Two-dimensional orthogonal polynomials for vibration of rectangular composite plates

Study on flexural vibration of triangular composite plates influenced by fibre orientation

Most of the work done for the vibration of composite plates published in the literature is either analytical or numerical studies with few experimental results available on composites with unidirectional fibers. The present study involves extensive experimental works to investigate the free vibration of industry driven woven fiber glass/epoxy composite plates with different boundary conditions including free–free cases. The modern modal testing and subsequent analysis with powerful computer and digital analysis system is an important tool for prediction of behavior of structures. The specimens of woven glass fiber and epoxy matrix composite plates are manufactured by the hand-layup technique. Elastic parameters of the plate are also determined experimentally by tensile testing of specimens using INSTRON 1195. An experimental investigation is carried out using modal analysis technique with Fast Fourier Transform Analyzer, PULSE lab shop, impact hammer and contact accelerometer to obtain the frequency response functions. The computational results are compared with results of previous studies in literature wherever available. The experimental results are also compared with the FEM numerical analysis based on first-order shear deformation theory. The effects of different geometrical parameters including number of layers, aspect ratio, fiber orientation and different boundary conditions of woven fiber composite plates are studied in detail. It is observed that comparisons performed between numerical predictions and experimental tests have a good correlation. The natural frequency is very less for cantilever than simply supported and fully clamped boundary conditions. The prediction of dynamic behavior of laminated composite plates plays a significant role in the future applications of structural composites.

The present study deals with both experimental and numerical investigation on the free vibration behavior of laminated composite plates subjected to varying temperature and moisture. A simple laminated plate model is developed for the vibration of composite plates subjected to hygrothermal loading. A computer program based on finite element method in the MATLAB environment is developed to perform all necessary computations. The woven fiber glass/epoxy specimens were hygrothermally conditioned in a humidity cabinet where the conditions were maintained at temperatures of 300–425 K and relative humidity ranging from 0% to 1.0% for moisture concentrations. Quantitative results are presented to show the effects of geometry, material and lamination parameters of woven fiber laminate on the free vibration of composite plates for different temperature and moisture concentrations. The numerical and experimental results show that there is reduction in natural frequency in Hz with the increase in temperature and moisture concentration for laminates with simply supported and clamped boundary conditions with different aspect ratio and side-to-thickness ratios.

In order to predict the effects of different fiber orientations on the elastic constants of composites, this paper takes carbon fiber reinforced polypropylene composites as an example, and adopts the Mori-Tanaka method to establish the Random Volume Element (RVE) model of fiber composites with five different fiber orientations, namely, 0 °, 30 °, 45 °, 60 °, and 90 °, and investigates the effects of the fiber The effects of fiber orientation and fiber volume fraction on their elastic constants were investigated to obtain the required data by this method instead of experiment. By improving the Halpin-Tsai model, the value of the orientation factor was determined on the basis of the random orientation factor, and the original shape factor was modified to an exponential shape factor, the orientation degree factor was introduced, and finally, the relationship equations between the modified exponential shape factor and the volume fraction and orientation degree were obtained. The results show that for the same fiber orientation and volume fraction, the smaller the value of shape factor, the higher the elastic modulus. The fitting errors of the four values of elastic constants were also analyzed, and it was found that the improved Halpin-Tsai model could be used to predict the elastic constants of carbon fiber-reinforced polypropylene composites in a certain range, thus providing a method to study the prediction of the elastic constants of composites by fiber orientation.

An efficient C0 finite element modeling of an inverse hyperbolic shear deformation theory for the flexural and stability analysis of laminated composite and sandwich plates

In this study, the effect of fiber orientations on the natural frequencies of the hybrid composite laminate (HCGFRE) that is consisted of sequential stacking of plain woven carbon fiber reinforced epoxy (CFRE) and plain woven glass fiber reinforced epoxy (GFRE) fibers was investigated. A finite element approach was carried out in order to determine the natural frequencies of hybrid composite laminate. Analyzes were performed using the LS-DYNA® software. In the finite element analysis, the natural frequencies corresponding to the first three modes were determined separately for each fiber orientation (00,300,450). Besides the modal analysis of hybrid composite laminates formed by sequential stacking of the same fiber orientations, the natural frequencies of hybrid composite laminates formed by stacking in different fiber orientations were also examined within the scope of the study. The same boundary conditions were applied for all fiber orientations since it is essential to study with a similar degree of freedom. In addition, the effect of the mesh sensitivity used in the finite element approach on the natural frequency is also considered. it is seen that both the change of fiber orientation and the stacking of composite plates with different fiber orientations directly affect the natural frequency values for all modes.

Aeroelastic behavior of a composite plate wing with structural damping

Some recent developments on integrated damping mechanics for unidirectional composites, laminates, and composite structures are reviewed. Simplified damping micromechanics relate the damping of on-axis and off-axis composites to constituent properties, fiber volume ratio, fiber orientation, temperature, and moisture. Laminate and structural damping mechanics for thin composites are summarized. Discrete layer damping mechanics for thick laminates, including the effects of interlaminar shear damping, are developed and semianalytical predictions of modal damping in thick simply supported specialty composite plates are presented. Applications show the advantages of the unified mechanics, and illustrate the effect of fiber volume ratio, fiber orientation, structural geometry, and temperature on the damping. Additional damping properties for composite plates of various laminations, aspect ratios, fiber content, and temperature illustrate the merits and ranges of applicability of each theory (thin or thick laminates).

Effect of fibre orientation on the vibration behaviour of orthotropic rectangular plates

Composite materials have revolutionized industries such as aerospace and automotive with their impressive strength-to-weight ratios and customizable properties. Ply angle and fiber orientation are critical factors that significantly impact the dynamic behavior of composite structures, influencing stiffness, strength, and vibrational characteristics. This research delves into the dynamic characteristics of composite plates, explicitly examining how ply angle and fiber orientation affect vibrational behavior. Through finite element analysis (FEA), composite plates with varying ply angles and fiber orientations were modeled to understand their influence on natural frequencies, mode shapes, and dynamic responses under various loading conditions. The study reveals that cross-ply [0/0/0/0] exhibits the highest stiffness and superior stress handling, while the cross-ply balanced laminate [90/0/0/90] demonstrates better vibrational characteristics. The findings highlight the intricate relationships between design parameters and structural vibrational behavior, offering opportunities for optimizing composite structures. Additionally, harmonic analysis showed that a cut-out increases the natural frequency. The results underscore the importance of optimizing composite plate configurations to enhance vibrational characteristics and align natural frequencies with operational requirements, thereby mitigating resonance-related issues.

The inter-ply sliding behavior is one of the important factors affecting the quality of carbon fiber composite products. In this paper, the inter-ply sliding behavior of the unidirectional prepreg was investigated for the preforming process. The inter-ply sliding resistance of prepreg under different conditions was measured by the homemade measuring device and the lubricating effect of inter-ply resin was identified by the micromorphology. The effect of fiber orientation was quantified by the combined roughness. With the increase of sliding distance, the inter-ply sliding resistance initially increased significantly, and finally maintained a constant value. A phenomenological model of the inter-ply sliding resistance was developed to explain the effects of pressure, velocity, and fiber orientation. This model can accurately describe the inter-ply sliding behavior of prepreg, which can be used for numerical simulation and the optimization of preforming process.

In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Galerkin method, the nonlinear differential equation of free vibrations of initially stressed composite plate is obtained. This nonlinear equation is solved using two different analytical perturbation methods, namely method of multiple scales (MTS) and homotopy perturbation method (HPM), to analyze the nonlinear vibrations of initially stressed cross-ply composite plates. Effects of tensile and compressive biaxial initial stresses, initial vibration amplitude, thickness, and aspect ratios of the composite plates on the frequency behavior are investigated. The validity of the results is confirmed by making a comparison with those reported in the literature. According to the results, both analytical solutions show increasing trends for natural frequency parameters by increasing normal initial stresses. Regardless of the value of initial biaxial stresses, for both symmetric and non-symmetric plates, the results of MTS and HPM are in close agreement for the smallest initial amplitude. However, for compressive initial stresses, by increasing initial amplitude ratios, the discrepancies between the results of HPM and MTS increase for symmetric and non-symmetric plates. Although HPM includes less computational effort (smaller length of formulation) than MTS, the linear-to-nonlinear frequency ratios obtained using MTS method become closer to those obtained by HPM as initial vibration amplitude is decreased and initial stress is increased.

The paper reports an algorithm to analytically solve one of the problems in the mechanics of elastic bodies, which is associated with studying the natural vibrations of a composite two-stage plate whose concave part is smoothly aligned with the part of a constant thickness. We have defined patterns for stating the boundary and transitional conditions, which should be taken into account when considering the natural vibrations of a two-stage plate.The ratios have been obtained, which make it possible to study the distribution of deflections and determine the values of amplitudes of the curved vibrations of the plate. It was noted that the modes of vibrations are based on the symmetry and factorization methods that we had developed and refined earlier. Specifically, it has been found that the deflections can be explored through expressions that are derived through the sum of relevant solutions to two linear second-order differential equations with variable coefficients.Based on the proposed approach, a system consisting of eight homogeneous algebraic equations has been defined, which allowed us to build a frequency equation for the plate rigidly fixed along the inner contour and free along the outer contour. We have determined the values for the plate’s natural frequencies for the first three modes of natural vibrations. Moreover, in order to verify and expand a set of plates of different configurations, the plates with two types of concave in their variable part have been considered. The new approaches and the ratios based on them could be useful for the further advancement of methods for solving similar problems in mathematical physics on natural values. A practical implementation is the problems about the vibrations of plates with variable thickness and of different modes

In this paper, the modal-model of the composite structure is predicted and viewed to decide the optimal position of the PZT sensors on the composite structures. The novelty of this work is to systematically study the effect of fiber orientations and boundary conditions on the modal-model and the optimal location of the PZT sensors on the composite structures. The glass fibers are reinforced in a polyester matrix at different fiber orientations such as 0°, 30°, 45°, 60° and 90°. It is used for various engineering applications, especially in the aerospace and automobile sector, and it is very important to measure its dynamical response. The PZT patches can be embedded on the composite structures to measure their vibrational response. In this paper, ABAQUS software is used to build the finite element model of the PZT-composite structure. The composite structure is modeled with different boundary conditions. It is observed that the orientation of the fibers as well as the boundary condition directly put their effect on the modal-model of the composite structure and also on the selection of the optimal position of the PZT patches. It is found that the optimal position of the PZT directly depends upon the fiber orientation.

The effect of fiber orientation is studied on the failure load of a laminated curved panel subjected to uniaxial compression for a combination of simply supported and clamped boundary conditions. The failure modes are specified as buckling and first-ply failure, with the failure load defined as the minimum of these two loads. The panel is taken as a shear-deformable symmetrically laminated angle-ply laminate, and the effect of fiber orientation on the failure load is investigated by considering several laminations consisting of 0, 90, and θ° ply angles and by determining the failure load for different aspect ratios and panel thicknesses. The best ply angles for each stacking sequence are determined to maximize the failure load and the stacking sequence giving the highest failure load. The numerical results are obtained using an eight-noded shell finite element that avoids the parasitic shear or shear locking problem. It is observed that the rotational restraints at the curved edges have a major effect on the failure load.