Technical noteEffect of fibre orientation on the vibration behaviour of orthotropic rectangular plates
Abstract
The effect of fibre orientation on the fundamental frequency of thin rectangular/square orthotropic plates is studied using a high precision triangular orthotropic finite element. In the case of a square plate with a simply supported boundary condition, the fundamental frequency increases as the fibre orientation varies from 0 to 45° and decreases symmetrically from 45 to 90°. An opposite trend is observed in the case of a square plate with clamped boundary conditions. The element is useful in studying plates of arbitrary plan form and arbitrary fibre orientation.
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Cited by (18)
Vibration transmission and power flow of laminated composite plates with inerter-based suppression configurations
2021, International Journal of Mechanical SciencesThis paper investigates the vibration transmission and power flow behaviour of harmonically excited laminated composite plates attached with different inerter-based suppression configurations. The substructure approach based on analytical and numerical methods is employed to obtain the steady-state dynamic response. Power flow analysis is carried out to determine the time-averaged power flow input and transmission as well as the kinetic energy of the plate. The power flow density vector is used to show explicitly the vibration transmission paths within the composite plate. It is shown that the fibre orientation and stacking sequences can have significant effects on the time-averaged power flow characteristics as well as the dominant vibration transmission paths. It is also shown that passive spring, damper and inerter elements may be attached to the plate to modify its vibration response and transmission according to specific design requirements. The proposed inerter-based suppression device with two different configurations can reduce the vibration level over a wide frequency range for vibration suppression. The findings may provide insights for the enhanced dynamic designs of laminated composite plates, and the suppression of their vibrations using inerter-based devices.
Optimum design of composite laminates for frequency constraints
2007, Composite StructuresA method for minimum thickness multilayer rectangular composite laminates is presented which is based on a layerwise optimization procedure under natural frequency limitations. In this method, all types of boundary conditions and their combinations can be taken into account. Analysis is based on the Ritz approximations, and no limitations exist on the number of layers that can be considered or the plate’s aspect ratio. Coupling of flexural and torsional stiffness terms need not be zero in any of the cases. Optimization constraints can be either limits on the fundamental frequency or separation between two natural frequencies. Hybrid combination of layers is also made possible in order to enhance the laminate economy, and a short cut procedure is recommended to save total computational efforts.
Examples are offered that illustrate the method’s capabilities, and the results are verified by comparison to some published ones.
Free vibrations of rectangular unsymmetrically laminated composite plates with internal line supports
2001, Computers and StructuresFree vibrations of rectangular unsymmetrically laminated composite plates with internal line supports in one or two directions are studied. The static beam functions, which are the complete solutions of a unit width strip taken from the plate in the direction parallel to the edges of the plate and under a series of transverse static sinusoidal loads, are used as the trial functions of the transverse bending deflection of the plate. Besides, the vibrating bar functions are used as the trial functions of the in-plane stretching deformation of the plate. The Rayleigh–Ritz method is applied to arrive at the governing eigenfrequency equation in which the coupling effect of bending and stretching is contained. Different transverse boundary conditions combining with various in-plane constraints are considered in the analysis. The effects of fiber orientation angles and locations of internal line supports on eigenfrequencies of cross-ply and antisymmetric angle-ply laminated composite plates of two layers are investigated in detail. Convergence and comparison study show the correctness and effectiveness of the proposed method. Sets of valuable results are presented for the first time, which can serve as benchmarks for future reference.
On the use of the domain decomposition method for vibration of symmetric laminates having discontinuities at the same edge
1994, Journal of Sound and VibrationA free vibration analysis of symmetrically laminated plates with mixed edge boundary conditions is presented. A highly efficient and accurate domain decomposition method is employed. To establish the model, the original domain is first assumed to be an assemblage of small subdomains, with the admissible functions of each subdomain represented by sets of orthogonal polynomials. These polynomials are generated by using the Gram-Schmidt procedure. The continuity matrices resulting from the geometric compatibilities between the subdomains are used to couple the eigenvectors of adjacent subdomains. The stiffness and mass matrices of each subdomain, after pre- and post-multiplying by the respective continuity matrices, are assembled to form the global stiffness and mass matrices. To demonstrate this method, the free vibrations of symmetrically laminated plates of various types of mixed edge boundaries are calculated.
Method of domain decomposition in vibrations of mixed edge anisotropic plates
1993, International Journal of Solids and StructuresThis paper presents the first known study on the flexural vibration of anisotropic plates with mixed discontinuous periphery boundaries. A newly developed domain decomposition method is used in the analysis to derive the governing eigenvalue equation. In the solution process, the complex plate domain is decomposed into appropriate subdomains. The displacement functions of each subdomain are represented by sets of orthogonally generated polynomials that satisfy the essential geometric boundary conditions. From the compatibility requirements at the interconnecting boundaries, sets of continuity matrices are computed. These matrices are used to couple the respective eigenvectors of the adjacent subdomains. The stiffness and mass matrices of each subdomain after being pre- and post-multiplied by the corresponding continuity matrix, are assembled to form the global stiffness and mass matrices of the anisotropic plate. Convergence and comparison studies have been carried out on selected cases to establish the rate of convergence and degree of accuracy of the present formulation. A comprehensive range of frequency parameters and deflection mode shapes of anisotropic plates with different mixed edge configurations are obtained using the proposed method. The effects of fiber orientation and the partial mixed ratio on the vibrational response of these plates have been investigated in detail.
Eigen analysis of fiber-reinforced composite plates
1993, Composite StructuresComposites plates of various orientation and thickness with fiber-reinforced plastics (FRP) find increasing applications in aerospace and automotive structures (due to their high strength, stiffness to weight ratios, and high damping characteristics). Determination of the dynamic characteristics and the investigation of such structures are essential not only in the design but also in manufacture development.
In the present paper, the eigen analysis of laminated square plates with various fiber orientations, various boundary fixations, and different stacking sequences has been presented and discussed. The experimental analysis and finite element techniques are utilized to study the effect of fiber orientation and boundary conditions on the dynamic characteristics of frequency and mode shapes. The vibrational system technique is utilized for experimental measurements. The results show agreement between experimental and theoretical investigations. Also, these results show a close connection between damping and stiffness characteristics in glass-fiber composites.