Vibration characteristics of a rotating pre-twisted composite laminated blade

Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets

Abstract: This paper investigates the free vibrations of the rotating pretwisted functionally graded (FG) composite cylindrical panels reinforced with the graphene platelets (GPLs) by considering the cantilever boundary conditions. The weight fraction of the graphene platelets in each ply may be different, which leads to the layer-wise functionally graded composite cylindrical panels reinforced with the GPLs. The effective Young's modulus is calculated by the modified Halpin-Tsai model. The effective Poisson's ratio and mass density are derived by the rule of the mixture. The strain-displacement relationship is acquired by the Green strain tensor. Based on the first-order shear deformation theory, Chebyshev-Ritz method is used to obtain the natural frequencies of the rotating pretwisted functionally graded composite cylindrical panel reinforced with the GPLs. The natural frequencies are discussed by considering different material and geometry parameters of the rotating pretwisted functionally graded composite cylindrical panel reinforced with the GPLs, such as the GPL distribution pattern, the GPL weight fraction, the geometries of the GPLs, the pretwisted angle, the presetting angle and the rotating speed. Several validations are carried out, the numerical results are in good agreement with the results of the literature and ANSYS.

Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers

Abstract: A new dynamic model of the rotating tapered cantilever cylindrical panel with the graphene coating layers is developed to investigate the vibration characteristics of the rotating pretwisted tapered blade. It is assumed that the graphene platelets (GPLs) are randomly oriented and uniformly dispersed in the top layer and the bottom layer of the rotating pretwisted composite tapered blade. The modified Halpin-Tsai model is used to estimate the effective Young's modulus. The rule of the mixture is used to calculate the effective Poisson's ratio and mass density. Based on the Green strain tensor, an accurate strain-displacement relationship is acquired. The effects of the centrifugal force and Coriolis force are considered in the formulation. The Chebyshev-Ritz method is utilized to obtain the natural frequencies and mode shapes of the rotating pretwisted composite tapered blade with the graphene coating layers. The accuracy of the proposed model is validated through several comparison studies with the results of the present literatures and ANSYS. The free vibration characteristics are analyzed by considering different material and geometry parameters of the rotating pretwisted composite tapered cantilever cylindrical panel with the graphene coating layers, such as the graphene platelet (GPL) geometry, GPL weight fraction, taper ratio, length-to-radius ratio, pretwist angle, presetting angle and rotating speed. The frequency veering and the mode shape shift phenomena are found in the rotating pretwisted tapered cantilever cylindrical panel with the graphene coating layers.

Saturation phenomena and nonlinear resonances of rotating pretwisted laminated composite blade under subsonic air flow excitation

Abstract: The purpose of the present investigation is to reveal the saturation phenomena and the primary resonance of a rotating pretwisted laminated composite blade subjected to a subsonic airflow excitation in the case of 1:2 internal resonance. The flexible compressor blade is treated as a rotating laminated composite cantilever rectangular plate clamped on the rigid disk with the pretwisted and the preset angles. The subsonic air flow is regarded as the transverse excitation around the finite length of the plate. The subsonic air force is derived by using Vortex Lattice method. The third-order shear deformation plate theory, von Karman geometry nonlinearity and Hamilton principle are utilized to derive the nonlinear partial differential governing equations of motion for the rotating plate subjected to the subsonic aerodynamic force. Chebyshev-Ritz method is used to obtain the natural frequencies of the composite cantilever plate with varying rotating speed. Using Galerkin method, the partial differential governing equations of motion is discretized into a two-degree-of-freedom nonlinear system. The nonlinear torsional-bending coupled vibrations with 1:2 internal response are investigated by the method of multiple scales. The saturation and the jumping phenomena between the torsional vibration mode and the bending vibration mode are investigated for the rotating cantilever plate. Numerical simulations demonstrate that the rotating plate exhibits the complicated nonlinear dynamic behaviors under the effect of the excitation detuning parameter, damping parameter and stiffness coupling coefficients. The energy transfer phenomenon is observed for the composite cantilever plate under the subsonic air flow force.

Predicting vibration characteristics of rotating composite blades containing CNT-reinforced composite laminae and damaged fiber-reinforced composite laminae

Abstract: Existing of cracks within blade structures can cause stiffness degradation and hence changes their vibration characteristics This study investigates the vibration behaviors of rotating pre-twisted hybrid composite blades containing functionally graded carbon nanotube-reinforced composite (FG-CNTRC) laminae and damaged fiber-reinforced composite (FRC) laminae The degraded stiffness of the cracked lamina is modeled through the self-consistent model (SCM) The blade is modeled as a shell structure that is formed by twisting a plate around its mean line With the help of the differential geometry theory, a novel shell model has been derived to describe the kinetics of the blade The effect of the Coriolis and centrifugal force are both presented in the formulation, which results in a damped-like free vibration system governed by a system of second-order ordinary differential equations (ODEs) Utilizing the state space technique, the system is reformulated to a system of first-order ODEs The IMLS-Ritz method is then used for discretizing the ODEs After carefully validating the effectiveness of the presented model through a series of comparison studies, parametric studies including CNT distribution configuration, rotating speed, geometrical parameters on the vibration responses of cross-plied composite blades are systematically examined The vibration characteristics of angle-plied composite blades are also investigated

Dynamic stability of rotating cantilever composite thin walled twisted plate with initial geometric imperfection under in-plane load

Abstract: The initial geometric imperfections in manufacturing structure are unavoidable. Critical buckling load and dynamic instability of the rotating cantilever cross ply laminate thin walled twisted plate with exponential function type initial geometric imperfection are investigated for the first time. The mode shapes are obtained by using Rayleigh-Ritz method and shallow shell theory including the influence of rotational speed and imperfection. Based on the Lagrange equations and the obtained mode shape function, motion equations considering the first three modes of the system are derived. The mode shapes, critical loads and dynamic instability obtained in present have been verified by comparing them with other researcher results. The detail studies about the effect of rotating speed, twisted angle, stacking sequence and imperfection factors of the rotating thin walled twisted plate subjected to the in-plane load on the static critical buckling load and dynamic instability are carried out.

Mechanics of Laminated Composite Plates and Shells : Theory and Analysis, Second Edition

Abstract: The use of composite materials in engineering structures continues to increase dramatically, and there have been equally significant advances in modeling for general and composite materials and structures in particular. To reflect these developments, renowned author, educator, and researcher J.N. Reddy created an enhanced second edit

Mechanics of laminated composite plates and shells : theory and analysis

Abstract: Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods Fiber-Reinforced Composite Materials Mathematical Preliminaries Equations of Anisotropic Entropy Virtual Work Principles Variational Methods Summary Introduction to Composite Materials Basic Concepts and Terminology Constitutive Equations of a Lamina Transformation of Stresses and Strains Plan Stress Constitutive Relations Classical and First-Order Theories of Laminated Composite Plates Introduction An Overview of Laminated Plate Theories The Classical Laminated Plate Theory The First-Order Laminated Plate Theory Laminate Stiffnesses for Selected Laminates One-Dimensional Analysis of Laminated Composite Plates Introduction Analysis of Laminated Beams Using CLPT Analysis of Laminated Beams Using FSDT Cylindrical Bending Using CLPT Cylindrical Bending Using FSDT Vibration Suppression in Beams Closing Remarks Analysis of Specially Orthotropic Laminates Using CLPT Introduction Bending of Simply Supported Rectangular Plates Bending of Plates with Two Opposite Edges Simply Supported Bending of Rectangular Plates with Various Boundary Conditions Buckling of Simply Supported Plates Under Compressive Loads Buckling of Rectangular Plates Under In-Plane Shear Load Vibration of Simply Supported Plates Buckling and Vibration of Plates with Two Parallel Edges Simply Supported Transient Analysis Closure Analytical Solutions of Rectangular Laminated Plates Using CLPT Governing Equations in Terms of Displacements Admissible Boundary Conditions for the Navier Solutions Navier Solutions of Antisymmetric Cross-Ply Laminates Navier Solutions of Antisymmetric Angle-Ply Laminates The Levy Solutions Analysis of Midplane Symmetric Laminates Transient Analysis Summary Analytical Solutions of Rectangular Laminated Plates Using FSDT Introduction Simply Supported Antisymmetric Cross-Ply Laminated Plates Simply Supported Antisymmetric Angle-Ply Laminated Plates Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported Transient Solutions Vibration Control of Laminated Plates Summary Theory and Analysis of Laminated Shells Introduction Governing Equations Theory of Doubly-Curved Shell Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells Linear Finite Element Analysis of Composite Plates and Shells Introduction Finite Element Models of the Classical Plate Theory (CLPT) Finite Element Models of Shear Deformation Plate Theory (FSDT) Finite Element Analysis of Shells Summary Nonlinear Analysis of Composite Plates and Shells Introduction Classical Plate Theory First-Order Shear Deformation Plate Theory Time Approximation and the Newton-Raphson Method Numerical Examples of Plates Functionally Graded Plates Finite Element Models of Laminated Shell Theory Continuum Shell Finite Element Postbuckling Response and Progressive Failure of Composite Panels in Compression Closure Third-Order Theory of Laminated Composite Plates and Shells Introduction A Third-Order Plate Theory Higher-Order Laminate Stiffness Characteristics The Navier Solutions Levy Solutions of Cross-Ply Laminates Finite Element Model of Plates Equations of Motion of the Third-Order Theory of Doubly-Curved Shells Layerwise Theory and Variable Kinematic Model Introduction Development of the Theory Finite Element Model Variable Kinematic Formulations Application to Adaptive Structures Layerwise Theory of Cylindrical Shell Closure Subject Index

Nonlinear Vibrations and Stability of Shells and Plates

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

Vibration of laminated shells and plates

Abstract: 1. INTRODUCTION 2. SHELL THEORIES 3. METHODS OF ANALYSIS 4. CURVED BEAMS 5. PLATES SHALLOW SHELLS CYLINDRICAL SHELLS 8. CONICAL SHELLS 9. SPHERICAL SHELLS 10. COMPLICATING EFFECTS REFERENCES

On a curve veering aberration

Abstract: In numerous places in the literature of eigenvalue problems of mathematical physics one finds curves which approach each other and suddenly veer away. The author postulates that this ugly behavior may be the result of approximation in the representation of physical reality. In the present paper such behavior is demonstrated to arise from the application of the well-known Ritz-Galerkin method to the classical eigenvalue problem of the free vibration of a rectangular membrane.