A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton's principle

2013 ◽  
Vol 332 (5) ◽  
pp. 1355-1371 ◽  
Author(s):  
Jia Sun ◽  
Leif Kari ◽  
Ines Lopez Arteaga
Keyword(s):  
Plate Theory ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Classical Plate Theory ◽  
Rotating Blade ◽  
Stagger Angle ◽  
Blade Model

Imperfection Sensitivity of Post-Buckling Behavior and Vibration Response in Pre- and Post-Buckled Regions of Nanoscale Plates Considering Surface Effects

2018 ◽  
Vol 10 (03) ◽  
pp. 1850027 ◽  
Author(s):  
Raheb Gholami ◽  
Reza Ansari
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Displacement Vector ◽  
Vibration Response ◽  
Hamilton’S Principle ◽  
Imperfection Sensitivity ◽  
Hamilton's Principle ◽  
External Work ◽  
Buckling Behavior ◽  
Post Buckling

This paper aims to investigate the imperfection sensitivity of the post-buckling behavior and the free vibration response under pre- and post-buckling of nanoplates with various edge supports in the thermal environment. Formulation is based on the higher-order shear deformation plate theory, von Kármán kinematic hypothesis including an initial geometrical imperfection and Gurtin–Murdoch surface stress elasticity theory. The discretized nonlinear coupled in-plane and out-of-plane equations of motion are simultaneously obtained using the variational differential quadrature (VDQ) method and Hamilton’s principle. To this end, the displacement vector and nonlinear strain–displacement relations corresponding to the bulk and surface layers are matricized. Also, the variations of potential strain energies, kinetic energies and external work are obtained in matrix form. Then, the VDQ method is employed to discretize the obtained energy functional on space domain. By Hamilton’s principle, the discretized quadratic form of nonlinear governing equations is derived. The resulting equations are solved employing the pseudo-arc-length technique for the post-buckling problem. Moreover, considering a time-dependent small disturbance around the buckled configuration, the vibrational characteristics of pre- and post-buckled nanoplates are determined. The influences of initial imperfection, thickness, surface residual stress and temperature rise are examined in the numerical results.

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
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