横向载荷下弯曲的解析解.另外本文还研究了硬夹芯夹层板弯曲问题的有限元法,推导了四节点四边形等参单元的有限元列式,并用MATLAB编程求解了具体算例.     

负泊松比蜂窝夹层板的振动特性研究

研究了负泊松比蜂窝夹层板几何参数变化对板振动频率的影响,并得到了频率随泊松比的变化规律。在Reddy高阶剪切变形理论的基础上,利用Hamilton原理,推导出四边简支边界条件下的负泊松比蜂窝夹层板的偏微分运动方程。根据修正后的Gibson公式,考虑了蜂窝胞元壁板的弯曲和伸缩变形,重新计算了蜂窝芯层胞元的等效弹性参数。利用Navier法,选择合适四边简支边界条件的模态函数,得出板的长厚比分别为0.01、0.05、0.10,芯厚比分别为0.80、0.85、0.90、0.95和蜂窝芯胞元倾角分别为-30°、-60°、0°、30°、60°等情况下系统的前五阶固有频率。研究结果表明,系统的固有频率随板的芯厚比、蜂窝芯胞元倾角、蜂窝芯壁厚与斜壁之比的增加都在减小,而随着板长厚比的增加而增加。分析了泊松比的变化对系统固有频率的影响,发现负泊松比蜂窝夹层板的固有频率要明显小于传统正泊松比蜂窝夹层板。本文所得结果对进一步研究系统的多模态共振具有指导意义,为负泊松比蜂窝夹层结构的工程应用在减振设计方面提供一定的理论依据。     

轻质金属点阵夹层板热屈曲临界温度分析

本文针对均匀温度场下四边简支和四边固支金属点阵夹层板的临界热屈曲温度进行了求解和参数影响分析。将点阵夹芯等效为均匀连续体,并且将夹层板的剪切刚度近似为点阵夹芯的抗剪切刚度,忽略夹芯的抗弯刚度且认为夹层板主要由面板来提供抗弯刚度。对于无法获得解析解的四边固支条件,通过对未知变量进行双傅里叶展开的方法求解了Ressiner夹层板模型的临界屈曲温度,理论分析结果与有限元计算结果吻合良好。进一步分析了不同边界条件、点阵胞元构型、点阵材料相对密度、面板厚度等对临界屈曲温度的影响规律。     

Deflection of sandwich plates in terms of corresponding Kirchhoff plate solutions

Summary This study presents exact relationships between the deflections of isotropic sandwich plates and their corresponding Kirchhoff plates. The governing equilibrium equations for the sandwich plates are derived on the basis of the Reissner-Mindlin shear deformation plate theory. The considered plates are either (i) simply supported, of general polygonal shape and under any transverse loading condition or (ii) simply supported and clamped circular plates under axisymmetric loading. As the relationships are exact under the assumptions used in the plate theories, one may obtain exact deflection solutions of sandwich plates if the Kirchhoff plate solutions are exact. The relationships should also be useful for the development of approximate formulas for plates with other shapes, boundary and loading conditions, and may serve to check numerical deflection values computed from sandwich plate analysis software.     

电炮加载下芳纶蜂窝夹芯板的动力响应

研究了方形钛-芳纶蜂窝夹芯板在电炮驱动的高速聚酯飞片撞击加载下的动力响应,给出了面板和蜂窝芯层在不同冲击速度下的变形及失效模式。采用VISAR(velocity interferometer system for any reflector)测速技术测量了后面板中心点的速度时程,分析了芳纶蜂窝夹芯板的动态响应过程,讨论了冲击速度对夹芯板动力响应和抗冲击能力的影响。研究结果表明,低波阻抗的芳纶蜂窝破碎行为阻断了应力波向后面板的传播途径,破碎的蜂窝和塑形大变形的前面板吸收了高速冲击的大部分能量,充分发挥了钛合金的高强度和芳纶蜂窝的缓冲吸能特性,提高了夹芯板整体的防护能力。     

基于双曲面蜂窝夹层结构等效模型的研究及数值分析

蜂窝夹层结构在轻量化设计领域一直备受关注,相关的理论研究也日趋完善.然而,很多研究主要集中在平面蜂窝夹层结构上,而对于曲面结构的相关研究甚少.本文对双曲面蜂窝夹芯进行了力学分析,建立了曲面蜂窝夹层板的等效力学模型,同时建立了双曲面蜂窝夹层板详细模型和基于三明治夹层板理论以及曲面夹层板理论的等效模型,最后通过有限元方法对...     

BENDING RESPONSES OF AN EXPONENTIALLY GRADED SIMPLY-SUPPORTED ELASTIC/VISCOELASTIC/ELASTIC SANDWICH PLATE

The bending response for exponentially graded composite (EGC) sandwich plates is investigated.The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories.Four types of sandwich plates are considered taking into account the symmetry of the plate and the thickness of each layer.The effective moduli and Illyushin’s approximation methods are used to solve the equations governing the bending of simply-supported EGC fiber-reinforced viscoelastic sandwich plates.Then numerical results for deflections and stresses are presented and the effects due to time parameter,aspect ratio,side-to-thickness ratio and constitutive parameter are investigated.     

Natural Frequency for Rectangular Orthotropic Corrugated-Core Sandwich Plates with All Edges Simply-Supported

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分析蜂窝夹芯板脱胶问题的片条合成-能量法

本文提出了分析蜂窝夹芯板脱胶问题的片条合成－能量法。在文献[2]建立的分析模型的基础上，根据分析蜂窝夹芯梁脱胶问题得到的位移模态，用片条合成的方法构造蜂窝夹芯脱胶板的位移模态，然后用最小势能原理进行求解，得到了位移幅值，应力分布和幅值。通过算例对本文方法的适用性和有效性进行了讨论，分析表明本文的结果与文献[2]中双三角级数解法所得的结果吻合的很好。而利用片条合成－能量法，可以得到蜂窝夹芯板脱胶问题的闭合形式解答，便于工程应用。     

The resistance of metallic plates to localized impulse

The responses of metallic plates and sandwich panels to localized impulse are examined by using a dynamic plate test protocol supported by simulations. The fidelity of the simulation approach is assessed by comparing predictions of the deformations of a strong-honeycomb-core panel with measurements. The response is interpreted by comparing and contrasting the deformations with those experienced by the same sandwich panel (and an equivalent solid plate) subjected to a planar impulse. Comparisons based on the center point displacement reveal the following paradox. The honeycomb panel is superior to a solid plate when subjected to a planar impulse, but inferior when localized. The insights gained from an interpretation of these results are used to demonstrate that a new design with a doubly-corrugated soft core outperforms solid plates both for planar and localized impulses.     

Metallic sandwich panels subjected to multiple intense shocks

The mechanical response and fracture of metal sandwich panels subjected to multiple impulsive pressure loads (shocks) were investigated for panels with honeycomb and folded plate core constructions. The structural performance of panels with specific core configurations under multiple impulsive pressure loads is quantified by the maximum transverse deflection of the face sheets and the core crushing strain at mid-span of the panels. A limited set of simulations was carried out to find the optimum core density of a square honeycomb core sandwich panels under two shocks. The panels with a relative core density of 4%–5% are shown to have minimum face sheet deflection for the loading conditions considered here. This was consistent with the findings related to the sandwich panel response subjected to a single intense shock. Comparison of these results showed that optimized sandwich panels outperform solid plates under shock loading. An empirical method for prediction of the deflection and fracture of sandwich panels under two consecutive shocks – based on finding an effective peak over-pressure – was provided. Moreover, a limited number of simulations related to response and fracture of sandwich panels under multiple shocks with different material properties were performed to highlight the role of metal strength and ductility. In this set of simulations, square honeycomb sandwich panels made of four steels representing a relatively wide range of strength, strain hardening and ductility values were studied. For panels clamped at their edge, the observed failure mechanisms are core failure, top face failure and tearing at or close to the clamped edge. Failure diagrams for sandwich panels were constructed which reveal the fracture and failure mechanisms under various shock intensities for panels subjected to up to three consecutive shocks. The results complement previous studies on the behavior and fracture of these panels under high intensity dynamic loading and further highlights the potential of these panels for development of threat-resistant structural systems.