基于复合耗能假设的黏弹夹芯梁振动的有限元分析

建立了一种新的有限元模型用于研究黏弹夹芯梁的振动和阻尼特性。该模型同时考虑了黏弹性层的剪切和压缩阻尼。建模时将约束层和基梁层视作欧拉-伯努利(Euler-Bernoulli)梁,假定中间黏弹性层同时承受纵向剪切和横向压缩变形以耗散振动能量。应用该模型研究了不同边界条件和几何参数的黏弹夹芯梁结构的振动和阻尼特性。通过与精确解析法及其它常用数值法的对比,结果证明该模型具有良好的精度和适用性,在对夹芯梁结构固有频率和损耗因子的预测中,其精度要高于常规的几种数值模型。最后通过实验结果进一步地验证了该有限元模型的正确性。     

Biot本构模型黏弹夹芯梁振动特性分析及其实验研究

黏弹夹芯结构广泛用于薄壁构件的振动和噪声抑制,对其动力学行为的研究一直广受重视。以黏弹夹芯梁为研究对象,提出了一种建立其有限元动力学模型的方法。建模时弹性表面层按欧拉梁处理,中间黏弹性层不可压缩,认为阻尼来只自其纵向剪切变形。Biot本构模型用来描述黏弹性材料参数的频率依赖性动力学行为,通过耗散坐标将其引入到黏弹夹芯梁的有限元方程中。最后对黏弹夹芯梁结构的振动和阻尼特性进行了数值分析及实验研究。结果表明所提出的夹芯梁有限元建模方法是正确、简单和有效的,对工程实际应用具有一定的参考价值。     

阻尼夹芯复合材料加筋板的振动分析与数值模拟

以阻尼夹芯复合材料加筋板为研究对象,依据一阶剪切变形理论(FSDT)和Hamilton原理,推导板和加强筋的应变能、动能表达式,采用变分原理建立控制微分方程,根据相关边界条件和傅里叶级数求解方程。建立了ANSYS阻尼夹芯复合材料加筋板的有限元模型,该模型考虑到阻尼夹芯复合材料加筋板中阻尼材料与纤维预浸料间的结合方式,用模态应变能有限元数值模拟方法研究了结构的动力学性能,并通过对数值模拟结果与理论解的比较,验证了模型的合理性和有效性。探讨了不同的筋条尺寸、不同的筋条数量、不同的筋条分布方式对阻尼夹芯复合材料加筋板动力学性能的影响,得出了阻尼夹芯复合材料加筋板的一阶模态频率和损耗因子随不同参数的变化曲线,其结论为阻尼夹芯复合材料加筋板的优化设计提供参考。     

夹芯复合材料结构阻尼特性研究

从粘弹性材料的本构关系出发,应用复特征值理论推导了夹芯复合材料结构阻尼的计算方法;同时基于能量损耗原理和阻尼的产生机理,研究了夹芯复合材料结构阻尼计算的模态应变能方法;提出了两种承载/减振夹芯复合材料结构模型,应用动态力学热分析方法测量了芯材的阻尼参数;应用两种阻尼计算理论和有限元数值分析相结合的方法研究了两种夹芯结构模型的损耗因子,并与试验结果进行了比较;分析了夹芯厚度对结构损耗因子的影响.     

轴向运动粘弹性夹层梁热力耦合振动频率分析

研究了温度场与位移场相互耦合时,轴向运动粘弹性夹层梁的横向振动特性。基于Euler-Bernouli梁理论和Kelvin粘弹性材料本构关系,建立了轴向运动粘弹性夹层梁横向振动控制方程;考虑材料变形与传热的相互影响,得到相应的热力耦合状态下轴向运动粘性夹层梁的耦合控制方程。采用Galerkin截断得到相应的热力耦合动力系统。用数值方法分析了相关热参数对梁振动频率的影响。     

利用厚度剪切压电效应的自适应压电复合材料夹芯结构的研究

提出了利用厚度剪切压电效应的压电复合材料(PCM TS) 作为夹芯结构芯材的新型驱动方式, 分析了PCM TS 的驱动原理。针对含有1-3 型PCM TS 芯材的夹芯梁结构, 实验研究了PCM TS 在静电场作用下的驱动特性, 并利用PCM TS 芯材对夹芯梁的振动进行了主动控制实验。结果表明, 利用PCM TS 作为驱动元件, 夹芯梁获得了比较理想的变形量, 其振动也能得到较为有效的控制, 因此是一种很有应用前途的驱动方式。      

一种高阶模态涡振试验新气弹模型的模型参数优化设计

多点弹性支撑连续梁气弹模型是一种研究大跨桥梁主梁高阶竖弯模态涡激振动的新型气弹模型。为了使该模型的频率、模态质量和振型与原桥梁缩尺后的动力特征更好地匹配,提出了基于动力系统矩阵方程的模型参数优化方法。以模型的频率、模态质量和振型为优化目标,利用结构的振动方程,建立优化目标函数,采用最小二乘法获得芯梁刚度、弹簧刚度和附加质量的最优设计。通过数值分析对该方法进行了验证分析。以两座不同形式的悬索桥为例进行了该方法的可行性分析。研究结果表明:采用该方法设计的气弹模型能很好地与原结构相匹配。     

共固化阻尼薄膜夹嵌复合材料梁的振动分析EI北大核心CSCD

为研究共固化阻尼薄膜夹嵌复合材料固支梁的自由振动特性。将1阶剪切变形理论、变分原理和Hamilton原理相结合,建立了共固化阻尼薄膜复合材料梁自由振动的理论模型,提出使用伽辽金法求解该模型在固支边界条件下的自由振动理论解。通过构建有限元模型、制作阻尼薄膜夹嵌复合材料梁试件与所搭建的试验平台,分别将理论解与模拟结果、试验结果进行对比,验证了理论模型的有效性;最后,进一步探究了阻尼层在复合材料中的分布以及结构几何参数对阻尼薄膜夹嵌复合材料梁动力学性能影响的规律,为阻尼薄膜复合材料梁结构的优化设计提供理论依据。     

斜入射下水中隐身夹芯复合材料附体结构声学设计

摘 要：将隐身夹芯复合材料代替附体结构钢质壳板,建立了斜入射条件下水中隐身夹芯复合材料结构的声学模型;从水声波动方程出发,推导了二维空间声波斜入射时的传递矩阵,及带空腔水附体结构的声反射系数和吸声系数表达式;对带空腔水附体结构模型进行了垂直入射声学试验,试验结果与传递矩阵法数值计算吻合较好;对试验模型进行了斜入射下声学性能数值计算,分析了入射角对反射系数和吸声系数的影响;考虑斜入射下夹芯层厚度、密度、损耗因子、及水层厚度等对隐身附体结构声学性能的影响,应用数值方法对水中隐身夹芯复合材料附体结构进行了声学设计,分析了各层材料参数和几何参数对隐身结构反射系数和吸声系数的影响规律。     

主动约束层阻尼结构的一种新模型

提出一种主动约束层阻尼结构的新力学模型.该模型假定阻尼层既横向剪切变形又横向拉压变形,主动约束层和基层存在不同的横向位移.使用有限元法建立主动约束层阻尼梁的动力学方程,并针对典型算例进行数值计算.与传统模型比较发现:粘弹性层的横向拉压变形不但会影响系统的动态特性,而且会降低压电层的主动控制作用.研究表明,粘弹性层横向压缩变形不应忽略.     

Vibration Modeling of Multilayer Composite Structures with Viscoelastic Layers

This work deals with the vibration of orthotropic multilayer sandwich structures with viscoelastic core. A finite element model is derived from a classical zigzag model with shear deformation in the viscoelastic layer. The aim of the present work is to establish numerical models and develop numerical tools to design multilayer composites structures with high damping properties. To fulfill this purpose, a finite element model has been developed for vibration analysis of a sandwich plate (elastic orthotropic)/(viscoelastic orthotropic)/(elastic orthotropic). A numerical study from the variation of the damping properties of the structures was performed according to the faces materials fibers orientation.     

Free vibration analysis of simply supported sandwich beams with lattice truss core

Free vibration of AISI 304 stainless steel sandwich beams with pyramidal truss core is investigated in the present paper. The lattice truss core is transformed to a continuous homogeneous material. Considering the deformation characteristics of the sandwich beam, the following assumptions are made: (1) the thickness of the sandwich beam remains constant during deformation; (2) for the thin face sheets, only bending deformation is considered, neglecting the effect of transverse shear deformation; (3) for the core, only shear deformation is considered as the core is too weak to provide a significant contribution to the bending stiffness of the sandwich beam. The shear stress is assumed to be constant along the thickness of the core. The governing equation of free vibration is derived from Hamilton's principle, and the natural frequencies are calculated under simply supported boundary conditions. Finally, numerical simulation is carried out to get the mode shapes and natural frequencies. Our results show that the theoretical solutions agree well with the numerical results. It indicates the present method would be useful for free vibration analysis of sandwich beams with lattice truss core.     

考虑芯层横向变形的粘弹性复合材料夹层板结构的声振特性分析

夹层板结构具有很高的比强度和比刚度。若芯层采用粘弹性阻尼材料，夹层板结构还具有良好的隔振和隔声特性，因此在工程结构中得到广泛应用。以往的夹层板理论大多忽略了芯层的横向正应变和横向正应力，在分析芯层较厚的夹层板或者夹层结构的高频振动问题时由于不能体现芯层的横向压缩变形，往往显得不够合理。针对这一不足，构造了一个复合材料夹层板单元：夹层板的上下面板采用基于一阶剪切变形理论的Mindlin假定以及层合板理论进行分析；采用文献[6，7]中提出的Timoshenko层合厚梁理论构造了单元每边的转角和剪应变场，消除了Mindlin板单元当板厚变小时的剪切锁死问题；假定芯层的位移沿厚度方向线性变化，并用上下面板的自由度表示，最终形成以上下面板自由度表示的系统总的运动方程。该单元不仅考虑了芯层的横向剪切变形，还考虑了芯层的横向压缩变形。数值计算结果表明：无论对于静力问题、动力问题还是声辐射等问题，考虑芯层的横向压缩变形是合理的，也是有必要的。     

A layerwise finite element formulation for vibration and damping analysis of sandwich plate with moderately thick viscoelastic core

Abstract

Most previous studies of viscoelastic sandwich plates were based on the assumption that damping was only resulting from shear deformation in the viscoelastic core. However, extensive and compressive deformations in the viscoelastic core should also be considered especially for sandwich plates with moderately thick viscoelastic core. This paper presents a finite element formulation for vibration and damping analysis of sandwich plates with moderately thick viscoelastic core based on a mixed layerwise theory. The face layers satisfy the Kirchhoff theory while the viscoelastic core meets a general high-order deformation theory. The viscoelastic core is modeled as a quasi-three-dimensional solid where other types of deformation such as longitudinal extension and transverse compression are also considered. To better describe the distribution of the displacement fields, auxiliary points located across the depth of the sandwich plate are introduced. And based on the auxiliary points, the longitudinal and transverse displacements of the viscoelastic core are interpolated independently by Lagrange interpolation functions. Quadrilateral finite elements are developed and dynamic equations are derived by Hamilton’s principle in the variation form. Allowing for the frequency-dependent characteristics of the viscoelastic material, an iterative procedure is introduced to solve the nonlinear eigenvalue problem. The comparison with results in the open literature validates the remarkable accuracy of the present model for sandwich plates with moderately thick viscoelastic core, and demonstrates the importance of the higher-order variation of the transverse displacement along the thickness of the viscoelastic core for the improvement of the analysis accuracy. Moreover, the influence of the thickness and stiffness ratios of the viscoelastic core to the face layers on the damping characteristics of the viscoelastic sandwich plate is discussed.     

High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexible core

Free vibration analysis of functionally graded material sandwich plates is studied using a refined higher order sandwich panel theory. A new type of FGM sandwich plates, namely, both functionally graded face sheets and functionally graded flexible core are considered. The functionally graded material properties follow a power-law function. The first order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for the core. On the basis of continuities of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are obtained by using Hamilton’s principle. The accuracy of the present approach is validated by comparing the analytical results obtained for a degradation model (functionally graded face sheets and homogeneous flexible core) with ones published in the literatures, as well as the numerical results obtained by finite element method and good agreements are reached. Then, parametric study is conducted to investigate the effect of distribution of functionally graded material properties, thickness to side ratio on the vibration frequencies.     

A Viscoelastic Sandwich Finite Element Model for the Analysis of Passive,Active and Hybrid Structures

In this paper we present a finite element model for the analysis of active sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers, as well as piezoelectric sensor and actuator layers. The model is formulated using a mixed layerwise approach, by considering a higher order shear deformation theory (HSDT) to represent the displacement field of the viscoelastic core and a first order shear deformation theory (FSDT) for the displacement field of the adjacent laminated anisotropic face layers and exterior piezoelectric layers. The dynamic problem is solved in the frequency domain with viscoelastic frequency dependent material properties for the core. Control laws are also implemented for the piezoelectric sensors and actuators. The model behaviour in dynamics is assessed with the few solutions found in the literature, including experimental data, and a laminated composite active sandwich application is proposed. In this numerical application, velocity feedback control law is implemented for active control, using co-located piezoelectric patch sensors and actuators.     

Vibration and Buckling of Truss Core Sandwich Plates on An Elastic Foundation Subjected to Biaxial In-plane Loads

Truss-core sandwich plates are thin-walled structures comprising a truss core and two thin flat sheets. Since no direct analytical solution for the dynamic response of such structures exists, the complex three dimensional (3D) systems are idealized as equivalent 2D homogeneous continuous plates. The macroscopic effective bending and transverse shear stiffness are derived. Two representative core topologies are considered: pyramidal truss core and tetrahedral truss core. The first order shear deformation theory is used to study the flexural vibration of a simply supported sandwich plate. The buckling of the truss core plate on an elastic foundation subjected to biaxial in-plane compressive loads is also investigated. It's found that the lowest buckling loads and modes are dependent on the foundation stiffness as well as bending and transverse shear stiffness of the plate. The geometric parameters of a sandwich plate are optimized to obtain strongest buckling resistance per unit weight. To verify the accuracy of analytical solutions, 3D finite element (FE) models are established, and good agreement is observed between them. It's obvious that the homogenization procedure leads to great savings in computational effort.     

Optimal design and parameter estimation of frequency dependent viscoelastic laminated sandwich composite plates

Recent developments in optimization and parameter estimation of frequency dependent passive damping of sandwich structures with viscoelastic core are presented in this paper. A finite element model for anisotropic laminated plate structures with viscoelastic frequency dependent core and laminated anisotropic face layers has been formulated, using a mixed layerwise approach, by considering a higher order shear deformation theory (HSDT) to represent the displacement field of the viscoelastic core, and a first order shear deformation theory (FSDT) for the displacement fields of adjacent laminated face layers. The complex modulus approach is used for the viscoelastic material behaviour, and the dynamic problem is solved in the frequency domain, using viscoelastic material data for the core, assuming fractional derivative constitutive models. Constrained optimization of passive damping is conducted for the maximisation of modal loss factors, using the Feasible Arc Interior Point Algorithm (FAIPA). Identification of the frequency dependent material properties of the sandwich core is conducted by estimating the parameters that define the fractional derivative constitutive model. Optimal design and parameter estimation applications in sandwich structures are presented and discussed.     

Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations

The investigation of bending response of a simply supported functionally graded (FG) viscoelastic sandwich beam with elastic core resting on Pasternak’s elastic foundations is presented. The faces of the sandwich beam are made of FG viscoelastic material while the core is still elastic. Material properties are graded from the elastic interfaces through the viscoelastic faces of the beam. The elastic parameters of the faces are considered to be varying according to a power-law distribution in terms of the volume fraction of the constituent. The interaction between the beam and the foundations is included in the formulation. Numerical results for deflections and stresses obtained using the refined sinusoidal shear deformation beam theory are compared with those obtained using the simple sinusoidal shear deformation beam theory, higher- and first-order shear deformation beam theories. The effects due to material distribution, span-to-thickness ratio, foundation stiffness and time parameter on the deflection and stresses are investigated.     

玻璃纤维增强塑料夹层板振动能量流可视化研究

为探索复合材料结构在外部激励作用下的振动能量传递及分布特性,基于结构声强法对玻璃纤维增强塑料夹层板的振动能量可视化技术进行了研究。基于结构声强概念,结合复合材料结构层合理论推导了玻璃纤维增强塑料夹层板的结构声强解析表达式;给出了基于有限元数值方法的结构声强可视化计算实现流程,利用Python和Matlab语言编写了相应计算程序;接着从固有频率、振型及结构声强矢量三个方面验证了所提出可视化程序的有效性;以玻璃纤维增强塑料夹层板为例,利用结构声强技术提供的图形信息实现了激励源定位及振动能量传递特性的可视化分析;最后提取了剪切分量、扭转分量和弯曲分量对结构声强矢量的贡献情况,直观展示了剪切分量在振动能量传递过程中的决定性作用。