Vibration characteristics of a rotating pre-twisted composite laminated blade
TL;DR: In this article, a new dynamic model based on the shell theory is presented to investigate the vibration behavior of a rotating composite laminated blade with a pre-twisted angle, where the effects of the Coriolis and centrifugal forces due to the rotation motion of the blade are considered in the formulation.
About: This article is published in Composite Structures.The article was published on 2019-01-15. It has received 45 citations till now. The article focuses on the topics: Vibration & Normal mode.
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TL;DR: In this paper, the vibration characteristics of the rotating pretwist functionally graded (FG) sandwich blades operating in the thermal environment are studied for the first time, where the FG sandwich blade is composed of a single metallic core combined with two FG surface layers and is assumed to be in a steady state temperature field.
16 citations
TL;DR: In this paper, the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment were dealt with.
Abstract: This paper deals with the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment. The imperfect beam contains different modes of geometric imperfections such as sine, global, and local modes, and it is restrained by an elastic root. Three types of CNTs distributions including FG-X, UD, and FG-O distributions are considered and the material is temperature-dependent. First, bending–bending coupled governing equations are established through the Hamilton’s principle based on the Euler–Bernoulli beam theory. By setting different parameters, the governing equations can solve the problems of free vibration, buckling, and dynamic stability of the beam. Then, the differential quadrature method (DQM) is employed to get the discrete equations and numerical solutions of the natural frequency, critical buckling load, and instability region. Finally, parametric studies are carried out to present the effects of hub radius, rotating speed, material properties, geometric imperfections, and rigidity of the elastic root on the natural frequencies, critical buckling load, and instability regions. Results show that the elastic root and imperfection mode have obvious influence on the instability regions.
16 citations
TL;DR: In this paper, a quasi-three-dimensional (quasi-3D) dynamic model for rotating pre-twisted functionally graded (FG) blades based on the three-dimensional elasticity shell theory and Carrera unified formulation is provided.
15 citations
TL;DR: In this paper, a composite cantilever plate model with variable high speed rotating blade subject to transverse aerodynamic force and centrifugal force is established and the nonlinear partial differential governing equations of motion are established for the rotating blade with variable rotating speed.
Abstract: A composite cantilever plate model with variable high speed rotating blade subject to transverse aerodynamic force and centrifugal force is established. Based on the third-order shear deformation theory, von Karman large deformation theory and Hamilton's principle, the nonlinear partial differential governing equations of motion are established for the rotating blade with variable rotating speed. The two-degree-of-freedom nonlinear ordinary differential equations of motion are obtained by using Galerkin method with Chebyshev polynomials for the rotating blade. The influences of different structural parameters on the natural frequencies of the blade with variation of the rotating speed are investigated. The method of multiple scales is applied to obtain the averaged equations with the primary parametric resonance-1/2 subharmonic resonance and the relationship of 1:2 internal resonance. Numerical simulations are performed to portray the frequency-response curves and the complex nonlinear dynamic behaviors of the rotating blade by discussing the effect of the aerodynamic force. The effects of the varying rotating speed, the centrifugal force, the pre-twist angle and the pre-setting angle are taken into account on the nonlinear dynamics of the rotating blade. It is observed from the frequency-response curves that the rotating blade exhibits the hardening nonlinear behaviors as well as the jumping phenomena. The bifurcation diagrams, the phase portraits and the waveforms are utilized to illustrate the complex nonlinear dynamic behaviors of the rotating blade, such as the periodic, the quasi-periodic and the chaotic motions.
13 citations
TL;DR: In this paper, the maximum vibration amplitudes of composite fan blades at different rotational speeds could be affected by stacking sequences and the responses of metal blade are more sensitive to the natural frequencies of the second to the fifth blade modes than those of the composite blades.
12 citations
References
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Book•
19 Nov 1996TL;DR: The use of composite materials in engineering structures continues to increase dramatically, and there have been significant advances in modeling for general and composite materials and structures in particular as discussed by the authors. But the use of composites is not limited to the aerospace domain.
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
5,301 citations
Book•
01 Jan 2004
TL;DR: In this article, the authors present an analysis of the properties of composite materials using the classical and first-order theories of Laminated Composite Plates and shells, as well as a detailed analysis of their properties.
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
3,457 citations
Book•
01 Aug 2014
TL;DR: In this article, a comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells is presented. But the authors do not consider the effect of boundary conditions on the large-amplitude vibrations of circular cylinders.
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.
862 citations
Book•
01 Jan 2004
TL;DR: In this paper, the authors present a method for analyzing the effect of different kinds of shells on the performance of different types of shells, such as: CURVED BEAMS, PLATES SHALLOW SHELLS, CYLINDRICAL SHELLs, SPHERICAL SHELS, etc.
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
485 citations
TL;DR: In this article, the Ritz-Galerkin method is applied to the classical eigenvalue problem of the free vibration of a rectangular membrane, and it is shown that the behavior of curves which approach each other and suddenly veer away may be the result of approximation in the representation of physical reality.
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.
221 citations