Three-Dimensional Vibration Analysis of Rotating Laminated Composite Blades

1993 ◽  
Author(s):  
O. G. McGee ◽  
H. R. Chu
Keyword(s):  
Vibration Analysis ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Three Dimensional ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Composite Fiber ◽  
Coriolis Acceleration ◽  
Composite Blade ◽  
Composite Blades

This work offers the first known three-dimensional (3-D) continuum vibration analysis for rotating, laminated composite blades. A cornerstone of this work is that the dynamical energies of the rotating blade are derived from a 3-D elasticity-based, truncated quadrangular pyramid model incorporating laminated orthotropicity, full geometric nonlinearity using an updated Lagrangian formulation and Coriolis acceleration terms. These analysis sophistications are included to accommodate the nonclassical directions of modern blade designs comprising thin, wide chord lifting surfaces of laminated composite construction. The Ritz method is used to minimize the dynamical energies with displacements approximated by mathematically complete polynomials satisfying the vanishing displacement conditions at the blade root section exactly. Several tables and graphs are presented which describe numerical convergence studies showing the validity of the assumed displacement polynomials used herein. Nondimensional frequency data is presented for various rotating, truncated quadrangular pyramids, serving as first approximations of practical blades employed in aircraft engines and fans. A wide scope of results explain the influence of a number of parameters coined to rotating, laminated composite blade dynamics, namely aspect ratio (a/b), chord ratio (c/b), thickness ratio (b/h), variable thickness distribution (hl/ht), blade pretwist angle (ϕo), composite fiber orientation angle (θ), and angular velocity (Ω). Additional examples are given which elucidate the significance of the linear and nonlinear kinematics used in the present 3-D formulation along with the importance of the Coriolis acceleration terms included in the analysis.

Three-Dimensional Vibration Analysis of Rotating Laminated Composite Blades

1994 ◽  
Vol 116 (3) ◽  
pp. 663-671 ◽  
Author(s):  
O. G. McGee ◽  
H. R. Chu
Keyword(s):  
Vibration Analysis ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Three Dimensional ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Composite Fiber ◽  
Coriolis Acceleration ◽  
Composite Blade ◽  
Composite Blades

This work offers the first known three-dimensional continuum vibration analysis for rotating, laminated composite blades. A cornerstone of this work is that the dynamic energies of the rotating blade are derived from a three-dimensional elasticity-based, truncated quadrangular pyramid model incorporating laminated orthotropicity, full geometric nonlinearity using an updated Lagrangian formulation and Coriolis acceleration terms. These analysis sophistications are included to accommodate the nonclassical directions of modern blade designs comprising thin, wide chord-lifting surfaces of laminated composite construction. The Ritz method is used to minimize the dynamic energies with displacements approximated by mathematically complete polynomials satisfying the vanishing displacement conditions at the blade root section exactly. Several tables and graphs are presented that describe numerical convergence studies showing the validity of the assumed displacement polynomials used herein. Nondimensional frequency data are presented for various rotating, truncated quadrangular pyramids, serving as first approximations of practical blades employed in aircraft engines and fans. A wide scope of results explain the influence of a number of parameters coined to rotating, laminated composite blade dynamics, namely aspect ratio (a/b), chord ratio (c/b), thickness ratio (b/h), variable thickness distribution (h1/ht), blade pretwist angle (φ0), composite fiber orientation angle (θ), and angular velocity (Ω). Additional examples are given that elucidate the significance of the linear and nonlinear kinematics used in the present three-dimensional formulation along with the importance of the Coriolis acceleration terms included in the analysis.

Vibration Analysis of Laminated Composite Rectangular Plates With General Boundary Conditions

2018 ◽  
Author(s):  
Yu Fu ◽  
Jianjun Yao ◽  
Zhenshuai Wan ◽  
Gang Zhao
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Geometric Parameters ◽  
General Boundary ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Benchmark Solutions

In this investigation, the free vibration analysis of laminated composite rectangular plates with general boundary conditions is performed with a modified Fourier series method. Vibration characteristics of the plates have been obtained via an energy function represented in the general coordinates, in which the displacement and rotation in each direction is described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate any possible jumps and boundary discontinuities. All the expansion coefficients are then treated as the generalized coordinates and determined by Rayleigh-Ritz method. The convergence and reliability of the current method are verified by comparing with the results in the literature and those of Finite Element Analysis. The effects of boundary conditions and geometric parameters on the frequencies are discussed as well. Finally, numerous new results for laminated composite rectangular plates with different geometric parameters are presented for various boundary conditions, which may serve as benchmark solutions for future research.

3D Vibration Analysis of Hermetic Capsules by Using Ritz Method

2017 ◽  
Vol 17 (03) ◽  
pp. 1750040
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Eigenvalue Problem ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Legendre Polynomials ◽  
Present Method ◽  
Ritz Method ◽  
Three Dimensional ◽  
Dynamic Equations ◽  
Vibration Frequencies ◽  
Good Agreement

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of a hermetic capsule comprising a cylinder closed with hemi-ellipsoidal caps at both ends. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components [Formula: see text], [Formula: see text], and [Formula: see text] in the radial, circumferential, and axial directions, respectively, are taken to be periodic in [Formula: see text] and in time, and the Legendre polynomials in the r and z directions instead of ordinary ones. Potential (strain) and kinetic energies of the hermetic capsule are formulated, and the Ritz method is used to solve the eigenvalue problem, thereby yielding upper bound values of the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Typical convergence studies are carried out for the first five frequencies. The frequencies from the present 3D method are in good agreement with those obtained from other 3D approach and 2D shell theories proposed by previous researchers.

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

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