Vibration suppression of laminated composite beams with a piezo-electric damping layer

An analytical formulation is derived for modelling the behaviour of laminated composite beams with integrated piezoelectric sensor and actuator. The major difference in approach to the solution compared to previous studies is that the analytical solution for active vibration control and suppression of smart laminated composite beams is presented in this paper. The governing equation is based on the first-order shear deformation theory (Mindlin plate theory), which is applicable for both thin and moderately beams, and includes the coupling between mechanical and electrical deformations. The voltage generated by the sensor layer and response of the beam to the actuator voltage can be computed independently. In this study, the new assumption of harmonic vibration is introduced, which includes both of the sine and cosine terms. Another contribution of this paper is introducing the transformation method of complex numbers to reduce the order of the governing equation of smart laminated beams. Thus, the exact solution of the reduced governing equation can be obtained by using MATLAB and the entire numerical results are presented. The behaviour of the output voltage from the sensor layer and the input voltage acting on the actuator layer is also studied. Graphical results are presented to demonstrate the ability of closed-loop system to actively control the vibration of laminated beams and it shows a good control effect. The influence of stacking sequence on the controlled transient response of the laminated beam is examined. Finally, the experiential formulation of the amplitude of beam vibration varying with the negative velocity feedback control gain has also been evaluated. The present method has a general application in this field of study.     

Fabrication and mechanical testing of glass fiber entangled sandwich beams: A comparison with honeycomb and foam sandwich beams

The aim of this paper is the fabrication and mechanical testing of entangled sandwich beam specimens and the comparison of their results with standard sandwich specimens with honeycomb and foam as core materials. The entangled sandwich specimens have glass fiber cores and glass woven fabric as skin materials. The tested glass fiber entangled sandwich beams possess low compressive and shear modulus as compared to honeycomb and foam sandwich beams of the same specifications. Although the entangled sandwich beams are heavier than the honeycomb and foam sandwich beams, the vibration tests show that the entangled sandwich beams possess higher damping ratios and low vibratory levels as compared to honeycomb and foam sandwich beams, making them suitable for vibro-acoustic applications where structural strength is of secondary importance, e.g., internal paneling of a helicopter.     

A damping analysis of composite laminates using the closed form expression for the basic damping of Poisson's ratio

Various methods have been presented to obtain the effective damping of a symmetric laminated composite. In this paper, modified classical lamination theory based upon the elastic–viscoelastic correspondence principle was utilized by developing the basic damping of Poisson's ratio for accurately predicting the damping of laminated composite beams. The analysis involves an extension of the elastic–viscoelastic approach. Futhermore, Ni and Adams' theory was used for verifying the modified classical lamination theory. Six typical laminated composites with [±θ]_s,[0/θ]_s,[0/±θ/90]_s,[90/±θ/0]_s,[0/90/±θ]_s and [90/0/±θ]_s, stacking sequences were employed for this study. Numerical results have shown that damping values were in some difference among prediction methods over the particular range of fiber orientation.     

Vibration characteristics of laminated composite beams with magnetorheological layer using layerwise theory

Vibration characteristics of laminated composite beams with magnetorheological (MR) layer are investigated using layerwise theory. In most studies, shear strain across the thickness of MR layer has been considered as a constant value, which does not precisely describe the shear strain. In this study, layerwise theory is employed to develop a finite element formulation to investigate MR-laminated beams. Experimental tests under different magnetic fields are carried out to verify the numerical results. Layerwise numerical results are compared with the experimental results and other theories. An empirical expression for complex shear modulus is presented. The effects of MR layer thickness on vibration of MR-laminated beams are examined.     

基于剪切耗能假设的黏弹性夹芯梁的振动和阻尼特性

基于一阶剪切变形理论和哈密顿原理建立了三层粘弹性夹芯梁结构的有限元模型并对其振动和阻尼特性进行了研究。建模时认为粘弹材料层不可压缩,振动能量是依靠粘弹性层的剪切变形来耗散的。为验证本模型的正确性,将其与解析解作了对比。同时,为了证明本方法的优越性,将其与常用的“实特征模态”、“近似复特征模态”、“钻石法”和“近似法”四种数值方法做了比较。结果表明本方法的精度在这几种数值方法中是最好的。最后,讨论了粘弹性夹芯梁结构参数变化对系统固有频率和损耗因子的影响,得到了一些有工程实际意义的结论。     

A numerical study of free and forced vibration of composite sandwich beam with viscoelastic core

In this article, higher order theory for sandwich beam with composite faces and viscoelastic core is achieved by considering independent transverse displacements on two faces and linear variations through the depth of the beam core. In addition, the effects of Young modulus, rotational inertia and core kinetic energy are considered to modify the “Mead & Markus” theory that is used frequently for sandwich beam. These assumptions have not been considered together in previous articles. A finite element code is developed for structural response analysis of the free and forced vibration. The obtained results are compared with the corresponding results of previous researches. The effects of impressive parameters including fiber angle, thickness of faces and core thickness on the loss factors and natural frequencies of the beam are examined. Frequency response of the beam for two cases, constant and frequency dependent core shear modulus are obtained. Finally, time response of the beam is presented based on the Newmark method. Obtained results show that, when the core is soft or hard, “Mead & Markus” theory cannot accurately predict the frequency responses of the system in comparison with the presented theory in this paper; whereas for moderately hard core, both methods lead to the same results. In addition, when the beam is unsymmetrical about its neutral axis, i.e. one face sheet is weaker than the other face sheet, the inaccuracy of the “Mead & Markus” theory increases, even at low frequencies.     

A mixed‐enhanced finite‐element for the analysis of laminated composite plates

This paper presents a new 4‐node finite‐element for the analysis of laminated composite plates. The element is based on a first‐order shear deformation theory and is obtained through a mixed‐enhanced approach. In fact, the adopted variational formulation includes as variables the transverse shear as well as enhanced incompatible modes introduced to improve the in‐plane deformation. The problem is then discretized using bubble functions for the rotational degrees of freedom and functions linking the transverse displacement to the rotations. The proposed element is locking free, it does not have zero energy modes and provides accurate in‐plane/out‐of‐plane deformations. Furthermore, a procedure for the computation of the through‐the‐thickness shear stresses is discussed, together with an iterative algorithm for the evaluation of the shear correction factors. Several applications are investigated to assess the features and the performances of the proposed element. Results are compared with analytical solutions and with other finite‐element solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

粘弹性复合材料夹芯板的稳态响应分析

芯材采用Kelvin粘弹性本构模型,推导了复合材料夹芯板的动力学方程,运用模态正交原理,以Navier完备解形式求解了四边简支正交对称铺层层合板的稳态响应,并给出了固有频率和结构损耗因子的解析解。通过固有频率的有限元解对比验证了数值计算的可靠性。分析了芯材剪切模量和芯材厚度对结构固有频率和损耗因子的影响。探讨了稳态响应的收敛性,并得到结构稳态响应振幅与频率的关系,分析了芯材损耗因子对结构稳态响应的影响。结果表明：芯材剪切模量存在最佳设计值;结构首阶模态特性主导结构的稳态动态响应。     

A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation

Based on a modified couple stress theory, a model for composite laminated beam with first order shear deformation is developed. The characteristics of the theory are the use of rotation–displacement as dependent variable and the use of only one constant to describe the material’s micro-structural characteristics. The present model of beam can be viewed as a simplified couple stress theory in engineering mechanics. An example as a cross-ply simply supported beam subjected to cylindrical bending loads of f_w = q₀ sin (πx/L) is adopted and explicit expression of analysis solution is obtained. Numerical results show that the present beam model can capture the scale effects of microstructure, and the deflections and stresses of the present model of couple stress beam are smaller than that by the classical beam mode. Additionally, the present model can be reduced to the classical composite laminated Timoshenko beam model, Isotropic Timoshenko beam model of couple stress theory, classical isotropic Timoshenko beam, composite laminated Bernoulli–Euler beam model of couple stress theory and isotropic Bernoulli–Euler beam of couple stress theory.     

Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory

This article proposes a higher-order shear deformation beam theory for free vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in a thermal environment. The temperature-dependent material properties of functionally graded carbon nanotube-reinforced composite beams are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. The governing equations and boundary conditions are derived by using Hamilton's principle, and the Navier solution procedure is used to achieve the natural frequencies of the sandwich beam in a thermal environment. A parametric study is led to carry out the effects of carbon nanotube volume fractions, slenderness ratio, and core-to-face sheet thickness ratio on free vibration behavior of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Numerical results are also presented in order to compare the behavior of sandwich beams including uniformly distributed carbon nanotube-reinforced composite face sheets to those including functionally graded carbon nanotube-reinforced composite face sheets.     

A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates

In this paper, a nth-order shear deformation theory is proposed to analyze the free vibration of laminated composite plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy’s third-order theory can be considered as a special case of present nth-order theory (n = 3). Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties are computed by present nth-order theory and a meshless radial point collocation method based on the thin plate spline radial basis function. The results are compared with available published results which demonstrate the accuracy and efficiency of present nth-order theory.     

A cell‐based smoothed discrete shear gap method (CS‐FEM‐DSG3) based on the C0‐type higher‐order shear deformation theory for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle

A cell‐based smoothed discrete shear gap method (CS‐FEM‐DSG3) based on the first‐order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. In this paper, the CS‐FEM‐DSG3 is extended to the C⁰‐type higher‐order shear deformation plate theory (C⁰‐HSDT) and is incorporated with damping–spring systems for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle. At each time step of dynamic analysis, one four‐step procedure is performed including the following: (1) transformation of the weight of a four‐wheel vehicle into the sprung masses at wheels; (2) dynamic analysis of the sprung mass of wheels to determine the contact forces; (3) transformation of the contact forces into loads at nodes of plate elements; and (4) dynamic analysis of the plate elements on viscoelastic foundations. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available numerical results. Copyright © 2014 John Wiley & Sons, Ltd.