A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 2: Example Calculations

1996 ◽  
Vol 118 (3) ◽  
pp. 318-322 ◽  
Author(s):  
D. J. Segalman ◽  
C. R. Dohrmann ◽  
A. M. Slavin
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Membrane Structure ◽  
Flexible Structures ◽  
Preceding Paper ◽  
General Linear ◽  
Rotation Rates ◽  
Deformation Modes ◽  
Modal Coordinates

The problem of calculating the vibrations of rotating structures has challenged analysts since the observation that use of traditional modal coordinates in such problems leads to the prediction of instability involving infinite deformation when rotation rates exceed the first natural frequency. A method using a system of nonlinearly coupled deformation modes to analyze rotating general, linear (unjointed) structures that addresses the problem of erroneously predicting infinite deformations has been presented in a preceding paper (Segalman and Dohrmann, 1995). This technique is employed to address several types of problems ranging from simple beams to an inflated membrane structure. Some of the details of exploiting existing finite element codes to evaluate the relevant matrices are also developed.

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation

1996 ◽  
Vol 118 (3) ◽  
pp. 313-317 ◽  
Author(s):  
D. J. Segalman ◽  
C. R. Dohrmann
Keyword(s):  
Natural Frequency ◽  
Configuration Space ◽  
Flexible Structures ◽  
Second Order ◽  
General Linear ◽  
New Approach ◽  
Kinematic Constraints ◽  
Rotation Rates ◽  
Deformation Modes

The problem of calculating the vibrations of rotating structures has challenged analysts since it was observed that the use of traditional modal approaches may incorrectly lead to the prediction of infinite deformation when rotation rates exceed the first natural frequency. Much recently published work on beams has shown that such predictions are artifacts of incorporating incomplete kinematics into the analysis, but only simple structures such as individual beams and plates are addressed. The authors present a new approach to analyzing rotating flexible structures that applies to the rotation of general linear (unjointed) structures, using a system of nonlinearly coupled deformation modes. This technique, tentatively named a Method of Quadratic Components, utilizes a nonlinear configuration space in which all kinematic constraints are satisfied up to second order.

Simulation and Analysis of Cantilever-Membrane Structure for Piezoresistive Micro-Accelerometers

2012 ◽  
Vol 503 ◽  
pp. 87-90 ◽  
Author(s):  
Yan Liu ◽  
Yu Long Zhao ◽  
Lu Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Frequency Band ◽  
Membrane Structure ◽  
Measurement Sensitivity ◽  
First Order ◽  
Working Frequency ◽  
Element Method

Dynamic and static performances are the most important parameters for accelerometers. The natural frequency decides the sensor’s working frequency band, and the accompanying stress represents the measurement sensitivity. In this paper, a novel sensing structure, cantilever-membrane structure, for piezoresistive accelerometers is studied, in order to detect the structural dimension’s effect on the sensor. With the help of FEM (Finite element method) software, the first order natural frequency of the cantilever-membrane based accelerometer is investigated with the different combinations of membrane’s dimensions. The accompanying stress of the sensing structure is also simulated in this paper. The results show that the membrane’s dimensions affect the frequency and stress more tempestuously when the membrane is short, but the tendency become gentle when the width of the membrane increases.

Absolute Nodal Coordinate Formulation Coupled Deformation Modes

2006 ◽  
Author(s):  
Bassam A. Hussein ◽  
Hiroyuki Sugiyama ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Structures ◽  
Mindlin Plate ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Geometric Stiffening ◽  
General Continuum ◽  
Deformation Modes

The finite element absolute nodal coordinate formulation (ANCF) leads to beam and plate models that relax the assumption of the classical Euler-bernoulli and Timoshenko beam and Mindlin plate theories. In these more general models, the cross section is allowed to deform and it is no longer treated as a rigid surface. The coupling between the bending and cross section deformations leads to the new ANCF-coupled deformation modes that are examined in this study. While these coupled deformation can be source of numerical and convergence problems when thin and stiff beam models are considered, the inclusion of the effect of these modes in the dynamic model is necessary in the case of very flexible structures. In order to examine the effect of these coupled deformation modes in this investigation, three different large deformation dynamic beam models are discussed. Two of these models, which differ in the way the beam elastic forces are calculated in the absolute nodal coordinate formulation, allow for systematically eliminating the coupled deformation modes, while the third allows for including these modes. The first of these models is based on a general continuum mechanics approach that leads to a model that includes the ANCF-coupled deformation modes; while the second and third methods that can be used to eliminate the coupled deformation modes are based on the elastic line approach and the Hellinger-Reissner principle. It is shown in this study that the inclusion of the ANCF-coupled deformation modes introduces geometric stiffening effects that can not be captured using other finite element models.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

Optimum Design for the Frame of Open Type Abrasive Flow Polish Machine

2012 ◽  
Vol 497 ◽  
pp. 89-93
Author(s):  
Liang Liang Yuan ◽  
Ke Hua Zhang ◽  
Li Min
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Methods ◽  
Optimization Design ◽  
Low Cost ◽  
Three Dimensional ◽  
Force Model ◽  
Optimization Analysis ◽  
Open Type ◽  
Set Up

In order to process heterotype hole of workpiece precisely, an open abrasive flow polish machine is designed, and the optimization design of machine frame is done for low cost. Firstly, basing on the parameters designed with traditional ways, three-dimensional force model is set up with the soft of SolidWorks. Secondly, the statics and modal analysis for machine body have been done in Finite element methods (FEM), and then the optimization analysis of machine frame has been done. At last, the model of rebuild machine frame has been built. Result shows that the deformation angle value of machine frame increased from 0.72′ to 1.001′, the natural frequency of the machine decreased from 75.549 Hz to 62.262 Hz, the weight of machine decreased by 74.178 Kg after optimization. It meets the strength, stiffness and angel stiffness requirement of machine, reduces the weight and cost of machine.

Vibration-based delamination evaluation in GFRP composite beams using ANN

2021 ◽  
pp. 096739112110033
Author(s):  
TG Sreekanth ◽  
M Senthilkumar ◽  
S Manikanta Reddy
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Composite Structures ◽  
Composite Beams ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Aviation Industry ◽  
Frequency Data ◽  
Fiber Reinforced ◽  
Back Propagation Algorithm

Delamination is definitely an important topic in the area of composite structures as it progressively worsens the mechanical performance of fiber-reinforced polymer composite structures in its service period. The detection and severity analysis of delaminations in engineering areas like the aviation industry is vital for safety and economic considerations. The existence of delaminations varies the vibration characteristics such as natural frequencies, mode shapes, etc. of composites and hence this indication can be effectively used for locating and quantifying the delaminations. The changes in vibration characteristics are considered as inputs for the inverse problem to determine the location and size of delaminations. In this paper Artificial Neural Network (ANN) is used for delamination evaluationof glass fiber-reinforced composite beams using natural frequency as typical vibration parameter. The Finite Element Analysis is used for generating the required dataset for ANN. The frequency-based delamination prediction technique is validated by finite element models and experimental modal analysis. The results indicate that the ANN-based back propagation algorithm can predict the location and size of delaminations in composites with good accuracy for numerical natural frequency data but the accuracy is comparitivelyless for experimental natural frequency data.

The Finite Element Analysis and Optimization for the Grinder Based on the Joint Surface

2013 ◽  
Vol 281 ◽  
pp. 165-169 ◽  
Author(s):  
Xiang Lei Zhang ◽  
Bin Yao ◽  
Wen Chang Zhao ◽  
Ou Yang Kun ◽  
Bo Shi Yao
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Element Model ◽  
Joint Surface ◽  
Weak Links ◽  
Response Analysis ◽  
Element Analysis ◽  
Static And Dynamic Analysis ◽  
Harmonic Response Analysis ◽  
Grinding Machine

Establish the finite element model for high precision grinding machine which takes joint surface into consideration and then carrys out the static and dynamic analysis of the grinder. After the static analysis, modal analysis and harmonic response analysis, the displacement deformation, stress, natural frequency and vibration mode could be found, which also helps find the weak links out. The improvement scheme which aims to increase the stiffness and precision of the whole machine has proposed to efficiently optimize the grinder. And the first natural frequency of the optimized grinder has increased by 68.19%.

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