TY - JOUR
T1 - A revisit of spinning disk models. Part I
T2 - Derivation of equations of motion
AU - Baddour, N.
AU - Zu, J. W.
PY - 2001/7
Y1 - 2001/7
N2 - Previous models of spinning disks have focused on modelling the disk as a spinning membrane. The effect of bending stiffness was then incorporated by adding the appropriate term to the previously derived spinning membrane equation. A pure spinning plate model does not exist in the literature. Furthermore, in both existing linear and nonlinear models of spinning disks, the in-plane inertia and rotary inertia of the disk have been ignored. This paper revisits the derivation of the equations of motion of a spinning plate. The derivation focuses on the use of Hamilton's principle with linear Kirchhoff and nonlinear von Karman strain expressions. In-plane and rotary inertias of the plate are automatically taken into account. The use of Hamilton's principle guarantees the correct derivation of the corresponding boundary conditions. The resulting equations and boundary conditions are discussed.
AB - Previous models of spinning disks have focused on modelling the disk as a spinning membrane. The effect of bending stiffness was then incorporated by adding the appropriate term to the previously derived spinning membrane equation. A pure spinning plate model does not exist in the literature. Furthermore, in both existing linear and nonlinear models of spinning disks, the in-plane inertia and rotary inertia of the disk have been ignored. This paper revisits the derivation of the equations of motion of a spinning plate. The derivation focuses on the use of Hamilton's principle with linear Kirchhoff and nonlinear von Karman strain expressions. In-plane and rotary inertias of the plate are automatically taken into account. The use of Hamilton's principle guarantees the correct derivation of the corresponding boundary conditions. The resulting equations and boundary conditions are discussed.
KW - Derivation of equations
KW - Hamiltonian
KW - Modelling
KW - Spinning disk
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U2 - 10.1016/S0307-904X(00)00065-2
DO - 10.1016/S0307-904X(00)00065-2
M3 - Article
AN - SCOPUS:0035395197
SN - 0307-904X
VL - 25
SP - 541
EP - 559
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 7
ER -