Vibration Characteristics Analysis of the Rotating Blade Based on a Polynomial Aerodynamic Force

2017 ◽  
Author(s):  
Ming Hui Yao ◽  
Li Ma ◽  
Ming Ming Zhang ◽  
Wei Zhang
Keyword(s):  
Shear Deformation ◽  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Rotating Blade ◽  
Characteristics Analysis ◽  
Method Effects ◽  
Geometric Relationship ◽  
Nonlinear Geometric

In this paper, aerodynamic expressions in forms of the series and the polynomial for a blade with low speed in low pressure compressor are deduced by numerical simulation. Considering shear deformation and cross-section warping effect, the blade is simplified as a pre-twist, pre-setting rotating cantilever plate, which subjected to the aerodynamic force and the centrifugal force. Based on the first-order shear deformation theory and von-Karman nonlinear geometric relationship, nonlinear partial differential dynamic equation of the rotating blade is derived by using Hamilton principle. Equations of motion are converted into a series of ordinary differential equations using Galerkin method. The dynamic frequency and the dynamic deformation of the blade are explored and contrasted with results obtained by finite element method. Effects of parameters on vibration characteristics of the blade under different rotation speed are analyzed. Results show that the explicit expression of the aerodynamic force for the blade has a good applicability.

scholarly journals Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

2020 ◽  
Vol 41 (12) ◽  
pp. 1861-1880
Author(s):  
Li Ma ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Dongxing Cao
Keyword(s):  
Aerodynamic Force ◽  
Shear Deformation Theory ◽  
Phase Portraits ◽  
Cantilever Plate ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Rotating Speed ◽  
Geometric Relationship ◽  
Asymptotic Perturbation ◽  
Nonlinear Geometric

AbstractTurbo-machineries, as key components, have a wide utilization in fields of civil, aerospace, and mechanical engineering. By calculating natural frequencies and dynamical deformations, we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies. In this paper, the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed. The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations, including the centrifugal force and the aerodynamic force. In view of the first-order shear deformation theory and von-Kármán nonlinear geometric relationship, the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle. The second-order ordinary differential equations are acquired by the Galerkin approach. With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance, the averaged equation is derived by the asymptotic perturbation methodology. Bifurcation diagrams, phase portraits, waveforms, and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

Vibration control of magnetostrictive plate under multi- physical loads via trigonometric higher order shear deformation theory

2015 ◽  
Vol 23 (19) ◽  
pp. 3057-3070 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Z Khoddami Maraghi ◽  
H Khani Arani
Keyword(s):  
Elastic Medium ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Feedback Gain ◽  
First Time ◽  
Free Vibration Response

For the first time in this research, a feedback control system is used to study the free vibration response of rectangular plate made of magnetostrictive material. In this regard, magnetostrictive plate (MsP) is analyzed by trigonometric higher order shear deformation theory that involved six unknown displacement functions and does not require shear correction factor. The MsP is supported by elastic medium as Pasternak foundation which considers both normal and shears modules. Also the MsP undergoes in-plane forces in x and y directions. Considering simply supported boundary condition, six equations of motion are derived using Hamilton’s principle and solved by differential quadrature method. Results indicate the effect of aspect ratio, thickness ratio, elastic medium, compression and tension loads on vibration behavior of MsP. Also, findings show the controller effect of velocity feedback gain to minimize the frequency as far as other parameters become ineffective. These findings can be used to active noise and vibration cancellation systems in many structures.

scholarly journals Thermal Free Vibration Analysis of Temperature-Dependent Functionally Graded Plates Using Second Order Shear Deformation

2011 ◽  
Vol 471-472 ◽  
pp. 133-139 ◽  
Author(s):  
Ali Shahrjerdi ◽  
Faizal Mustapha ◽  
S.M. Sapuan ◽  
M. Bayat ◽  
Dayang Laila Abang Abdul Majid ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Second Order ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Functionally Graded Plates ◽  
Temperature Dependent

This research has been conducted to approach second-order shear deformation theory (SSDT) to analysis vibration characteristics of Functionally Graded Plates (FGP’s). Material properties in FGP's were assumed to be temperature dependent and graded along the thickness using a simple power law distribution in term of the volume fractions of the constituents. FGP was subjected to a linear and nonlinear temperature rise. The energy method was chosen to derive the equilibrium equations. The solution was based on the Fourier series that satisfy the simply supported boundary condition (Navier's method). Numerical results indicated the effect of material composition, plate geometry, and temperature fields on the vibration characteristics and mode shapes. The results revealed that, the temperature field and volume fraction distribution had significant effect on the vibration of FGPs. It was observed the second order theory was very close to the other shear deformation theorem as reported in the literature.

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

2021 ◽  
pp. 107754632110399
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Well Posedness ◽  
Governing Equations ◽  
Two Phase

In this article, the well-posedness of several common nonlocal models for higher-order refined shear deformation beams is studied. Unlike the case of classic beams models, both strain-driven and stress-driven purely nonlocal theories lead to an ill-posed issue (i.e., there are excessive mandatory boundary conditions) when considering higher-order shear deformation assumption. As an effective remedy, the well-posedness of strain-driven and stress-driven two-phase nonlocal (StrainDTPN and StressDTPN) models is pertinently evidenced by studying the free vibration problem of nanobeams. The governing equations of motion and standard boundary conditions are derived from Hamilton’s principle. The integral constitutive relation is transformed equivalently to a differential form equipped with two constitutive boundary conditions. Using the generalized differential quadrature method (GDQM), the governing equations in terms of displacements are solved numerically. Numerical results show that both the StrainDTPN and StressDTPN models can predict consistent size-effects of beams with different boundary conditions.

Dynamic Stiffness Analysis of a Beam Based on Trigonometric Shear Deformation Theory

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Jun Li ◽  
Hongxing Hua ◽  
Rongying Shen
Keyword(s):  
Shear Deformation ◽  
Stiffness Matrix ◽  
Deformation Theory ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Beam Element ◽  
Mode Shapes ◽  
Dynamic Stiffness Matrix ◽  
Stiffness Analysis

The dynamic stiffness matrix of a uniform isotropic beam element based on trigonometric shear deformation theory is developed in this paper. The theoretical expressions for the dynamic stiffness matrix elements are found directly, in an exact sense, by solving the governing differential equations of motion that describe the deformations of the beam element according to the trigonometric shear deformation theory, which include the sinusoidal variation of the axial displacement over the cross section of the beam. The application of the dynamic stiffness matrix to calculate the natural frequencies and normal mode shapes of two rectangular beams is discussed. The numerical results obtained are compared to the available solutions wherever possible and validate the accuracy and efficiency of the present approach.

scholarly journals Free vibration characteristics of thick doubly curved variable stiffness composite laminated shells using higher-order shear deformation theory

2018 ◽  
Vol 172 ◽  
pp. 03010 ◽  
Author(s):  
Anand Venkatachari ◽  
K. Ramajeyathilagam
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Mode Shapes ◽  
Laminated Shells ◽  
Surface Displacements ◽  
Edge Conditions ◽  
Geometric Variables

In the present work, the natural frequencies of cylindrical and spherical laminated shells with variable stiffness are numerically studied using a shear flexible isogeometric finite element. The kinematics relies on cubic shear deformation theory in which cubic variation is assumed for the surface displacements and a quadratic variation for the traverse displacement along the thickness. A zig-zag function, used for the in-plane displacements, accounts for the abrupt discontinuity at the boundaries of the laminae. The Lagrangian equations of motion is deployed to solve the frequencies of curved panels. A detailed parametric analysis examines the influence of fibre centre/edge angles, shell geometric variables, material anisotropy and edge conditions on frequencies and mode shapes.

scholarly journals A New Sinusoidal Shear Deformation Theory for Static Bending Analysis of Functionally Graded Plates Resting on Winkler–Pasternak Foundations

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Pham Minh Phuc ◽  
Vu Nguyen Thanh
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Solution Technique ◽  
Functionally Graded Plates ◽  
Bending Analysis ◽  
Foundation Parameters ◽  
Sinusoidal Shear Deformation Theory

In this article, a new sinusoidal shear deformation theory was developed for static bending analysis of functionally graded plates resting on elastic foundations. The proposed theory used an undefined integral term to reduce the number of the unknown to four without any shear correction factors. The high accuracy and efficiency of the proposed theory were proved thanks to the comparisons of the present results with other available solutions. And then, the proposed theory was successfully applied to investigate the bending behavior of the functionally graded plates resting on Winkler–Pasternak foundations. The governing equations of motion were established by using Hamilton’s principle, and the Navier’s solution technique was employed to solve these equations. The effects of some factors of the geometrics, the materials properties, and the elastic foundation parameters on the bending behaviors of the FGM plates were investigated intensely. Also, some novel results and special phenomenon were carried out.

scholarly journals Fundamental Frequency of Laminated Composite Thick Spherical Shells

2019 ◽  
Vol 11 (1) ◽  
pp. 57
Author(s):  
Mohammad Zannon
Keyword(s):  
Shear Deformation ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Composite Shells ◽  
Software Packages ◽  
Element Technique ◽  
Laminated Composite Shells

In this study, we apply third-order shear deformation thick shell theory to analytically derive the frequency characteristics of the free vibration of thick spherical laminated composite shells. The equations of motion are derived using Hamilton’s principle of minimum energy and on the basis of the relationships between forces, moments, and stress displacements in the shell. We confirm the derived equations and analytical results through the finite element technique by using the well-known software packages MATLAB and ANSYS. We consider the fundamental natural frequencies and the mode shapes of simply supported spherical cross-ply (0, 90), (0, 90, 0), and (0, 90, 90, 0) laminated composite shells. Then, to increase accuracy and decrease calculation efforts, we compare the results obtained through classical theory and first-order shear deformation theory.

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