scholarly journals Vibration Analysis of Circular Arch Element Using Curvature

2008 ◽  
Vol 15 (5) ◽  
pp. 481-492 ◽  
Author(s):  
H. Saffari ◽  
R. Tabatabaei ◽  
S.H. Mansouri
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Axial Strain ◽  
Mode Shapes ◽  
Element Formulation ◽  
Equilibrium Equations ◽  
Lagrangian Equation ◽  
Circular Arch ◽  
Nodal Displacements ◽  
Element Technique

In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

Evaluation of a Strain Energy Equivalence Principle (SEEP)-Based Continuum Damage Model

2007 ◽  
Vol 353-358 ◽  
pp. 1199-1202
Author(s):  
Usik Lee ◽  
Deokki Youn ◽  
Sang Kwon Lee
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Damage Model ◽  
Elastic Stiffness ◽  
Constitutive Law ◽  
Mode Shapes ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Square Plate

A new continuum damage theory (CDT) has been proposed by Lee et al. (1997) based on the SEEP. The CDT has the apparent advantage over the other related theories because the complete constitutive law can be readily derived by simply replacing the virgin elastic stiffness with the effective orthotropic elastic stiffness obtained by using the proposed continuum damage theory. In this paper, the CDT is evaluated by comparing the mode shapes and natural frequencies of a square plate containing a small line-through crack with those of the same plate with a damaged site replaced with the effective orthotropic elastic stiffness computed by using the CDT.

A Damage Identification Method Using Vibration Modal Parameters Through Finite Element Discretization

2003 ◽  
Author(s):  
Xiaoping Zhou ◽  
Abhijit Gupta
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Damage Identification ◽  
Least Squares Method ◽  
Modal Testing ◽  
Mode Shapes ◽  
Element Formulation ◽  
Element Discretization ◽  
Damage Indices ◽  
Actual Damage

Natural frequencies and mode shapes of a structure will change whenever the structure has any kind of damage. This paper introduces a technique to quantify and locate the damage when the natural frequencies and mode shapes of undamaged and damaged structure are known. Aluminum beams (with and without damage) are used for numerical simulation and experimental verification. To establish the theoretical basis of this method, finite element formulation is used. A set of undetermined equations involving damage indices and natural frequencies and mode shapes of undamaged and damaged structures are obtained. The damage indices are computed using non-negative least squares method. Impact modal testing was conducted with three aluminum beams and damage indices based on experimental data are compared with actual damage cases to establish the effectiveness of this method to identify the damage.

scholarly journals Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Erasmo Viola ◽  
Marco Miniaci ◽  
Nicholas Fantuzzi ◽  
Alessandro Marzani
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Internal Boundary ◽  
Radius Of Curvature ◽  
Inertia Effects ◽  
Circular Arch

AbstractThis paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.

Vibration and Modal Analysis of Induction Motor

2012 ◽  
Vol 226-228 ◽  
pp. 92-97 ◽  
Author(s):  
Rui Li ◽  
Qi Fen Jia ◽  
Shun Zhong
Keyword(s):  
Induction Motor ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Acoustic Noise ◽  
Mode Shapes ◽  
Electrical Machine ◽  
3D Finite Element ◽  
Motor Mode ◽  
Element Technique ◽  
Motor Vibration

Calculation of the induction motor machine modal frequencies of an electrical machine accurately is the base of reducing acoustic noise and vibration. This paper presents a detailed research on the induction motor mode shapes and natural frequencies of induction motor by using 3D finite element technique, based on simplified modal, The influence of and mounting feet and rotor on mode shapes and natural frequencies are investigated systematically. Mounting feet and rotor have a great effect on natural frequencies, the mounting feet and rotor will result in the number of the motor low-vibration mode increases\the frequencies rise obviously, the mounting feet result in motor vibration mode becomes more complicated, rotor modals become an important part of motor mode shapes, the number of the motor low-vibration mode increases. Predictions are validated against experimental results.

Third Paper: Dynamic Analysis of an Automobile Chassis Frame

1970 ◽  
Vol 185 (1) ◽  
pp. 683-690 ◽  
Author(s):  
R. Ali ◽  
J. L. Hedges ◽  
B. Mills
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Experimental Results ◽  
Mode Shapes ◽  
Finite Element Technique ◽  
Inertia Matrix ◽  
Element Technique

The finite element technique has been used for the prediction of natural frequencies and mode shapes of a chassis structure. The program developed in Paper 1 was extended by adding an inertia matrix. The effects of shear and tapered beams were also considered and predictions of frequencies and mode shapes are compared with experimental results.

A New Approach for Plate Vibrations: Combination of Transfer Matrix and Finite-Element Technique

1972 ◽  
Vol 94 (2) ◽  
pp. 526-530 ◽  
Author(s):  
M. A. Dokainish
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Present Method ◽  
Degrees Of Freedom ◽  
Matrix Multiplication ◽  
Mode Shapes ◽  
Equilibrium Equations ◽  
Plate Vibrations ◽  
Left And Right ◽  
Element Technique

When the finite-element method is used in the vibration analysis of plates and shells, it results in large matrices requiring a large digital computer. A commonly used method of reducing the matrix size is to eliminate certain “slave” displacements by minimizing strain energy. The approach requires good judgement in the selection of the “master” displacements and involves additional approximations and some loss of accuracy. In the present method small matrices are obtained without any further approximations and without reducing the number of degrees of freedom. The transfer matrix technique, generally known as the Holzer-Myklestad method, is well known for beams and shafts. The present method is an extension of this idea to plates. The structure is divided into several strips, with a number of nodes on the left and right sections of each strip. Each strip is subdivided into elements and the stiffness and mass matrices are obtained for individual strips. The nodal equilibrium equations are rearranged to obtain a relation between the section variables of the left and the right sections. The section variables are the forces and the displacements of all the nodes on the section. Requirements of displacement continuity and force equilibrium at the nodes, on common sections of two adjacent strips, gives the transfer matrix relation. Successive matrix multiplication finally relates the variables of the left and right boundary of the structure. Boundary conditions require the determinant of a portion of the overall transfer matrix to vanish at the correct frequency. By calculating the determinant at various assumed values of frequency, the correct frequencies are obtained. The method also gives the corresponding mode shapes. The method as applied to several plate problems gives satisfactory results.

Computer-Aided Design Applied to a Model of a Chassis Type Structure Using Finite Element Techniques

1969 ◽  
Vol 184 (1) ◽  
pp. 15-24
Author(s):  
R. Ali ◽  
J. L. Hedges ◽  
B. Mills
Keyword(s):  
Finite Element ◽  
Computer Program ◽  
Computer Aided Design ◽  
Computation Time ◽  
Type Structure ◽  
Scale Model ◽  
Mode Shapes ◽  
Nodal Displacements ◽  
Element Technique ◽  
Aided Design

The finite element technique has been used for the examination of a chassis-type structure. A computer program was developed to predict the static and dynamic behaviour of frames. The program is quite general but its use has been restricted to structures consisting of beam elements only. A scale model of a production car chassis was made in perspex. Nodal displacements of the model, in bending and torsion, natural frequencies and corresponding mode shapes were predicted by the computer program and confirmed experimentally in the laboratory. Several coarser idealizations of the model were examined to study the effect on the accuracy of predictions and the computation time.

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