Vibration Analysis Of Composite Laminates Research Articles

A new finite strip formulation based on Carrera unified formulation for the free vibration analysis of composite laminates

In this article, a new finite strip formulation based on Carrera unified formulation (CUF) is developed to perform the free vibration analysis of cross- and angle-ply composite laminated plates. The FSM discretizes the plate by a number of strips which are connected through the nodal lines, and calls for use of simple polynomial shape functions in one direction of the plane of strips and harmonic series in the other. In the present formulation, all three components are considered for displacement field in each nodal line. CUF approach which is obtained in the framework of the Carrera unified formulation, permits stating the unknown variables as a set of the function expansions depending on the thickness coordinate and the corresponding variable depending on the in-plane coordinates. Several numerical examples for the analysis of laminated plates are presented and the effect of the number of strips, order of expansion, different relative thickness ratio and various boundary conditions are demonstrated.

Modeling vibration behavior of delaminated composite laminates using meshfree method in Hamilton system

Free vibration analysis of composite laminates with delaminations is performed based on a three-dimensional semi-analytical model established by introducing the local radial point interpolation method (LRPIM) into a Hamilton system. The governing equation is derived with a transfer matrix technique and a spring layer model based on a local weak-form equivalent to the modified Hellinger-Reissner variational principle. Main superiority of the present model is that the scale of the governing equation involves only the so-called state variables at the top and bottom surfaces, and is insensitive to the thickness and the layer number of the composite laminates. Several numerical examples for analyzing the vibration frequencies and mode shapes of delaminated composite beams and plates are given to validate the model. The results are in good agreement with the pre-existing results.

Free Vibration Analysis of Composite Laminates with Delamination Based on State Space Theory

A semi-analytical solution based on the modified H-R (Hellinger-Reissner) variational principle and a nonlinear spring-layer model is presented to analyze the free vibration problem of laminates with a delamination in the Hamilton system. This nonlinear spring-layer model between the upper and lower sub-laminates ensures the exact continuous transverse stresses and displacements in the un-delaminated region by specifying the infinite values of springs and avoids the possibility of penetration phenomenon in the delaminated region. As an application of this method, the influence of the delamination size, depth, and boundary conditions on the first three natural frequencies of delaminated composite laminates is investigated.

Natural Vibration Analysis of Composite Laminates with Non-Penetrating Damage Repaired by Two Kinds of Bonding Methods

The three dimensional finite element model of composite laminates made of carbon fiber reinforced bismaleimide resin is built, and the natural vibration of the square composite laminates with clamped edges is analyzed. The natural vibration frequencies and modes of laminates without damage are given based on finite element method. The three dimensional finite element models of the same square laminates with non-penetrating damage repaired by two kinds of bonding methods are built. The natural vibration frequencies and modes are also given. It is showed that the three dimensional models can simulate the geometric and physical features of the real composite laminates. It is concluded that the natural vibration frequencies of the composite laminates all increase after it is repaired either by scarf bonding method or scarf and surface bonding method. After scarf bonding repairing, the lowest natural frequency increases about 3.6% and the second natural frequency increases 3.7%. After scarf and surface bonding repairing, the lowest natural frequency increases about 4.5% and the second frequency increases about 6.4%. The natural vibration modes of different repairing models are similar. The increase of natural frequencies may cause temporary vibration of aircraft skin made of composite laminates. The risk of resonance caused by bonding repairing is small.

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

AbstractIn this paper, the free vibration analysis of simply‐supported and clamped composite laminates, especially thick laminates, is carried out. The three‐dimensional theory of elasticity is integrated into a layerwise model via differential quadrature discretization. All physical governing equations are satisfied, including the additional constraints of the characteristics of continuity and discontinuity of interfacial transverse and in‐plane strains and stresses along the interfaces of composite laminates. Effects of plate aspect and thickness ratios on the free vibration of these laminates are examined in detail. This study demonstrates the applicability, accuracy, and stability of the present methodology, for vibration analyses of composite structures of thick laminated constitution. Copyright © 2003 John Wiley & Sons, Ltd.

An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape

An element free Galerkin (EFG) method is proposed to analyze the natural frequencies of composite laminates of complicated shape. The present method uses moving least squares (MLS) approximation to construct shape functions based on a set of nodes scattered in the problem domain. The dynamic equations of the system are formulated using the Lagrangian equation. The essential boundary conditions are imposed using their weak forms with Lagrange multipliers. Orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. The present EFG method is coded in Fortran. Numerical examples are presented for plates of square, elliptical and complicated shapes with different boundary conditions.

Forced Vibration Analysis of Composite Laminates Using a Discrete Layer Stress Based Model

Although modern displacement based plate theories are capable of predicting the deflected shape and lower frequencies of a loaded plate with a high degree of precision, their ability to predict stresses, particularly interlaminar stresses, has been poor. A discrete layer stress based theory for composite laminates that assumes a linear distribution of in-plane stresses across each lamina was presented and showed good prediction of interlaminar stresses. The present study extends that work to forced vibration response of a composite plate subjected to a time varying transverse load.