scholarly journals A holomorphic semigroup approach to the lumped mass finite element method

2004 ◽  
Vol 169 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Norikazu Saito
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lumped Mass ◽  
Holomorphic Semigroup ◽  
Semigroup Approach ◽  
Element Method

Semi-Discrete Analytical Solution of Lumped Mass Finite Element Method for the Longitudinal Vibrations of an Elastic Bar

2013 ◽  
Vol 273 ◽  
pp. 234-239
Author(s):  
Jing Song Pan ◽  
Ji Chan Wang
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Analytical Solution ◽  
Longitudinal Vibration ◽  
Analytical Approximation ◽  
Longitudinal Vibrations ◽  
Lumped Mass ◽  
Elastic Bar ◽  
Element Method

The objective of this paper is to present semi-discrete analytical method for the longitudinal vibration of an elastic bar. Using lumped mass finite element method, we first obtain a system of second order ordinary differential equations. In terms of some transform technique we obtain the exact solution to the system, i.e. excellently semi-discrete analytical approximation to the longitudinal vibration. An example is given to illustrate the effectiveness of the proposed method.

Modeling of Rotor Shafting for Lower Mode Accuracy: Influence of Section L/D

1995 ◽  
Author(s):  
R. G. Kirk ◽  
S. Baheti ◽  
K. Ramesh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Forced Response ◽  
Reduction Technique ◽  
Mass Reduction ◽  
Lumped Mass ◽  
Lower Mode ◽  
Continuous Mass ◽  
Element Method

Abstract The transfer matrix and finite element methods are currently widely used to model rotor shafting for calculation of critical speeds, forced response, and stability. For many rotors, long uniform shafting sections occur on the ends of the rotors which could be treated without consideration of section L/D. The use of finite element continuous mass models makes it possible to consider longer sections than previously considered using lumped inertia models. This paper will review a major mass reduction technique which has been used for transfer matrix lumped mass models and compares the results to those obtained by the continuous mass finite element method. The required section L/D for desired accuracy of the lowest eight modes of a uniform shaft (4 forward, 4 backward) will be studied for both simple property splitting and a modified major mass reduction technique. The necessary section L/D for desired accuracy for varying bearing to shaft stiffness ratios will be presented. A comparison of the finite element method required section L/D to that of the transfer matrix major mass method is presented for both a uniform shafting geometry and a typical centrifugal compressor model. Conclusions and recommendations will be given concerning the required section L/D for improved rotor system analysis accuracy when using lumped inertia rotor models.

scholarly journals Nonlinear Dynamic Analysis of Axisymmetric Solids by the Finite Element Method

1974 ◽  
Vol 96 (2) ◽  
pp. 103-112 ◽  
Author(s):  
M. Hartzman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Plastic Behavior ◽  
The Finite Element Method ◽  
Lumped Mass ◽  
Mass System ◽  
The Impact ◽  
Element Method

A method for calculating the dynamic response of deformable axisymmetric solids, subjected to time-dependent axisymmetric loads is described. The nonlinearities considered in this analysis include material nonlinearity (elastic-plastic behavior) and geometric nonlinearity, which includes finite deformation. The finite-element method is applied to approximate the continuum by a lumped-mass system connected by axisymmetric elements. The equations of motion are solved by applying a step-by-step numerical technique. The analysis is illustrated by application to the collapse of a built-in spherical dome with varying thickness and to the impact of a cylinder against a rigid wall. Close agreement is obtained between the results from the present technique and results obtained from the literature.

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