Microendmill Dynamics Including the Actual Fluted Geometry and Setup Errors—Part II: Model Validation and Application

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Sinan Filiz ◽  
O. Burak Ozdoganlar
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Laser Doppler Vibrometer ◽  
Mode Shapes ◽  
Fe Model ◽  
Dynamics Model ◽  
Free Boundary Conditions ◽  
Dynamic Excitation ◽  
Piezoelectric Elements ◽  
Modal Behavior

This paper presents a study to validate the microendmill dynamics model derived in Part I. A laser Doppler vibrometer system that is coupled with a microscope is used to measure the natural frequencies and mode shapes of nonrotating microendmills with different geometries. Free-free boundary conditions are obtained by suspending the microendmills using elastic bands. The dynamic excitation is delivered through miniature piezoelectric elements attached to the microendmill shanks. In each case, the model is compared to experimental results and solid-element finite-element (FE) models. To evaluate the model in the presence of rotational effects, the model is compared to an FE model. In most cases, the model was seen to capture the dynamic behavior of microendmills accurately. The validated model is used to investigate the effects of microendmill geometry, and radial and tilt runouts on the modal behavior of microendmills. Furthermore, possible geometric simplifications to fluted region are evaluated based on the accuracy of the predicted natural frequencies of the microendmills.

Free Vibration Analysis of PZT Glide Heads

1999 ◽  
Vol 121 (4) ◽  
pp. 984-988 ◽  
Author(s):  
Alex Y. Tsay ◽  
Jin-Hui Ouyang ◽  
C.-P. Roger Ku ◽  
I. Y. Shen ◽  
David Kuo
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Laser Doppler Vibrometer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Bonding Length ◽  
Measured Displacement

This paper studies natural frequencies and mode shapes of a glide head with a piezoelectric transducer (PZT) through calibrated experiments and a finite element analysis. In the experiments, the PZT transducer served as an actuator exciting the glide head from 100 kHz to 1.3 MHz, and a laser Doppler vibrometer (LDV) measured displacement of the glide head at the inner or outer rail. The natural frequencies were measured through PZT impedance and frequency response functions from PZT to LDV. In the finite element analysis, the glide head was meshed by brick elements. The finite element results show that there are two types of vibration modes: slider modes and PZT modes. Only the slider modes are important to glide head applications. Moreover, natural frequencies predicted from the finite element analysis agree well with the experimental results within 5% of error. Finally, the finite element analysis identifies four critical slider dimensions whose tolerance will significantly vary the natural frequencies: PZT bonding length, wing thickness, slider thickness, and air bearing recess depth.

scholarly journals Linear Finite Element Modeling of Joined Structures With Riveted Connections

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
J. S. Kim ◽  
Y. F. Xu ◽  
W. D. Zhu
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Modeling Method ◽  
Test Structure ◽  
Mode Shapes ◽  
Fe Model ◽  
Fe Modeling ◽  
Engineering Structures ◽  
Modal Assurance Criterion ◽  
Linear Finite Element

Abstract Riveted connections are widely used to join basic components, such as beams and panels, for engineering structures. However, accurately modeling joined structures with riveted connections can be a challenging task. In this work, an accurate linear finite element (FE) modeling method is proposed for joined structures with riveted connections to estimate modal parameters in a predictive manner. The proposed FE modeling method consists of two steps. The first step is to develop nonlinear FE models that simulate riveting processes of solid rivets. The second step is to develop a linear FE model of a joined structure with the riveted connections simulated in the first step. The riveted connections are modeled using solid cylinders with dimensions and material properties obtained from the nonlinear FE models in the first step. An experimental investigation was conducted to study accuracy of the proposed linear FE modeling method. A joined structure with six riveted connections was prepared and tested. A linearity investigation was conducted to validate that the test structure could be considered to be linear. A linear FE model of the test structure was constructed using the proposed method. Natural frequencies and corresponding mode shapes of the test structure were measured and compared with those from the linear FE model. The maximum difference of the natural frequencies was 1.63% for the first 23 out-of-plane elastic modes, and modal assurance criterion values for the corresponding mode shapes were all over 95%, which indicates high accuracy of the proposed linear FE modeling method.

Follower Effect of Internal Pressure on Modal Analysis of a Space Inflatable Structure

2015 ◽  
Vol 727-728 ◽  
pp. 578-582
Author(s):  
Fei Liu ◽  
Wei Liang He
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Fem Model ◽  
Configuration Change ◽  
Modal Behavior ◽  
Good Agreement ◽  
Inflatable Structure

The stress distribution and modal behavior of a space inflatable torus was investigated by nonlinear finite element numerical method. This paper focused on the effect of follower pressure on the modal analysis of the torus, including the effect of configuration change and follower pressure stiffness, and focused on validating the follower pressure stiffness FEM model and its applicability to modal analysis. Research shows that the changed configuration slightly increases the natural frequencies. The follower pressure stiffness significantly reduces the natural frequencies and changes mode shapes order. The modal results are in good agreement with the corresponding shell theory solutions, indicating that the finite element model of the follower pressure stiffness for the inflatable structure modal analysis in this paper is accurate enough and reasonable.

scholarly journals Using Pade´ Approximants and Curve-fitting to Approximate Eigenvalues and Eigenvectors for Large Design Changes

1996 ◽  
Vol 118 (1) ◽  
pp. 151-153 ◽  
Author(s):  
J. M. Vance ◽  
J. E. Bernard
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Solution Process ◽  
Mode Shapes ◽  
Eigenvalues And Eigenvectors ◽  
Computational Burden ◽  
Design Change ◽  
Design Changes ◽  
Develop Software ◽  
Unique Method

Our overall goal is to develop software that facilitates the interactive participation of the designer in the optimization process. We are focusing this research on problems which use finite element solutions as part of the objective function. One challenge to implementing interactive participation in these types of problems is the high computational burden of computing a finite element solution for each design change. The research presented here focuses on a unique method to develop fast approximations for natural frequencies and mode shapes which can be used to avoid the time-consuming re-solution process and which will facilitate interactive design for systems with even large design changes.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

Analysis of In-Plane Modal Characteristics of an Annular Disk With Multiple Point Supports

2009 ◽  
Author(s):  
S. Bashmal ◽  
R. Bhat ◽  
S. Rakheja
Keyword(s):  
Finite Element ◽  
Orthogonal Polynomials ◽  
Ritz Method ◽  
Element Model ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Multiple Point ◽  
Annular Disk ◽  
Free Boundary Conditions ◽  
Boundary Characteristic

In-plane free vibrations of an isotropic, elastic annular disk constrained at some points on the inner and outer boundaries are investigated. The presented study is relevant to various practical problems including disks clamped by bolts along the inner and outer edges or the railway wheel vibrations. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. The boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to realize clamped conditions at discrete points. The frequency parameters for different point constraint conditions are evaluated and compared with those computed from a finite element model to demonstrate the validity of the proposed method. The computed mode shapes are presented for a disk with different point constraints at the inner and outer boundaries to demonstrate the free in-plane vibration behavior of the disk. Results show that addition of point supports causes some of the modes to split into two different frequencies with different mode shapes. The effects of different orientations of multiple point supports on the frequency parameters and mode shapes are also discussed.

scholarly journals Dynamics Characteristics of Blast Furnace Shell

2011 ◽  
Vol 2-3 ◽  
pp. 1018-1020
Author(s):  
De Chen Zhang ◽  
Yan Ping Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Blast Furnace ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Theoretical Foundation ◽  
Structural Mechanics ◽  
Mode Shapes ◽  
The Future ◽  
Element Method

Finite element method and structural mechanics method are used to study the blast furnace shell modal analysis and the natural frequencies and mode shapes have been calculated. The two methods were compared and validated , and the results provide a theoretical foundation for the anti-vibration capabilities design of blast furnace shell in the future .

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

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