Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates

In the present study, (i) the classical Von Kárman theory, (ii) the first-order shear deformation theory and (iii) the higher-order (third-order) shear deformation theory are compared for studying the nonlinear forced vibrations of isotropic and laminate composite rectangular plates. In particular, the harmonic response in the frequency neighborhood of the fundamental mode of rectangular plates is investigated and the response curves computed by using the three different theories are compared. The boundary conditions of the plates are simply supported with immovable edges. Geometric imperfections are taken into account. Calculations for isotropic and laminated composite plates are presented and results are discussed. For isotropic plates, the frequency-response curves for large-amplitude vibrations obtained by using the three theories are almost coincident. For laminated composite plates, differences arise for relatively thick plates (ratio between the thickness and the edge equal to 0.1), while for thin plates (ratio between the thickness and the edge equal to 0.01), no difference is obtained. For all cases, the first-order shear deformation (with shear correction factor ) and the higher-order shear deformation theories give practically coincident results and differences are observed with respect to the classical Von Kárman theory.     

Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

In this paper, the incremental finite element equations for geometric non-linear analysis of piezoelectric smart structures are developed using a total Lagrange approach by using virtual velocity incremental variational principles. A four-node first order shear plate element model with reduced and selective integration is also developed. Geometrically non-linear transient vibration response and control of plates with piezoelectric patches subjected to pulse loads are investigated. Active damping is introduced on the plates by coupling a self-sensing and negative velocity feedback algorithm in a closed control loop. The numerical results show that piezoelectric actuators can introduce significant damping and suppress transient vibration effectively. The effects of the number and locations of the piezoelectric actuators on the control system are also discussed.     

A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness

This paper presents a simple and general variational approach for the study of the free vibration behaviour of polygonal isotropic plates with variable thickness. The Reissner-Mindlin plate theory is used to take into account the effects of shear deformation and rotary inertia in the analysis. Moreover, this theory allows obtaining greater accuracy of frequency coefficients corresponding to vibration higher modes, even for the thin plates.The governing eigenvalue equation is obtained employing the Ritz method. The plate geometry is approximated by using non-orthogonal triangular co-ordinates, while sets of independent polynomials, expressed in these co-ordinates, are employed to approximate the displacement and rotation fields. The developed algorithm allows obtaining approximated analytical solutions for plates with different aspect ratios, thickness variation and boundary conditions, including edges elastically restrained by both translational and rotational springs. Therefore, a unified program has been easily implemented. Convergence and comparison analyzes are carried out to verify the reliability and accuracy of the numerical solutions. Finally, sets of parametric studies are performed and the results are given in graphical and tabular form.     

Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite

We propose and demonstrate a new saturable absorber based on a fiber taper embedded in a carbon nanotube/polymer composite. Greater than a 10% reduction in absorption (due to saturation) is directly measured for our saturable absorber. Using an embedded fiber-taper saturable absorber, we built an all-fiber mode-locked ring laser, which produces 594 fs/1.7 nJ pulses with a repetition rate of 13.3 MHz.     

Natural frequencies and vibration modes of laminated composite plates reinforced with arbitrary curvilinear fiber shape paths

The development of tow-placement technology has made it possible to control fiber tows individually and place fibers in curvilinear distinct paths in each layer of a laminated plate. This paper presents an analytical method for determining natural frequencies and vibration modes of laminated plates having such curvilinear reinforcing fibers. Spline functions are employed to represent arbitrarily shaped fibers, and Ritz solutions are used to derive frequency equations using series type shape functions. The strain energy is evaluated by numerical integration involving the fiber orientation angle, and is calculated using the derivative of the spline function in minute intervals. The results show that the natural frequencies obtained by the present method agree well with results from finite element analyses. The vibration mode shape contour plots of the plates are seen to reflect clear influences of the fiber shapes.     

Multi-scale bending,buckling and vibration analyses of carbon fiber/carbon nanotube-reinforced polymer nanocomposite plates with various shapes

Using a finite element-based multi-scale modeling approach, the bending, buckling and free vibration of hybrid polymer matrix composites reinforced by carbon fibers and carbon nanotubes (CF/CNT-RP) are analyzed herein. Thick composite plates with rectangular, circular, annular and elliptical shapes are considered. First, the equivalent material properties of CF/CNT-RP are calculated for different volume fractions of CF and CNT. To accomplish this aim, a two-step procedure is presented through which the coupled effects of nano- and micro-scale are taken into account. In the first step, modeling of dispersion of CNTs into the polymer matrix is done with considering interphase formed by their chemical interaction with the matrix, and the equivalent properties of resulting composite material are determined accordingly. CFs are then dispersed into CNT-RP which is considered a homogenous material in this step. Both distributions of CNTs and CFs are assumed to be random. After computing the equivalent properties of CF/CNT-RP for different volume fractions of its constituents, the bending, buckling and free vibration analyses of plates with different shapes are performed. It is shown that the reinforcement of the polymer matrix with both CF and CNT significantly affects the bending, buckling and free vibration characteristics of plates.     

Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.     

Semi-analytical study of free vibration characteristics of shear deformable filament wound anisotropic shells of revolution

Free vibration characteristics of filament wound anisotropic shells of revolution are investigated by using multisegment numerical integration technique in combination with a modified frequency trial method. The applicability of multisegment numerical integration technique is extended to the solution of free vibration problem of anisotropic composite shells of revolution through the use of finite exponential Fourier transform of the fundamental shell equations. The governing shell equations comprise the full anisotropic form of the constitutive relations, including first-order transverse shear deformation, and all components of translatory and rotary inertia. The variation of the stiffness coefficients along the axis of the shell is also incorporated into the solution method. Filaments are assumed to be placed along the geodesic fiber path on the shell of revolution resulting in the variation of the stiffness coefficients along the axis of the composite shell of revolution with general meridional curvature. Sample solutions have been performed on the effect of the variation of the stiffness coefficients on the free vibration behavior of filament wound truncated conical and spherical shells of revolution.     

磁致伸缩/压电叠层复合材料磁-机-电耦合系数分析

分析和推导了磁致伸缩/压电叠层复合材料的机-电耦合系数、磁-机耦合系数及磁-电耦合系数与磁致伸缩层和压电层性能参数及几何参数之间的关系.进一步分析表明,叠层复合材料低频时的磁电电压系数正比于磁-电耦合系数,谐振时的磁电电压系数正比于磁-电耦合系数与机械品质因素的乘积;磁电电压系数还与复合结构的本征阻抗有关,本征阻抗越大磁电电压系数越大.通过性能差异较大的Terfenol-D和FeNi基弹性合金分别与压电材料PZT5-H和PZT8相互组合构成复合材料的比较分析,进一步阐明了磁电复合材料磁-电耦合系数和机械品 关键词： 磁电效应 磁-机-电耦合系数 磁致伸缩材料 压电材料     

Closed-form solution for free vibration of piezoelectric coupled annular plates using Levinson plate theory

Free vibration analysis of annular moderately thick plates integrated with piezoelectric layers is investigated in this study for different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Levinson plate theory (LPT). The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study the closed-form solution for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. To demonstrate the accuracy of the present solution, comparison studies is first carried out with the available data in the literature and then natural frequencies of the piezoelectric coupled annular plate are presented for different thickness-radius ratios, inner-outer radius ratios, thickness of piezoelectric, material of piezoelectric and boundary conditions. Present analytical model provides design reference for piezoelectric material application, such as sensors, actuators and ultrasonic motors.     

Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix

In the current work, the nonlinear vibration of an embedded double-walled carbon nanotube (DWCNT) aroused by nonlinear van der Waals (vdW) interaction forces from both surrounding medium and adjacent tubes is studied. Using both Euler–Bernoulli and Timoshenko beam models, the relation between deflection amplitudes and resonant frequencies of the DWCNT is derived through harmonic balance method. It is found that the nonlinear vdW forces from the surrounding medium result in noncoaxial vibration of the embedded DWCNT. The noncoaxial vibration includes both uni-directional and bi-directional vibration modes. It is found that the surrounding matrix has more prominent effect on the uni-directional vibration in comparison to the bi-directional vibration. The axial load effect on the vibrational behavior of the embedded DWCNT is also discussed. Due to the influence of the surrounding polymer, the prediction on the resonant frequencies of embedded CNTs is quite different from that for free-standing CNTs. A softening behavior for the deflection amplitude-resonant frequency relation is observed for the first time in the bi-directional vibration of the embedded DWCNT, which can only be obtained using the Timoshenko beam theory.     

A modified axisymmetric finite element for the 3-D vibration analysis of piezoelectric laminated circular and annular plates

A finite element is presented to analyze the three-dimensional (3-D) vibration of piezoelectric coupled circular and annular plates. The proposed finite element is a modification of a conventional axisymmetric finite element and is capable of conducting both axisymmetric and nonaxisymmetric vibration analysis of circular and annular laminated plates, with piezoelectric layers therein. The present formulation, a two-dimensional model itself, can investigate 3-D vibration of those plates for a preselected number of nodal diameters, and is therefore more economical than the conventional 3-D finite element analysis, yet still has almost the same accuracy and versatility as the 3-D analysis. In cases such as analysis of stators of traveling wave ultrasonic motors where only vibration modes with particular numbers of nodal diameters are of interest, the proposed approach is very convenient and useful.     

Free vibration of antisymmetric,angle-ply laminated plates including transverse shear deformation by the finite element method

A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented. The theory is a generalization of Mindlin's theory for isotropic plates to laminated anisotropic plates and includes shear deformation and rotary inertia effects. Finite element solutions are presented for rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of a highly anisotropic composite material. Two sets of material properties that are typical of high modulus fiber-reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. The numerical results are compared with the closed form results of Bert and Chen. As a special case, numerical results are presented for thick isotropic plates, and are compared with those for 3-D linear elasticity theory and Mindlin's thick plate theory.     

Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to determine the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.     

碳纳米管/聚苯胺纳米复合管的制备及其微波介电特性研究

用原位乳液聚合法在碳纳米管表面包覆聚苯胺，制备出了碳纳米管/聚苯胺一维纳米复合管.复合管的直径为50—80 nm，聚苯胺包覆层的厚度为20—30 nm，聚苯胺在碳纳米管表面以层状和枝晶状两种形态生长.研究了碳纳米管/聚苯胺复合管在2—18 GHz的微波介电特性.与纯碳纳米管相比，碳纳米管/聚苯胺复合管的介电常数的实部ε′和虚部ε″在2—18 GHz随频率变化较小，在低频波段介电常数值较小，作为微波吸收剂容易实现与自由空间的阻抗匹配，而且它的介电损耗角正切(tanδ=ε″/ε′)较高，是一种很好的微波吸收剂. 关键词： 碳纳米管 聚苯胺 微波介电特性 微波吸收剂     

Investigating the effect of interphase and surrounding resin on carbon nanotube free vibration behavior

The free vibration analysis of a carbon nanotube (CNT) embedded in a volume element is performed using 3D finite element (FE) and analytical models. Three approaches consist of molecular and continuum mechanics FE methods and continuum analytical method are employed to simulate the CNT, interphase region and surrounding matrix. The bonding between CNT and polymer is treated as non-perfect bonding using van der Waals and triple phase material interaction in first and second approaches. In analytical approach a perfect bonding is assumed between nanotube and matrix. First, natural frequencies of CNT under different boundary conditions and aspect ratios are obtained by three approaches and the results are compared with published data. The results show the frequency response variations of CNT in GHz to THz range. Subsequently, vibration behaviors of CNT/polymer are evaluated and the results revealed the importance of interphase region role in the performance of nanocomposites. The results also showed the convergence of the natural frequencies for 1–2.5% of CNT volume in high aspect ratios using three methods, so that the interphase effects is negligible. In addition, it is observed that the molecular method due to interphase role has proper performance in vibration behavior investigation of volume elements.     

Impedance spectroscopy of carbon nanotube/solid polymer electrolyte composites

New composite polymer electrolytes (CPE) have been prepared by a solution-casting technique, using polyethylene oxide, lithium hexafluorate (LiPF₆) as the doping salt, ethylene carbonate (EC) as the plasticizer and amorphous carbon nanotubes (αCNTs) as the filler. The crystallinity and ionic conductivity of the CPE are examined. Differential scanning calorimetry shows a decrease in melting temperature and crystallinity upon the addition of LiPF₆, EC and αCNTs to the polymer electrolyte system. The addition of salt increases the conductivity up to 10⁻⁵ S cm⁻¹. The incorporation of EC and αCNTs into the salted polymer shows a significant conductivity increase of 10⁻⁴ and 10⁻³ S cm⁻¹. The complexation process is examined using Fourier transform infrared spectroscopy. The Vogel-Tamman-Fulcher (VTF) plots suggest that the temperature dependence of conductivity is a thermally activated process.     

Relation between interfacial shear strength and compressive strength of carbon fiber/epoxy resin composite strands

The mechanism with which the fiber-matrix interfacial strength exerts its influence on the compressive strength of fiber reinforced composites has been studied by measuring the axial compressive strength of carbon fiber/epoxy resin unidirectional composite strands having different levels of interfacial shear strength. The composite strands are used for experiments in order to investigate the compressive strength which is not affected by the delamination taking place at a weak interlayer of the laminated composites. The interfacial strength is varied by applying various degrees of liquid-phase surface treatment to the fibers. The efficiency of the compressive strength of the fibers utilized in the strength of the composite strands is estimated by measuring the compressive strength of the single carbon filaments with a micro-compression test. The compressive strength of the composite strands does not increase monotonically with increasing interfacial shear strength but showes lower values at higher interfacial shear strengths. With increasing interfacial shear strength, the suppression of the interfacial failure in the misaligned fiber region increases the compressive strength, while at higher interfacial shear strengths, the enhancement of the crack sensitivity decreases the compressive strength.