On the angle ply higher order beam vibrations

Journal of Reinforced Plastics and Composites, 2006

The free vibrations of angle-ply laminated cylindrical shells are studied numerically and experimentally. The material of the cylindrical shell is a carbon fiber reinforced plastic (CFRP). First, the material properties for the lamina of the cylindrical shell are measured. Secondly, using the measured material properties of the lamina, the natural frequencies and mode shapes of the angle-ply laminated cylindrical shells with clamped edges are computed by the finite element method (FEM). Finally, the vibration tests of the angle-ply laminated cylindrical shells with clamped edges are carried out. By applying the experimental modal analysis technique, natural frequencies and mode shapes of the shells are obtained. From the comparison between experimental and numerical results, one can see the good agreement between these results. Furthermore, the effects of length of the angle-ply laminated cylindrical shells with clamped edges on the natural frequencies and mode shapes are investigated numerically and experimentally. An approximate frequency equation for the shell's length is proposed.

Computers & Structures, 1994

A refined higher-order shear deformation theory has been developed for large amplitude, in the sense of von K&mgn, free vibration analysis of fibre reinforced cross-ply composite and sandwich laminates by assuming cubic variations of in-plane displacement components and a constant transverse displacement component through the thickness of the laminate. The theory accounts for warping of the transverse cross-section, which cannot be modelled with the Reissner-Mindlin first-order shear deformation theory. The displacement-based finite element method of analysis using Co isoparametric nine-node quadrilateral elements of the Lagrangian family is adopted. A special mass matrix diagonalization scheme is employed which conserves the total mass of the element and includes the effects due to rotary inertia terms. The validity and efficiency of the present development is then established by obtaining the solutions to a wide range of problems and comparing them with the available two-and three-dimensional closed-form and finite element solutions. Some new results are also generated in a non-linear context for future comparisons.

In this study, the effect of the end conditions of cross-ply laminated composite beams (CLCB) on their non-dimensional natural frequencies of free vibration was investigated. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. In that model, a three-noded element with three degrees of freedom at each node is assumed. Numerical results were verified by comparisons with other relevant works. The end conditions of beams are: clamped _ free (CF), hinged _ hinged (HH), clamped _ clamped (CC), hinged _ clamped (HC), hinged _ free (HF), free _ free (FF). Each beam has either movable ends or immovable ends. It is found that the more constrained beams have the higher values of natural frequencies of transverse vibration. However, the free-free and hinged-free beams are found to have the highest frequencies of transverse vibration amongst all beams although they look less constrained. This behavior is due to the fact that the first mode of the two beams is equal zero (rigid body motion), and replaced by the second mode to be the fundamental mode. The values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only. But for immovable ends, the clamped-free and hinged-free beams have equal frequencies in longitudinal vibration, and those of the other beams are also the same.

In this study, the effect of the end conditions of cross-ply laminated composite beams (CLCB) on their non-dimensional natural frequencies of free vibration was investigated. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. In that model, a three-noded element with three degrees of freedom at each node is assumed. Numerical results were verified by comparisons with other relevant works. The end conditions of beams are: clamped-free (CF), hinged-hinged (HH), clamped-clamped (CC), hinged-clamped (HC), hinged-free (HF), free-free (FF). Each beam has either movable ends or immovable ends. It is found that the more constrained beams have the higher values of natural frequencies of transverse vibration. However, the free-free and hinged-free beams are found to have the highest frequencies of transverse vibration amongst all beams although they look less constrained. This behavior is due to the fact that the first mode of the two beams is equal zero (rigid body motion), and replaced by the second mode to be the fundamental mode. The values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only. But for immovable ends, the clamped-free and hinged-free beams have equal frequencies in longitudinal vibration, and those of the other beams are also the same.

Computers & Structures, 1989

This paper presents a refined higher-order theory for free vibration analysis of unsymmetricaliy laminated multilayered plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia effects. A simple Co linite element formulation is presented and the nine-noded Lagrangian element is chosen with seven degrees of freedom per node. Numerical results are presented showing the parametric effects of aspect ratio, length,&hickness ratio, number of layers, and lamination angle. The present theory predicts the frequencies more accurately when compared with firs&order and classical plate theories.

Composite Structures, 1997

Analytical solution to the natural frequency analysis of composite and sandwich beams based on a higher order refined theory is presented. This theory incorporates cubic axial, transverse shear and quadratic transverse normal strain components in the basic formulation-thus modelling the warping of cross section accurately and eliminating the need for a shear correction coefficient. Also, it considers each layer of the lamina to be orthotropic and in a two dimensional state of plane stress. The equations of equilibrium are derived using Hamilton's principle. Numerical experiments are carried out and from the results of thick and thin sections, conclusions are drawn.

Meccanica, 1993

This paper presents a new displacement-based one-dimensional model for the analysis of multilayered composite beams. The kinematic restriction of cross sections rigid in their own planes is introduced. The axial displacements over the cross sections are represented in terms of explicitly defined piecewise polynomial warping functions with discontinuous derivatives at the interlaminae, whereas the amplitude of the displacements along the beam axis is established by means of a variational formulation. It is proved that the proposed representation of the axial displacements yields the exact solution of the 'interior domain problem' for a beam subjected to a transverse load varying according to a polynomial law. It is shown that two or three coordinate functions are sufficient to yield continuous distributions of equilibrated stresses except for small neighborhoods of the constrained cross sections, where a higher number of warping functions could be used in order to obtain a better accuracy. The numerical results show excellent agreement with plane stress finite element and plane strain exact solutions.

Australian Journal of Mechanical Engineering, 2020

This approach present improved higher-order layer-wise theory for the investigation of flawlessly wedged sandwich-composite beams with general laminate configurations. Our analysis incorporates the continuity assumption of interlaminar shear stresses and in-plane and flexural displacements between interfaces. In addition, interlaminar shear stresses are constrained using the Lagrange multiplier technique by introducing new unknown variables. These unknown variables are expressed with interlaminar strain energy, assuming that the strain energy is continuous throughout the overall thickness of the beam. To govern the newly introduced and other unknown variables, the total potential energy (TPE) is minimised using variational calculus. The numerical analysis results show that our approach provides enhanced accuracy to examine sandwich-composite beams.

– First order shear deformation (FSDT) theory for laminated composite beams is used to study the free vibration of laminated composite beams, and the finite element method (FEM) is employed to obtain the numerical solution of the governing differential equations. Free vibration analysis of cross – ply symmetrically laminated beams with rectangular cross – section for various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency parameters are evaluated in comparison with previous work available in the literature. The good agreement with other available data demonstrates the capability and reliability of the finite element method and the adopted beam model used.

Journal of Sound and Vibration, 1989

Recently developed shear deformation theory is used to analyze vibrations of laminated composite and sandwich plates in conjunction with a C" isoparametric finite element formulation. The present theory is based on a higher order displacement model and the three-dimensional Hooke's laws for plate material, giving rise to a more realistic representation of the cross-sectional deformation. The theory does not require the usual shear correction coefficients generally associated with Reissner-Mindlin theories. A special mass lumping procedure is used in the dynamic equilibrium equations. The numerical examples presented are compared with 3-D elasticity/analytical and Mindlin's plate solutions, and it is demonstrated that the present model predicts the frequencies more accurately when compared with the first order shear deformation theories and classical plate theories.