A HIGH-ORDER FINITE ELEMENT FORMULATION FOR VIBRATION ANALYSIS OF BEAM-TYPE STRUCTURES

2009 ◽  
Vol 09 (04) ◽  
pp. 649-660 ◽  
Author(s):  
Y. WEN ◽  
Q. Y. ZENG
Keyword(s):  
Finite Element ◽  
Dynamic System ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Computational Effort ◽  
High Order ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Element Formulation ◽  
Analysis Model

A high-order finite element model is presented to perform the vibration analysis of beams. The equations of motion are formulated by applying the principle of total potential energy in elastic dynamic system and the "set-in-right-position" rule for the construction of system matrices first proposed by the author. The primary advantage of the principle and rule lies in its simplicity and efficiency in solving the modeling problem of complex dynamic system. The requirement of strain continuity has certainly not being met at element interfaces with the use of conventional cubic Hermitian formulation. Hence, it is difficult to predict the dynamic responses of beams accurately. In order to overcome this problem, a beam element with simple higher-order interpolation function is chosen as the analysis model. Although the number of nodal degrees of freedom is increased herein, usually a coarse mesh will suffice. The present formulation is able to provide results of high accuracy with low computational effort. For the purpose of illustration, the dynamic characteristics analysis and dynamic response analysis are carried out on beam models. The solutions obtained for all the examples are in good agreement with the exact solutions found by fundamental theory of vibration.

Dynamic Response Analysis of Wind Turbine Gearbox Using Simplified Local Tooth Stiffness of Internal Gear System

2015 ◽  
Vol 10 (4) ◽  
Author(s):  
J. R. Cho ◽  
K. Y. Jeong ◽  
M. H. Park ◽  
N. G. Park
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Dynamic Models ◽  
Gear Tooth ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Analysis Model ◽  
Wind Turbine Gearbox ◽  
Element Analysis

This paper presents a dynamic finite element analysis model for a wind turbine gearbox in which a number of internal gears mesh with each other in a complex pattern. Differing from the conventional dynamic models in which the detailed gear teeth are fully modeled or gears and shafts are replaced with lumped masses, the tooth contact between a pair of gears is modeled using a spring element. The equivalent spring constant is determined by computing the stiffness of a gear tooth using a finite element analysis. The numerical accuracy of the proposed dynamic model is verified through a benchmark experiment of a gearbox with simple gear transmission system. In addition, the natural frequencies and dynamic responses of a 5 MW wind turbine gearbox that are obtained by the proposed modeling technique are given to support its validity and effectiveness.

scholarly journals A finite element formulation for bending-torsion coupled vibration analysis of delaminated beams under combined axial load and end moment

2021 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Discrete Problem ◽  
Weighted Residual Method ◽  
Linear Eigenvalue Problem ◽  
Free Mode

Free vibration analysis of beams with single delamination undergoing bending-torsion coupling is made, using traditional finite element technique. The Galerkin weighted residual method is applied to convert the coupled differential equations of motion into to a discrete problem, where, in addition to the conventional mass and stiffness matrices, a delamination stiffness matrix, representing the extra stiffening effects at the delamination tips, is introduced. The linear eigenvalue problem resulting from the discretization along the length of the beam is solved to determine the frequencies and modes of free vibration. Both “free mode” and “constrained mode” delamination models are considered in formulation, and it is shown that the continuity (both kinematic and force) conditions at the beam span-wise locations corresponding to the extremities of the delaminated region, in particular, play a great role in “free mode” model formulation. Current trends in the literature are examined, and insight into different types of modeling techniques and constraint types are introduced. In addition, the data previously available in the literature and those obtained from a finite element-based commercial software are utilized to validate the presented modeling scheme and to verify the correctness of natural frequencies of the systems analyzed here. The paper ends with general discussions and conclusions on the presented theories and modeling approaches.

scholarly journals A finite element formulation for bending-torsion coupled vibration analysis of delaminated beams under combined axial load and end moment

2021 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Discrete Problem ◽  
Weighted Residual Method ◽  
Linear Eigenvalue Problem ◽  
Free Mode

Free vibration analysis of beams with single delamination undergoing bending-torsion coupling is made, using traditional finite element technique. The Galerkin weighted residual method is applied to convert the coupled differential equations of motion into to a discrete problem, where, in addition to the conventional mass and stiffness matrices, a delamination stiffness matrix, representing the extra stiffening effects at the delamination tips, is introduced. The linear eigenvalue problem resulting from the discretization along the length of the beam is solved to determine the frequencies and modes of free vibration. Both “free mode” and “constrained mode” delamination models are considered in formulation, and it is shown that the continuity (both kinematic and force) conditions at the beam span-wise locations corresponding to the extremities of the delaminated region, in particular, play a great role in “free mode” model formulation. Current trends in the literature are examined, and insight into different types of modeling techniques and constraint types are introduced. In addition, the data previously available in the literature and those obtained from a finite element-based commercial software are utilized to validate the presented modeling scheme and to verify the correctness of natural frequencies of the systems analyzed here. The paper ends with general discussions and conclusions on the presented theories and modeling approaches.

scholarly journals A Finite Element Formulation for Bending-Torsion Coupled Vibration Analysis of Delaminated Beams under Combined Axial Load and End Moment

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Discrete Problem ◽  
Weighted Residual Method ◽  
Linear Eigenvalue Problem ◽  
Free Mode

Free vibration analysis of beams with single delamination undergoing bending-torsion coupling is made, using traditional finite element technique. The Galerkin weighted residual method is applied to convert the coupled differential equations of motion into to a discrete problem, where, in addition to the conventional mass and stiffness matrices, a delamination stiffness matrix, representing the extra stiffening effects at the delamination tips, is introduced. The linear eigenvalue problem resulting from the discretization along the length of the beam is solved to determine the frequencies and modes of free vibration. Both “free mode” and “constrained mode” delamination models are considered in formulation, and it is shown that the continuity (both kinematic and force) conditions at the beam span-wise locations corresponding to the extremities of the delaminated region, in particular, play a great role in “free mode” model formulation. Current trends in the literature are examined, and insight into different types of modeling techniques and constraint types are introduced. In addition, the data previously available in the literature and those obtained from a finite element-based commercial software are utilized to validate the presented modeling scheme and to verify the correctness of natural frequencies of the systems analyzed here. The paper ends with general discussions and conclusions on the presented theories and modeling approaches.

Seismic Response Analysis of Soil-Structure Interaction on Base Isolation Structure

2013 ◽  
Vol 663 ◽  
pp. 87-91
Author(s):  
Ying Bo Pang
Keyword(s):  
Finite Element ◽  
Seismic Response ◽  
Soil Structure ◽  
Base Isolation ◽  
Soil Structure Interaction ◽  
Response Analysis ◽  
Analysis Model ◽  
Seismic Response Analysis ◽  
Structure Interaction ◽  
Calculation Results

As an effective way of passive damping, isolation technology has been widely used in all types of building structures. Currently, for its theoretical analysis, it usually follows the rigid foundation assumption and ignores soil-structure interaction, which results in calculation results distortion in conducting seismic response analysis. In this paper, three-dimensional finite element method is used to establish finite element analysis model of large chassis single-tower base isolation structure which considers and do not consider soil-structure interaction. The calculation results show that: after considering soil-structure interaction, the dynamic characteristics of the isolation structure, and seismic response are subject to varying degrees of impact.

scholarly journals On the Stream Function-Vorticity Finite Element Formulation for Incompressible Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stream Function ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Element Formulation ◽  
Discrete Problem

Stream function-vorticity finite element formulation for incompressible flow in porous media is presented. The model consists of the heat equation, the equation for the concentration, and the equations of motion under the Darcy law. The existence of solution for the discrete problem is established. Optimal a priori error estimates are given.

The Finite Element Analysis of Dynamic Interaction of High-Speed Shinkansen, the Rail, and Bridge

1993 ◽  
Author(s):  
Makoto Tanabe ◽  
Hajime Wakui ◽  
Nobuyuki Matsumoto
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
High Speed ◽  
Response Analysis ◽  
Element Formulation ◽  
Element Analysis ◽  
Finite Element Program ◽  
The Finite Element Analysis ◽  
Element Program ◽  
The Impact

Abstract A finite element formulation to solve the dynamic behavior of high-speed Shinkansen cars, rail, and bridge is given. A mechanical model to express the interaction between wheel and rail is described, in which the impact of the rail on the flange of wheel is also considered. The bridge is modeled by using various finite elements such as shell, beam, solid, spring, and mass. The equations of motions of bridge and Shinkansen cars are solved under the constitutive and constraint equations to express the interaction between rail and wheel. Numerical method based on a modal transformation to get the dynamic response effectively is discussed. A finite element program for the dynamic response analysis of Shinkansen cars, rail, and bridge at the high-speed running has been developed. Numerical examples are also demonstrated.

Sign in / Sign up

Export Citation Format

Share Document