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(1) The Hamilton's principle was employed to study the coupling longitudinal-transverse governing equations of motion for the rope in mine hoisting system.
Generalized Hamiltonian principle is applied to derive the nonlinear transverse vibration governing equation.
In this paper, the coupling longitudinal-transverse governing Eqs. of motion were established.
The partial differential equations governing transverse motion of the beam are derived from the extended form of Hamilton's principle.
The differential quadrature scheme is developed to solve numerically the partial differential equation governing transverse motion of axially accelerating viscoelastic beams.
Dimensional analysis of the equations governing transverse motion of a centrifugally tensioned, Kirchhoff plate and irrotational flow of a compressible fluid identifies three dimensionless parameters that characterize the state of stability of the fluid-plate system.
Our model includes interactions of dislocated and neighboring intact fibers through a system of fourth-order, differential equations governing transverse deformation, and also allows for local matrix plastic yielding and debonding from the fiber near and within the dislocation arrays.
A partial-differential equation governing the transverse vibration is derived from the Newton's second law.
The reduced-order model is derived from the equation governing the transverse deflection of the plate.
Therefore, integro-partial-differential equations are derived for governing the transverse vibrations of the belt spans.
The inplane inertia and damping are neglected, and hence the two equations are reduced to a single nonlinear fourth-order partial integral differential equation governing the transverse deformations.
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