Effect of mass and shear center offset on the dynamic response of a rotating blade

2015 ◽  
Vol 23 (14) ◽  
pp. 2235-2255 ◽  
Author(s):  
Mennatullah M Abdel Hafeez ◽  
Ayman A El-Badawy
Keyword(s):  
Finite Element Method ◽  
Strain Energy ◽  
Torsional Vibrations ◽  
Shear Center ◽  
Coupled Partial Differential Equations ◽  
Natural Modes ◽  
Rotating Blade ◽  
Centrifugal Stiffening ◽  
Initial Excitation ◽  
Stiffening Effect

In this work, a model that accounts for the extensional, chordwise, flapwise and torsional vibrations of a flexible rotating blade was developed. The model also takes into consideration the offset between the elastic and inertial axes of the blade. In order to account for the centrifugal stiffening effect, expression for the strain energy was obtained based on an ordering scheme that retains terms up to 2nd order. Hence, a set of four nonlinear coupled partial differential equations governing the deformations of the blade was derived. The linearized equations were non-dimensionalized and then spatially discretized by the FEM (Finite Element Method). State space techniques were used to obtain the blade's natural modes and response to initial excitation. Effect of the mass and shear center offset on the coupling between the modes and veering regions at different rotor speeds were investigated.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

A Two Step Damage Prognosis Method for Beam-Like Truss Structures

2014 ◽  
Vol 578-579 ◽  
pp. 1092-1095
Author(s):  
Hao Kai Jia ◽  
Ling Yu
Keyword(s):  
Finite Element Method ◽  
Strain Energy ◽  
Truss Structure ◽  
Truss Structures ◽  
Second Step ◽  
The Finite Element Method ◽  
Modal Strain Energy ◽  
Damage Prognosis ◽  
Modal Curvature ◽  
Simulation Results

In this study, a two step damage prognosis method is proposed for beam-like truss structures via combining modal curvature change (MCC) with modal strain energy change ratio (MSECR). Changes in the modal curvature and the elemental strain energy are selected as the indicator of damage prognosis. Different damage elements with different damage degrees are simulated. In the first step, the finite element method is used to model a beam-like truss structure and the displacement modes are got. The damage region is estimated by the MCC of top and bottom chords of a beam-like truss structure. In the second step, the elemental MSECR in the damage region is calculated and the maximum MSECR element is deemed as the damage element. The simulation results show that this method can accurately locate the damage in the beam-like truss structure.

The Strain Energy Tuning of the Shape Memory Alloy on the Post-Buckling of Composite Plates Using Finite Element Method

2012 ◽  
Vol 445 ◽  
pp. 577-582
Author(s):  
Zainudin A. Rasid ◽  
Saiful Amri Mazlan ◽  
Amran Ayob ◽  
Rizal Zahari ◽  
Dayang Laila Majid ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Strain Energy ◽  
Composite Plates ◽  
Post Buckling ◽  
Energy Tuning ◽  
Element Method

Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Jagadish Babu Gunda ◽  
Ranjan Ganguli
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Natural Frequencies ◽  
Basis Functions ◽  
Beam Equation ◽  
Rotating Beam ◽  
Rotating Beams ◽  
Centrifugal Stiffening ◽  
Convergence Study ◽  
Stiffening Effect

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

CONSISTENT APPROXIMATION FOR THE STRAIN ENERGY OF A 3D ELASTIC BODY ADEQUATE FOR THE STRESS STIFFENING EFFECT

2004 ◽  
Vol 04 (02) ◽  
pp. 279-292 ◽  
Author(s):  
YU. VETYUKOV
Keyword(s):  
Elastic Body ◽  
Strain Energy ◽  
Conventional Approach ◽  
Deformation Model ◽  
Geometrically Nonlinear ◽  
Consistent Approximation ◽  
New Strategy ◽  
Geometric Stiffening ◽  
Angular Velocities ◽  
Stiffening Effect

Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.

Effects of Free Damping Layers on Harmonic Response of Rotating Blades

1989 ◽  
Author(s):  
T. H. Young ◽  
T. N. Shiau ◽  
S. H. Chiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Loss Factor ◽  
Harmonic Excitation ◽  
The Finite Element Method ◽  
Harmonic Response ◽  
Rotating Blades ◽  
Rotating Blade ◽  
Triangular Elements

This paper studies the forced vibration of a rotating blade with free damping layers to harmonic excitation by means of the finite element method. The damping layers are made of viscoelastic material with complex elastic modulus, and the excitation may be either distributed or concentrated. Triangular elements with totally 15 d.o.f. are used to allow for a great variety of shapes and boundary conditions. The effects of various parameters, such as loss factor, storage modulus and thickness of damping layers, are investigated. The results show that the vibration amplitudes near resonances can be significantly reduced by the free damping layers.

Numeric Analysis for Resonant Frequency of Rotating Blade

2009 ◽  
Vol 16-19 ◽  
pp. 1365-1369
Author(s):  
Di Zhao ◽  
Ke Qin Ding ◽  
Xin Chun Shang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Resonant Frequency ◽  
Room Temperature ◽  
Vibration Characteristics ◽  
Resonance Analysis ◽  
Working Temperature ◽  
Rotating Blade ◽  
Dynamic Frequency

The paper implements numeric computation to analyze free vibration characteristics of rotating blade by the means of finite element method. The effects of rotate speed and temperature on the resonant frequency of blades are considered. The static frequency and the dynamic frequency under working speed for the room temperature and working temperature are calculated, and the various modes are obtained. The resonance analysis is given by Campbell graph in which shows the distribution of resonant points for resonant frequency and rotate speed under the different excitation.

Structural Stiffness of Tire Calculated From Strain Energy

2015 ◽  
Author(s):  
Namcheol Kang ◽  
Jong-Jin Bae ◽  
Jong Beom Suh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Method ◽  
Strain Energy ◽  
Vertical Force ◽  
Structural Stiffness ◽  
Contribution Ratio ◽  
The Finite Element Method ◽  
Vertical Stiffness ◽  
Strain Energy Method

The vertical stiffness of a tire is the ratio of the vertical force to the deflection; it can be expressed as the summation of the structural stiffness and air stiffness. However, the calculation of the structural stiffness is a challenging topic. This paper presents a new methodology for extracting the structural stiffness from the strain energy of a regular tire. In order to verify our proposed method, the vertical force-deflection results from the finite element method is compared with those from the strain energy method at zero air pressure. Also the results for an inflated tire are compared to calculate the structural stiffness. Finally, we calculated the contribution ratio of the tire components and used an alternative way of extracting the structural stiffness based on changing the Young’s modulus.

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