Free vibration and buckling analysis of laminated composite plates with cutouts of complicated shapes

Hygrothermal effects on the free vibration and buckling of laminated composites with cutouts

In recent years, natural fiber-reinforced composite (NFRC) materials have gained significant attention in applications due to their eco-friendly nature, biodegradability, low cost, lightweight, and satisfactory mechanical properties. Bast, flax, jute, and hemp are among the most popular natural fibers in composite applications. In this study, the pure and hybrid (with glass and carbon fibers) use of hemp fibers in the large amplitude (nonlinear) free vibration of laminated composite plates is investigated. The large amplitude free vibration equation is derived using the virtual work principle. Nonlinear Green-Lagrange strains are utilized in the derivation. Spatial derivatives in the free vibration equation are calculated using the Generalized Differential Quadrature (GDQ) method. The nonlinear free vibration equation is solved using a direct iterative procedure. Effects of stacking sequence, aspect ratio, and boundary conditions on the frequency of linear and nonlinear free vibration are also investigated. Linear modal analysis results indicate that carbon/hemp fiber-reinforced hybrid composite plates have slightly higher natural frequency values than carbon/glass fiber-reinforced hybrid composite plates for CHCHC (C: carbon, H: hemp) and CHHHC stacking sequences, regardless of the aspect ratio and boundary conditions. For nonlinear modal analyses, carbon/glass and carbon/hemp hybrid composite plates exhibit very similar frequency ratio ( ω N L / ω L ) values for CGCGC (G: glass) and CHCHC stacking sequences, as well as for the stacking sequences of CGGGC and CHHHC.

Buckling and free vibration behavior of functionally graded carbon nanotube reinforced polymer composite plate subjected to nonuniform temperature fields have been investigated using finite element approach. The effective material constants of the plate are obtained using the extended rule of mixture along with efficiency parameters of the carbon nanotube (to include geometry-dependent material properties). Influence of boundary conditions, aspect ratio, functional grading of the carbon nanotube, nonuniform thermal loading on thermal buckling and free vibration behavior of the heated plate are analyzed. It is observed that temperature fields and functional grading are influenced on the critical buckling temperature of the plates. Further, nature of functional grading showed significant change in buckling mode shapes irrespective of the boundary conditions. The first few natural frequencies of the plate under thermal load decreases as the temperature increases and they are influenced significantly by the nature of temperature field. Variations in free vibration mode shapes of the square plates found with not significant change as temperature increases. However, free vibration modes of the rectangular plates are sensitive to the nature of temperature field whenever there is a free edge associated with the boundary condition. Influence of functional grading on the free vibration mode shapes is not significant in contrast with the free vibration natural frequencies. The magnitude of free vibration natural frequencies of functional grade-X type carbon nanotube reinforcement showed higher in comparison with other two types of reinforcements considered here.

This study investigates the dynamic properties of the thickness tapered laminated composite plate. The governing differential equations of motion of the various configurations of a thickness tapered composite plate are presented in the finite element formulation using classical laminated plate theory. The validity of the developed finite element formulation is demonstrated by comparing the natural frequencies evaluated using the present finite element method with those derived from the experimental measurements and presented in available literature. Various parametric studies are also performed to investigate the effect of taper configuration, aspect ratio, taper angle and ply orientation on free vibration responses of the structures. The comparison of the free vibration mode shapes of uniform and various tapered configurations of tapered laminated composite plates are also presented. Influences of taper angle on the free vibration fundamental mode shapes under various boundary conditions and various ply configurations are also presented. The forced vibration response of a composite plate is also investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of a composite plate could be tailored by dropping of the plies to yield various tapered composite plate.

Many composite cantilever plate-like structures have found engineering applications in different industries. For attaining a meaningful assessment of the plate vibration characteristics, it is important to have efficient and effective methods for determining the natural frequencies/mode shapes of composite cantilever plates. In this paper, a method formulated on the basis of the Ritz method and a simple first-order shear deformation theory (SFSDT) is presented to analyze the free vibration of thin as well as thick rectangular composite cantilever plates for determining their natural frequencies. In the SFSDT, the total deflection is the sum of two deflection components, namely, bending and through-thickness shear-deformation-induced deflections. The successful application of the Ritz method together with the SFSDT for the free vibration analysis of thick composite plates relies on the selection of two independent sets of characteristic functions for the bending and through-thickness shear-deformation-induced deflections, respectively, to satisfy the requirements for the displacement and force conditions at the fixed edge of the plate. The novelty of the proposed method is that two independent sets of characteristic functions, namely, polynomials and trigonometric functions, which satisfy the displacement and force conditions at the fixed edge have been identified and used in the variational method to construct the eigenvalue problem for extracting the modal characteristics (natural frequencies and mode shapes) of the plate. It has been shown that the uses of the selected characteristic functions can produce excellent natural frequencies for both thin and thick composite cantilever plates. Some existing theoretical and experimental natural frequencies of thin as well as thick composite plates have been used to demonstrate the accuracy of the proposed method in predicting natural frequencies. The significant effects of through-thickness shear deformation on the natural frequencies of composite cantilever plates are studied to show the merit of the present method. Finally, for illustrating the application of the proposed method in free vibration analysis, a novel procedure established on the basis of the sensitivity analysis of natural frequencies is presented to assess the material degradation of composite cantilever plates. The numerical examples have shown that fewer than 10 iterations are required in the identification process to produce a good estimation of the current value for each material constant.

Studies of vibration of plates have matured and are a well-established branch of research in structural dynamics. They have a vast range of applications in engineering and technology. But not much work can be found on vibration analysis of Functionally Graded Materials (FGMs) as compared to isotropic and composite plates and shells. FGMs are those in which the volume fraction of the two or more constituent materials is varied, as a power-law distribution, continuously as a function of position along certain dimension(s) of the structure From the perspective of finite element method (FEM) studies of FGM, Praveen and Reddy [3], studied the static and dynamic responses of functionally graded (FG) ceramic-metal plate accounting for the transverse shear deformation, rotary inertia and moderately large rotations in the Von-Karman sense, in which the effect of an imposed temperature field on the response of the FG plate was discussed in detail. Ng et al. [4] dealt with the parametric resonance of FG rectangular plates under harmonic in-plane loading. Ferreira and Batra [5] provided a global collocation method for natural frequencies of FG plates by a meshless method with first order shear deformation theory (FSDT). Woo et al. [6] presented an analytical solution for the nonlinear free vibration behavior of FGM plates, where the fundamental equations were obtained using the Von-Karman theory for large transverse deflection, and the solution was based in terms of mixed Fourier series. Zhao et al. [7] studied the free vibration analysis of metal and ceramic FG plates using the element-free kp-Ritz method. The FSDT was employed to account for the transverse shear strain and rotary inertia, mesh-free kernel particle functions were used to approximate the two-dimensional displacement fields and the eigen-equation was obtained by applying the Ritz procedure to the energy functional of the system. Batra and Jin [8] used the FSDT coupled with the FEM to study the free vibrations of an FG anisotropic rectangular plate with various edge conditions. Also, Batra and Aimmanee [9] studied a higher order shear and normal deformable plate theory by FEM. Many studies conducted on FGMs are related to the analysis of free vibration by applying FSDT (see Other forms of shear deformation theory, such as the third order-shear deformation theory (TSDT) that accounts for the transverse effects, have been considered. Cheng and Batra [13] www.intechopen.

This study deals with bending, free vibration and buckling analysis of functionally graded composite plates reinforced with graphene nano platelets (GPL). A higher order non-polynomial shear deformation theory known as the trigonometric shear deformation theory is used which satisfy traction-free boundary condition at the top and bottom of the plate, hence no shear correction factor is required. These problems are solved numerically using in finite element analysis (FEA) by developing inhouse MATLAB codes. The 8-noded serendipity element with C 0 continuity is used for the mesh generation. The Hamilton’s principle is the primary variational principle used in this formulation to derive the plate governing equations. The structural behaviours of plate are analysed, focusing on the effects of stacking sequences, number of layers, weight percentage of GPL, size of GPL and ratio of length to thickness plate. The study explores both uniaxial and biaxial loading scenarios for buckling analysis and validates the results against existing literature for buckling and free vibration. The study reveals that, incorporating 1% of GPL to pure epoxy composite, the FG-X pattern exhibits a substantial reduction in static deflection by 81.7%, a marked increase in natural frequency by 133.8% and a significant enhancement in critical buckling load by 444.5%.

Thermal residual-stresses introduced during manufacture and their effect on the free vibration of stringer stiffened composite plates is investigated. The principal idea in the work is to include stiffeners on the perimeter of a composite plate in which the laminate for the stiffeners and the plate are different. Such an arrangement yields manufacturing induced thermal residual-stresses which result from the difference in manufacturing and operating temperatures as well as the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. The analysis is based on an enhanced Reissner-Mindlin plate theory and involves two separate calculations. In the first, the thermal residual-stress state is determined for an unconstrained plate. In the second, the free vibration problem is solved; thermal effects from the first calculation are included by way of nonlinear membrane-bending coupling which in turn defines the free vibration reference state. The problem is solved using a finite element formulation to determine the natural frequencies and vibration modes of the plates. Two different plate-stiffener geometries are used to illustrate the effects of stringer size, stringer placement and temperature difference. Two principal results are obtained: first, it is shown that thermal residual-stresses can have a significant effect on the natural frequencies; secondly, thermal residual-stresses can be tailored to increase natural frequencies.

Characterization of delamination effects on free vibration and impact response of composite plates resting on visco-Pasternak foundations

Predictions of the frequencies of bending-torsion coupled laminated composite plates with discontinuities: Novel analytical modeling and experimental validation

In this study trigonometric layerwise deformation theory is used for the analysis of free vibration of symmetric composite plates. A meshless discretization method based on global multiquadric radial basis functions is used. The equations of motion and the boundary conditions are derived and interpolated by radial basis functions. This method is applied to the free vibration analysis of composite and sandwich plates. The results are then compared with analytical and numerical solutions. The results show that the use of trigonometric layerwise deformation theory discretized with multiquadrics provides very good solutions for the free vibration of composite and sandwich plates.

This paper considers the free vibration and flutter of carbon nanotube (CNT) reinforced nanocomposite plates subjected to supersonic flow. From the literature review, a great deal of research has been conducted on the free vibration and flutter response of high-volume CNT/nanocomposite structures; however, there is little research on the flutter instability of low-volume CNT/nanocomposite structures. In this study, free vibration and flutter analysis of classical CNT/nanocomposite thin plates with aligned and uniformly distributed reinforcement and low CNT volume fraction are performed. The geometry of the CNTs and the definition of the nanocomposite material properties are considered. The nanocomposite properties are estimated based on micromechanical modeling, while the governing relations of the nanocomposite plates are derived according to Kirchhoff’s plate theory with von Karman nonlinear strains. Identification of vibrational modes for nanocomposite thin plates and analytical/graphical evaluation of flutter are presented. The novel contribution of this work is the analysis of the eigenfrequencies and dynamic instabilities of nanocomposite plates with a low fraction of CNTs aligned and uniformly distributed in the polymer matrix. This article is helpful for a comprehensive understanding of the influence of a low-volume fraction and uniform distribution of CNTs and boundary conditions on the dynamic instabilities of nanocomposite plates.

This paper researches the free vibrations and corresponding material parameters of a functional gradient graphene platelets-reinforced composite (FG-GPLRC) cantilever torsional plates with both pore and graphene variations in the transverse direction. Utilizing the feature of closed-cell cellular solids, the mixture rule, and the modified Halpin–Tsai model, the material parameters of the composite are determined for different volume fractions of component materials. Then, using the classical plate theory (CLPT), the Rayleigh–Ritz technique and polynomials, the dynamic equation that can be used to obtain the free vibration mode shapes and frequencies of the rotating cantilever torsional plate is given. Comparison studies with the previous calculation results from available literature and the finite element (FE) models of cantilever plates are conducted, and the correctness of the present theoretical formulation and numerical calculation is verified. Finally, the effects of graphene platelet (GPL) distribution, porosity distribution (PD), GPL content, rotational speed, and average geometric size of GPL on free vibrations of the system are studied in depth.

In this paper, a new meshfree moving least squares-Tchebychev (MLST) shape function is proposed to analyze the free vibration characteristics of laminated composite arbitrary quadrilateral plate with hole. The plate and hole have an arbitrary quadrilateral shape. The whole plate structure is separated into the segments with arbitrary quadrilateral shape by the domain decompose method, and these segments are modeled to a square plate through the coordinate mapping. The fourth order polynomial mapping approach is used as a mapping function for the coordinate mapping. The first-order shear deformation theory (FSDT) is adopted in theoretical formulation for the free vibration analysis of laminated composite arbitrary quadrilateral plate. The boundary and continuation conditions are generalized by the artificial spring technique. All the displacement functions containing the boundary and continuation conditions are expressed by the meshfree MLST shape function, on the base of this, the governing equation of arbitrary plate with hole are obtained. Thus, the natural frequency and mode shape of the laminated composite arbitrary quadrilateral plate with hole are obtained by solving the governing equation. The accuracy and reliability of the proposed method are verified by comparison with the results of literature and ABAQUS. Through numerical verification, it can be seen that the results of the proposed method are in good agreement with those of the literature and ABAQUS. The free vibration characteristics (i.e. natural frequency and mode shape) of the laminated composite arbitrary quadrilateral plate with arbitrary quadrilateral hole under different boundary conditions are proposed through the parameter research and some examples.

A UNIFORMIZING METHOD FOR THE FREE VIBRATION ANALYSIS OF METAL–PIEZOCERAMIC COMPOSITE THIN PLATES