Effect of lamination schemes on natural frequency and modal damping of fiber reinforced laminated beam using Ritz method

The current study focussed on analysing natural frequency and damping of laminated composite beams (LCBs) by varying fiber angle, aspect ratio, material property and boundary conditions. Ritz method with displacement field based on the shear and normal deformable theory is used and the modal damping is calculated using modal strain energy method. Effects of symmetric angle-ply and cross-ply, anti symmetric cross-ply, balanced and quasi-isotropic lay up schemes on modal damping are presented for the first time. Results revealed that influence of lay-up scheme on natural frequencies is significant for the thin beams while the modal damping of the thin beams are not sensitive to lay-up scheme. However, the lay-up scheme influences the damping significantly for the thick beams. Similarly, high strength fiber reinforced LCBs have higher natural frequency while low strength fiber reinforced LCBs have higher damping due to the better fiber-matrix interaction.

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Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

Journal of Vibration and Acoustics ◽

10.1115/1.2889641 ◽

1996 ◽

Vol 118 (2) ◽

pp. 141-146 ◽

Cited By ~ 2

Author(s):

S. Abrate

Keyword(s):

Natural Frequency ◽

Material Properties ◽

Composite Structures ◽

Natural Frequencies ◽

Ritz Method ◽

Laminated Composite ◽

Composite Plates ◽

Mode Shapes ◽

Fundamental Natural Frequency ◽

Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

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Implementation of the ultrasonic through-transmission technique for the elastic characterization of fiber-reinforced laminated composite

DYNA ◽

10.15446/dyna.v86n208.70279 ◽

2019 ◽

Vol 86 (208) ◽

pp. 153-161

Author(s):

Carlos A. Meza ◽

Ediguer E. Franco ◽

Joao L. Ealo

Keyword(s):

Laminated Composites ◽

Weight Ratio ◽

Laminated Composite ◽

High Strength ◽

Mechanical Tests ◽

Fiber Reinforced ◽

Transmission Technique ◽

Laminated Materials

Laminated composites are widely used in applications when a high strength-to-weight ratio is required. Aeronautic, naval and automotive industries use these materials to reduce the weight of the vehicles and, consequently, fuel consumption. However, the fiber-reinforced laminated materials are anisotropic and the elastic properties can vary widely due to non-standardized manufacturing processes. The elastic characterization using mechanical tests is not easy, destructive and, in most cases, not all the elastic constants can be obtained. Therefore, alternative techniques are required to assure the quality of the mechanical parts and the evaluation of new materials. In this work, the implementation of the ultrasonic through-transmission technique and the characterization of some engineering materials is reported. Isotropic materials and laminated composites of carbon fiber and glass fiber in a polymer matrix were characterized by ultrasound and mechanical tests. An improved methodology for the transit time delay calculation is reported.

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Free Vibration Analysis of Laminated Composite Plates with General Boundary Elastic Supports Under Initial Thermal Load

Al-Khwarizmi Engineering Journal ◽

10.22153/kej.2019.09.004 ◽

2019 ◽

Vol 15 (4) ◽

pp. 23-32

Author(s):

Mohammed B. Hammed ◽

Widad I. Majeed

Keyword(s):

Aspect Ratio ◽

Free Vibration ◽

Natural Frequency ◽

Thermal Load ◽

Ritz Method ◽

Laminated Composite ◽

Free Vibration Analysis ◽

Composite Plates ◽

Design Parameters ◽

Laminated Plate

Free vibration behavior was developed under the ratio of critical buckling temperature of laminated composite thin plates with the general elastic boundary condition. The equations of motion were found based on classical laminated plate theory (CLPT) while the solution functions consists of trigonometric function and a continuous function that is added to guarantee the sufficient smoother of the so-named remaining displacement function at the boundaries, in this research, a modified Fourier series were used, a generalized procedure solution was developed using Ritz method combined with the imaginary spring technique. The influences of many design parameters such as angles of layers, aspect ratio, thickness ratio, and ratio of initial in- plane thermal load in addition to different boundary conditions on the natural frequencies of laminated plate is analyzed. In general, the changes of fundamental natural frequency is inversely proportional with the ratio of thermal buckling load, also most parameters aspect ratio effect on the natural frequency about 35 – 40%. The present results were compared with those obtained by other researchers, and show good agreement.

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Natural Frequency for a Composite Structure Made with a Combination of Metal and Laminated Composites

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.f8402.038620 ◽

2020 ◽

Vol 8 (6) ◽

pp. 2340-2344

Keyword(s):

Modal Analysis ◽

Natural Frequency ◽

Composite Structure ◽

Laminated Composite ◽

High Strength ◽

Element Analysis ◽

Volume Percentage ◽

Steam Turbine Blade ◽

Laminated Composite Beam ◽

Natural Frequency Analysis

The need for low weight and high strength of the component is in high demand in various aerospace and defense industries and in line with this utilization of the combination of metal and composite increases. In this work, the natural frequency analysis of the structure, is carried out which is a combination of metal and composite. The natural frequency of the system is directly proportional to the stiffness of the system i.e. high natural frequency reflects high stiffness of materials. The structure considered like a cantilever beam, initially considering Titanium alloy the finite element analysis to get natural frequency carried out and validated using an analytical method. Then modal analysis performed using FEA for laminated composite structure and validate with the experimental results and received good agreement. The laminated composite beam manufactured using a hand layup method. Lastly, the structure modeled as a combination of laminated composite material & metal and FEA modal analysis done. The various volume percentage of composite and metal is studied and the best one finds out. The structure considered related to the last stage of the steam turbine blade.

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A two-step approach for damage detection in laminated composite structures using modal strain energy method and an improved differential evolution algorithm

Composite Structures ◽

10.1016/j.compstruct.2016.03.027 ◽

2016 ◽

Vol 147 ◽

pp. 42-53 ◽

Cited By ~ 48

Author(s):

T. Vo-Duy ◽

V. Ho-Huu ◽

H. Dang-Trung ◽

T. Nguyen-Thoi

Keyword(s):

Composite Structures ◽

Strain Energy ◽

Differential Evolution Algorithm ◽

Laminated Composite ◽

Modal Strain Energy ◽

Modal Strain Energy Method ◽

Laminated Composite Structures ◽

Evolution Algorithm ◽

Improved Differential Evolution Algorithm ◽

Strain Energy Method

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A Modified MSE Method for Viscoelastic Systems: A Weighted Stiffness Matrix Approach

Journal of Vibration and Acoustics ◽

10.1115/1.2873923 ◽

1995 ◽

Vol 117 (2) ◽

pp. 226-231 ◽

Cited By ~ 9

Author(s):

B.-G. Hu ◽

M. A. Dokainish ◽

W. M. Mansour

Keyword(s):

Stiffness Matrix ◽

Strain Energy ◽

Real Eigenvalue ◽

Modal Strain Energy ◽

Modal Strain Energy Method ◽

Damped System ◽

Modal Damping ◽

Weighted Matrix ◽

Error Index

The conventional Modal Strain Energy method (MSE is briefly discussed. Several indices are proposed to characterize a viscoelastically damped system. An Overall Error Index is proposed to assess the accuracy of the solution. A Modified MSE method is developed for a better evaluation of modal damping. Instead of neglecting the damping stiffness matrix in the determination of the eigenvectors, as is the case in the conventional MSE method, the authors used a weighted matrix to solve a real eigenvalue problem. With such modification the estimation of the modal damping is often improved. Numerical simulation of multi degree-of-freedom systems are reported using the proposed Modified MSE method and the indices.

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