Vibrations and stability of axially traveling laminated beams

In this paper, vibrations and stability of an axially traveling laminated composite beam are investigated analytically via the method of multiple scales. Based on classical laminated beam theory, the governing equations of motion for a time-variant axial speed are obtained using Newton’s second law of motion and constitutive relations. The method of multiple scales, an approximate analytical method, is applied directly to the gyroscopic governing equations of motion and complex eigenfunctions and natural frequencies of the system are obtained. The stability boundaries of the system near resonance are determined via the Routh-Hurwitz criterion. Finally, a parametric study is conducted which considers the effects of laminate type and configuration as well as the mean speed and amplitude of speed fluctuations on the vibration response, natural frequencies and stability boundaries of the system.     

Flexural Vibrations of Shafts with Delaminations

The purpose of this theoretical work is to present a general model of laminated rotating shaft with circumferential delaminations. The shaft is treated as a thin‐walled composite cylindrical shell. The delamination of constant width is parallel to the shell reference surface and it covers the entire circumference. The edge delamination is modeled by changing the effective reduced stiffnesses of debonded parts. The stabilizing effect of external damping and destabilizing effect of internal damping are taken into account in the dynamic stability analysis. The influence of the relative delamination length and configuration on the critical angular velocity of shaft is shown.     

Delamination of composite plates under tensile load

Conclusions Among the two configurations discussed, the beam has a rather theoretical importance, as an extension and generalization of the cracked beam problem. Unlike this, embedded delaminations can be found often in real constructions. The fact that the maximum value of SERR vs. fibre orientation angle curve for the circular embedded delamination is surpassed by that for the split beam only by three times and by that for the split beam under mode II loading approximately six times means that an embedded delamination can lead to difficulties when the plate is tensed (or compressed — even in an underbuckled state — within the linear approach the non-opening modes of stress concentration will just change their signs when the load changes its sign), especially under a cyclic loading. Of course, the shell model used is fairly rough and does not take in account several features or real delaminations extension and does not allow one to evaluate properly the stress field near the crack front; thus, more analytical and experimental studies would be needed, to establish the crack development process. The 3D analysis is necessary when initiating delaminations are studied, for the beam/plate assumptions can no longer be regarded as necessary since the delamination linear dimensions are comparable to or less than the thickness of the sublaminate.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 45–50, January–February, 1995.     

Mechanics of Delaminations in Laminate Composite Structures

A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.     

Wave propagation in composite multilayered structures with delaminations

Using the Rayleigh–Ritz method, the natural frequencies of layered cylindrical shells with delaminations are derived. The results are compared with FE computations and with data available in the literature. It is demonstrated that the transverse shear effects can play a significant role in a correct and accurate evaluation of the natural frequencies of such shells. Numerical investigations into the problem of radial excitations of cylinders with delaminations have also been performed. From the results obtained, it follows that their optimal excitation frequency is related to the natural frequency of a local region containing the delamination.     

Prediction and Measurement of Residual Strains for a Composite Bonded Joint

A quasi-isotropic composite laminate/adherend of IM6/3501-6 and a composite bonded specimen were manufactured and tested. The bonded specimen was fabricated by postbonding composite adherends together using a 177°C adhesive resin. Predictions for the residual curing strains in the composite adherends and the adhesively bonded composite specimen were performed using a thermomechanical linearly elastic analysis. The analysis was performed using a computer program based on a polynomial spline displacement approximation method [1]. The residual strains of the specimens were measured using the moiré interferometry technique. Diffraction gratings were replicated at room temperature onto the edges of polished laminated adherends and on the edge of a fully cured adhesively bonded specimen. The specimens were cut through their entire thickness in the middle of the diffraction grating area, resulting in a redistribution of the residual curing stresses, with corresponding changes in the strain field at the edges of the cut. A full-field deformation pattern was obtained in the grating area by analyzing the recorded fringe patterns. The deformation field induced by the cut in the laminated adherends and the adhesive bondline were estimated by the linear thermomechanical analysis. A good agreement between the analysis and the experimental results was obtained.     

Influence of free-edge delaminations on the extension-twist coupling of elastically tailored composite laminates

A closed form solution is developed in order to analyze the influence of free-edge delaminations on elastically tailored composite laminates. The analysis is based upon a shear deformation theory and a sublaminate approach. The solution is applied to predict the influence of free-edge delamination on the behavior of a class of laminates exhibiting extension-twist coupling. Comparison of analytical predictions with test data from laminates with mid-plane and off mid-plane free edge delaminations is performed. The results indicate that free-edge delamination can have a significant influence on extension-twist coupling.     

Two-step scheme for solution of the seismic response of liquid-filled composite cylindrical container

This paper presents the seismic response analysis of a cylindrical container made of laminated composite. The analytical homogenization is used for calculation of the material properties of unidirectional fiber-reinforced composite layer. Constitutive relations for laminate within the classical laminate theory are considered. Effective modulus of elasticity is obtained and put into a calculation of internal forces of the laminated composite cylindrical tank. The seismic analysis of liquid storage facilities has to have different approaches as the analysis of typical structures. Because of an earthquake, the hydrodynamic impulsive and convective pressures are generated in addition to hydrostatic pressure. The solved liquid-filled container made of the laminated composite was situated for the region of Slovak Republic and was analyzed in respect of Eurocode 8 recommendations.     

Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory

The free vibration of laminated composite plates on elastic foundations is examined by using a refined hyperbolic shear deformation theory. This theory is based on the assumption that the transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies the conditions of zero shear stresses at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In the analysis, the foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second foundation parameter is zero. The equation of motion for simply supported thick laminated rectangular plates resting on an elastic foundation is obtained through the use of Hamilton’s principle. The numerical results found in the present analysis for free the vibration of cross-ply laminated plates on elastic foundations are presented and compared with those available in the literature. The theory proposed is not only accurate, but also efficient in predicting the natural frequencies of laminated composite plates.     

Analytical analysis of free vibration of non-uniform and non-homogenous beams: Asymptotic perturbation approach

This paper applies the asymptotic perturbation approach (APA) to obtain a simple analytical expression for the free vibration analysis of non-uniform and non-homogenous beams with different boundary conditions. A linear governing equation of non-uniform and non-homogeneous beams is obtained based on the Euler–Bernoulli beam theory. The perturbative theory is employed to derive an asymptotic solution of the natural frequency of the beam. Finally, numerical solutions based on the analytical method are illustrated, where the effect of a variable width ratio on the natural frequency is analyzed. To verify the accuracy of the present method, two examples, piezoelectric laminated trapezoidal beam and axially functionally graded tapered beam, are presented. The results are compared with those results obtained from the finite element method (FEM) simulation and the published literature, respectively, and a good agreement is observed for lower-order beam frequencies.     

Simulation of Buckling-Induced Failure in Composite Laminates

This contribution presents a simple model for the analysis of buckling–induced failure in thin–walled composite laminates in the framework of the finite element method. The plies are modeled with shear deformable geometrically non–linear four–node shell elements which are layered according to the classical laminate theory. Shear locking effects are reduced via the well–known assumed natural strains (ANS) approach. A ply discount model is applied for the successive failure of the plies. The cohesive zone approach which is implemented in so–called interface elements is employed for delamination. The failure processes are history dependent leading to non–recurring stiffness degradation in areas where damage is detected. A numerical example with experimental evidence highlights the performance and applicability of the proposed model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Compressive stability of multilayered delaminations in composites

The behavior of defects of the near-surface crack type was investigated in laminated composites. Multilayered delaminations in compressed elements were examined on the assumption that cylindrical bending of the delamination is accompanied by shear within the framework of a model similar to the Timoshenko model. The effect of the mechanical properties and thickness and number of layers in the delaminated section on the critical buckling strain and strain corresponding to the beginning of growth of the delamination was investigated. It was shown that when the delaminated section contains several bearing layers and the rigidity of the composite with respect to interlaminar shear is small, consideration of the shear in the delaminated section can lead to a significant change in the critical compressive strains and/or critical size of the delamination.Translated from Mekhanika Kompozitnykh Materialov. Vol. 33, No. 3, pp. 312–320, May–June, 1997.     

具损伤压电智能层合板的非线性主动控制和损伤监测

基于Hamilton原理、高阶剪切变形板理论、von Krmn型几何非线性应变-位移关系以及应变能等效原理,考虑压电层的质量和刚度及复合材料层内的损伤效应,建立了具损伤压电智能层合板的非线性运动方程．采用耦合正、逆压电效应的负速度反馈控制原理,形成闭环控制回路,实现了对压电智能层合板的主动控制和损伤监测．数值计算中,以四边简支面内不可动的层合矩形板为例,讨论了压电层位置对振动控制的影响,以及损伤程度和损伤位置对传感层输出电压的影响,提出一种损伤监测的方法．     

Analysis of Dynamical Responses for the MDF Wooden Material

The nonlinear analysis have been performed on the experimental data of a beam vibration composed of a wooden material MDF (Medium-Density Fiberboard). Firstly, the beam was subjected to the harmonic excitation on the clamp with its first eigenfrequency. After reaching the eigenfrequency, the excitation was switched of and the velocity amplitudes were measured. To identify the frequencies and the damping of vibrations, we applied nonlinear methods including Hilbert transform and wavelets. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical elastic-plastic simulation of interlaminar stresses in a notched angle-ply thermoplastic composite laminate

A thermoplastic angle-ply AS4/PEEK laminate with a hole is considered. The interlaminar stresses along the hole edge at different interfaces under uniaxial extension are investigated. According to the symmetries of the structure and loading, a suitable finite-element model is developed. Utilizing a three-dimensional elastic-plastic finite-element procedure elaborated previously, a finite-element modeling of the interlaminar stresses in a thick angle-ply composite laminate is carried out. Based on the interlaminar stresses obtained, the dangerous locations of delamination initiation are predicted. The results obtained indicate that there is some relationship between the dangerous locations and fiber orientations in the adjacent layers, and it maybe inferred that the critical locations are near the regions where the hole edge is tangent to the fiber orientation in the layers adjacent to the interface. The interlaminar stresses at the same interfaces are not sensible to distances from the midplane of the laminate. Very high interlaminar tensile stresses are found to exist on the hole edge at the +25°/+25° or –25°/–25° interfaces, and delaminations can initiate there first. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 427-440, May-June, 2009.     

粘弹性梁的动力响应

本文利用Voigt力学模型对粘弹性简支梁进行动力分析,得到了梁的自由振动与强迫振动的若干解析解的表达式.并与S.Timoshenko给出的弹性简支梁的相应的结论进行了比较,指出了弹性动力分析的局限性.最后给出了二个数值例子.     

外部压力作用下复合材料层合圆柱壳的脱层扩展分析

含脱层的层合圆柱壳在承受外部压力作用时,容易发生脱层扩展,进而引起结构失效．基于可动边界变分原理并考虑脱层间的接触效应对圆柱壳在外部压力作用下的脱层扩展进行了分析,同时应用Griffith准则,导出了脱层前缘各点处的能量释放率表达式,且以轴对称脱层层合圆柱壳为例进行了数值计算,讨论了脱层大小、脱层深度、几何尺寸、材料性质及纤维铺层方式等因素对脱层扩展的影响．     

Transverse vibration of viscoelastic sandwich beam with time-dependent axial tension and axially varying moving velocity

Nonlinearly parametric resonances of axially accelerating moving viscoelastic sandwich beams with time-dependent tension are investigated in this paper. Based on the Kelvin differential constitutive equation, the controlling equation of the transverse vibration of a beam with large deflection is established. The system has been subjected to a time varying velocity and a harmonic axial tension. Here the governing equation of motion contains linear parametric terms and two frequencies, one is the frequency of axially moving velocity and the other one is the frequency of varying tension. The method of multiple scales is applied directly to the governing equation to obtain the complex eigenfunctions and natural frequencies of the system. The elimination of secular terms leads to the steady-state response and amplitude of vibrations. The influence of various parameters such as initial tension on natural frequencies and the amplitude of axial fluctuation, the phase angle between the two frequencies on response curves has been investigated for two different resonance conditions. With the help of numerical results, it has been shown that by using suitable initial tension, the amplitude of axial fluctuation, the phase angle, the vibration of the sandwich beam can be significantly controlled.     

Caracterización de la delaminación en materiales compuestos mediante la teoría de mezclas serie/paralelo

This paper presents a new procedure to deal with the delamination problem found in laminated composites, based in a continuum mechanics formulation. The procedure proposed obtains the composite constitutive performance with the Serial/Parallel mixing theory, developed by F. Rastellini. This theory characterizes composite materials by coupling the constitutive behaviour of the composite components, imposing an iso–strain relation among the components in the fibre (or parallel) direction and an iso-stress relation in the remaining directions (serial directions). The proposed procedure uses a damage formulation to characterize the constitutive behaviour of matrix component in order to obtain the stress-strain performance of this material.With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial directions, among them, the shear component. This stiffness reduction provides a composite performance equivalent to what is found in a delaminated material.To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.     

基于重构边界光滑离散剪切间隙法的复合材料层合板自由振动分析

重构边界光滑离散剪切间隙（RES-DSG3）法,利用边界光滑技术将域积分转化为沿光滑域边界的边界积分,结合基于全局坐标系的非等参离散剪切间隙（DSG）法,避免了坐标映射和Jacobi矩阵的计算,同时克服了“剪切自锁”现象,提高了计算的精度。基于一阶剪切变形理论,采用该文给出的方法,从不同材料参数、边厚比、边界条件等几个方面对复合材料层合板自由振动固有频率进行了数值分析,通过典型算例的计算,验证了该方法的可行性和有效性。