STABILITY AND VIBRATION ANALYSES OF AN INTERNALLY DAMPED TAPERED COMPOSITE DRIVESHAFT USING THE FINITE ELEMENT METHOD

2021 ◽  
Author(s):  
MOHSEN NAJAF ◽  
RAJAMOHAN GANESAN
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Rotational Velocity ◽  
Single Layer ◽  
Beam Theory ◽  
Instability Threshold ◽  
Element Formulation ◽  
Internal Damping ◽  
Critical Speeds ◽  
System Parameters

The present study considers the linear vibration and stability analyses of an internally damped rotating tapered composite shaft supported on rolling bearings. The Timoshenko beam theory is utilized to model the tapered drive-shaft based on Equivalent Single Layer Theory (ESLT). The ESLT considers a laminated driveshaft that consists of several lamina with different fiber orientations. Since the bearings are considered as rolling element bearings, the bearings stiffnesses are modeled using linear translational springs and dampers. The equations of motion are derived by applying Lagrange’s equation, including the hysteretic internal damping of composite material, and then finite element formulation is utilized to solve the equations. The effects of various system parameters on the natural frequencies and instability threshold are investigated. An extensive parametric study has been carried out to determine the effects of various system parameters including hysteresis internal damping, fiber orientation, stacking sequence, taper angle, rotational velocity, and bearings stiffness and damping on the natural frequencies, critical speeds, and instability thresholds of internally damped tapered composite drive-shafts. Furthermore, Campbell and critical speed map diagrams are depicted to present the effects of rotational velocity and bearings stiffness on natural frequencies and critical speeds. It is shown that the stability of the driveshaft is enhanced by increasing the damping of the bearings, whereas increasing the internal damping of the composite driveshaft may reduce the instability threshold.

Free Vibration and Instability Analysis of Sandwich Plates with Carbon Nanotubes-Reinforced Composite Faces and Honeycomb Core

2021 ◽  
Author(s):  
Sushila Chowdhary ◽  
Mesfin Kebede Kassa ◽  
Yitbarek Gashaw Tadesse ◽  
Ananda Babu Arumugam ◽  
Rajeshkumar Selvaraj
Keyword(s):  
Finite Element ◽  
Glass Fiber ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Element Formulation ◽  
The Core ◽  
Glass Fiber Reinforced ◽  
End Conditions ◽  
Honeycomb Sandwich ◽  
Instability Regions

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

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.

Thermal Robustness Assessment of a Rigidized Space Inflatable Boom via Experimental Modal Analysis and Finite Element Modeling

2010 ◽  
Author(s):  
Matthew Daly ◽  
Armaghan Salehian ◽  
Alireza Doosthoseini
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Frequency Response Function ◽  
Good Accuracy ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Element Model ◽  
Modal Testing ◽  
Environmental Temperatures ◽  
Robustness Assessment

The following paper presents the results of a thermal robustness assessment of a rigidized space inflatable boom. Modal testing is performed at three different environmental temperatures; spanning a range of 38°C, with the purpose of characterizing dynamic behavior and assessing changes in bending frequencies. Experimental results show that the natural frequencies of the boom shift only marginally within the tested bandwidth. A finite element model is developed in parallel with experiments to determine compatibility with beam theory. The resulting simulation shows that linear beam theory can be used to predict bending frequencies and frequency response function magnitudes with very good accuracy.

Analysis Behavior of a Rig Shafting Vibration Set Changes Bearing Parameters

2013 ◽  
Vol 437 ◽  
pp. 98-101 ◽  
Author(s):  
Van Thanh Ngo ◽  
Dan Mei Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Lateral Vibration ◽  
Eigenvalues And Eigenvectors ◽  
Fem Model ◽  
Critical Speeds ◽  
Bearing Stiffness

Frequently, in the design of machines, some of parameters that directly affect the rotordynamics of the machines are not accurately known. In particular, bearing stiffness support is one such parameter. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using finite element method (FEM). The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes. Then critical speeds and mode shapes are analyzed by set bearing stiffness changes. The model permitted to identify the critical speeds and bearings that have an important influence on the vibration behavior.

scholarly journals On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature

Shear-deformable hybrid finite-element formulation for lateral-torsional buckling analysis of composite thin-walled members

2020 ◽  
Author(s):  
Emre Erkmen ◽  
Vida Niki ◽  
Ashkan Afnani
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Hybrid Finite Element ◽  
Thin Walled ◽  
Shear Deformable

A shear deformable hybrid finite element formulation is developed for the lateral-torsional buckling analysis of fiber-reinforced composite thin-walled members with open cross-section. The method is developed by using the Hellinger-Reissner functional. Comparison to the displacement-based formulations the current hybrid formulation has the advantage of incorporating the shear deformation effects easily by using the strain energy of the shear stress field without modifying the basic kinematic assumptions of the thin-walled beam theory. Numerical results are validated through comparisons with results based on other formulations presented in the literature. Examples illustrate the effects of shear deformations and stacking sequence of the composite layers in predicting bucking loads.

Buried Pipe Modeling With Initial Imperfections

2004 ◽  
Vol 126 (2) ◽  
pp. 250-257 ◽  
Author(s):  
Junes A. Villarraga ◽  
Jose´ F. Rodrı´guez ◽  
Cora Martı´nez
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Beam Theory ◽  
Element Model ◽  
Problem Formulation ◽  
Element Formulation ◽  
Buried Pipe ◽  
Allowable Limit ◽  
Initial Imperfections ◽  
Nonlinear Elastic

A formulation using the finite element method is presented in this paper to analyze stresses and displacements of underground pipelines with initial imperfections. The formulation includes both thermal expansion of the pipeline and internal pressure. The method is based on large deformation beam theory with the finite element formulation based on Euler-Bernoulli beam elements of constant cross-section. The pipe-soil interaction is modeled as a nonlinear elastic foundation in the problem formulation. The resulting nonlinear finite element model with appropriate boundary conditions is solved using full Newton-Raphson as the iterative procedure. Numerical examples are provided to show the application of the methodology and to demonstrate the effect of the initial imperfections in the stress distribution of a buried pipe. The results show that initial imperfections have a considerable influence on the stress distribution of buried pipelines, leading in some cases to stress levels above the allowable limit established by the design codes. The results also help to identify the critical temperature at which buckling of the buried pipe might occur.

Finite Element Analysis of Beams With Constrained Damping Treatment Modeled Via Fractional Derivatives

1997 ◽  
Vol 50 (11S) ◽  
pp. S216-S224 ◽  
Author(s):  
Luis E. Sua´rez ◽  
Arsalan Shokooh ◽  
Jose´ Arroyo
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Single Layer ◽  
Element Model ◽  
Beam Element ◽  
Element Formulation ◽  
Beam Model ◽  
Element Analysis ◽  
Damping Material ◽  
Derivatives Of

This paper presents a finite element formulation for the modeling of beams and frames with artificial damping provided by means of a constrained single layer of damping material. The behavior of the damping material is described using the fractional derivative model of viscoelasticity. In this model, the first order derivatives of the strains in the constitutive equations of the viscoelastic materials are replaced by derivatives of order α < 1. The finite element model developed is a one-dimensional beam element with three degrees of freedom per node. The dynamic response is calculated with a procedure involving a transformation of the original equations of motion to the state space and its decoupling with the eigenvectors of a special eigenvalue problem. The accuracy of the modal properties obtained with the beam model is compared with those calculated from a more elaborate plane stress finite element model. It was found that the proposed beam element provides very accurate results and with much lower computational costs than the 2-D model.

scholarly journals Effect of Corrosion on the Natural and Whirl Frequencies of a Functionally Graded Rotor-Bearing System Subjected to Thermal Gradients

Materials ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 4546 ◽  
Author(s):  
Prabhakar Sathujoda ◽  
Bharath Obalareddy ◽  
Aneesh Batchu ◽  
Giacomo Canale ◽  
Angelo Maligno ◽  
...  
Keyword(s):  
Finite Element ◽  
Dynamic Characteristics ◽  
Beam Theory ◽  
Functionally Graded ◽  
Element Formulation ◽  
Thermal Gradients ◽  
The Finite Element Method ◽  
Fourier Law ◽  
Corrosion Defect ◽  
Nonlinear Temperature

Corrosion causes a loss of material resulting in the reduction of mass and stiffness of a component, which consequently affects the dynamic characteristics of any system. Fundamental frequency analysis of a corroded functionally graded (FG) rotor system, using the finite element method based on the Timoshenko beam theory, was investigated in the present paper. The functionally graded shaft consisting of an inner metallic core and an outer ceramic layer was considered with the radial gradation of material properties based on the power law. Nonlinear temperature distribution (NLTD) based on the Fourier law of heat conduction was used to simulate the thermal gradient through the cross-section of the FG rotor. The finite element formulation for a functionally graded shaft with a corrosion defect was developed and the dynamic characteristics were investigated, which is the novelty of the present work. The corrosion parameters such as length, depth and position of the corrosion defect in the shaft were varied and a parametric study was performed to investigate changes in the natural and whirl frequencies. An analysis was carried out for different power indexes and temperature gradients of the functionally graded shaft. The effects of corrosion were analysed and important conclusions are drawn from the investigations.

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