scholarly journals Modeling of a Magnetoelectric Laminate Ring Using Generalized Hamilton’s Principle

Materials ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1442 ◽  
Author(s):  
Ru Zhang ◽  
Shengyao Zhang ◽  
Yucheng Xu ◽  
Lianying Zhou ◽  
Futi Liu ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Theoretical Calculations ◽  
Complex Structures ◽  
Equation Approach ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
New Approach ◽  
Modeling Analysis ◽  
Ring Structures ◽  
Analytical Expressions

The mathematical modeling of the magnetoelectric (ME) effect in ME laminates has been established for some simple structures. However, these methods, which are based on the differential equation approach, are difficult to use in other complex structures (e.g., ring structures). In this work, a new established approach based on the generalized Hamilton’s principle is used to analyze the ME effect in an ME laminated ring. Analytical expressions for ME voltage coefficients are derived. A comparison with the conventional method indicates that this approach is more convenient when the modeling analysis is performed on complex structures. Further, experimental data are also obtained to compare with the theoretical calculations in order to validate the new approach.

scholarly journals Dynamic Analysis of Encastre Beams by Modification of the System’s Stiffness Distribution

2020 ◽  
Vol 5 (11) ◽  
pp. 1334-1342
Author(s):  
V. O. Okonkwo ◽  
C. H. Aginam ◽  
C. M. O. Nwaiwu
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Continuous Systems ◽  
Complex Structures ◽  
Hamilton’S Principle ◽  
Equilibrium Equations ◽  
Lumped Mass ◽  
Hamilton's Principle ◽  
Lumped Masses ◽  
Stiffness Distribution

Numerical and energy methods are used to dynamically analyze beams and complex structures. Hamilton’s principle gives exact results but cannot be easily applied in frames and complex structures. Lagrange’s equations can easily be applied in complex structures by lumping the continuous masses at selected nodes. However, this would alter the mass distribution of the system, thus introducing errors in the results of the dynamic analysis. This error can be corrected by making a corresponding modification in the systems’ stiffness matrix. This was achieved by simulating a beam with uniformly distributed mass with the force equilibrium equations. The lumped mass structures were simulated with the equations of motion. The continuous systems were analyzed using the Hamilton’s principle and the vector of nodal forces {P} causing vibration obtained. The nodal forces and displacements were then substituted into the equations of motion to obtain the modified stiffness values as functions of a set of stiffness modification factors. When the stiffness distribution of the system was modified by means of these stiffness modification factors, it was possible to predict accurately the natural fundamental frequencies of the lumped mass encastre beam irrespective of the position or number of lumped masses.

Dynamic Modeling of Satellite Tether Systems Using Newton’s Laws and Hamilton’s Principle

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Kalyan K. Mankala ◽  
Sunil K. Agrawal
Keyword(s):  
Dynamic Modeling ◽  
Continuous System ◽  
Variable Length ◽  
Variable Domain ◽  
Dynamic Equations ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Newton’S Laws

The objective of this paper is to derive the dynamic equations of a tether as it is deployed or retrieved by a winch on a satellite orbiting around Earth using Newton’s laws and Hamilton’s principle and show the equivalence of the two methods. The main feature of this continuous system is the presence of a variable length domain with discontinuities. Discontinuity is present at the boundary of deployment because of the assumption that the stowed part of the cable is unstretched and the deployed part is not. Developing equations for this variable domain system with discontinuities, specially using Hamilton’s principle, is a nontrivial task and we believe that it has not been adequately addressed in the literature.

Dynamics of 3D Micropolar Gyroelastic Beams

2014 ◽  
Author(s):  
Soroosh Hassanpour ◽  
G. R. Heppler
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Modeling ◽  
Dynamic Equations ◽  
Hamilton’S Principle ◽  
The Finite Element Method ◽  
Hamilton's Principle ◽  
Modeling And Analysis ◽  
Element Method

This paper is devoted to the dynamic modeling of micropolar gyroelastic beams and explores some of the modeling and analysis issues related to them. The simplified micropolar beam torsion and bending theories are used to derive the governing dynamic equations of micropolar gyroelastic beams from Hamilton’s principle. Then these equations are solved numerically by utilizing the finite element method and are used to study the spectral and modal behaviour of micropolar gyroelastic beams.

Modified Hamilton's Principle

1973 ◽  
Vol 41 (10) ◽  
pp. 1188-1190 ◽  
Author(s):  
John R. Ray
Keyword(s):  
Hamilton’S Principle ◽  
Hamilton's Principle
Sign in / Sign up

Export Citation Format

Share Document