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By eliminating dynamic equations using wide area measurements, the computation time is significantly reduced.
The effect of longitudinal deformation due to bending is systematically introduced to the dynamic equations using the principle of virtual work.
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The Marguerre type dynamic equations used for the analysis of shallow shells, when treated by the Galerkin method, will result in a system of total differential equations in the time functions, known as Duffing and Mathieu equations, from which the various kinds of non-linear vibration and dynamic instability are determined by using numerical methods.
For an introduction to the fluid dynamic equations used here, refer by Kay and Nedderman (1974).
In the future studies, we would intend to derive the multiplication rule of two generalized polynomials or to provide an approximation of other nonlinear q-partial dynamic equations by using the proposing method.
These equations have been recently solved numerically [Kirby, R., Yosibash, Z., 2004. Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method. Comp. Meth. Appl. Mech. Eng. 193 (6–8) 575–599 and Yosibash, Z., Kirby, R., Gottlieb, D., 2004.
Working fluid properties and auxiliary dynamic equations are used to model the processes in the ejector.
Dynamic equations which use a tire-like model to capture the characteristics of the implement are found to adequately describe the tractor implement yaw dynamics.
Several controllers are determined based on the Linear Quadratic Gaussian (LQG) theorem by which a dynamic output feedback equation using acceleration feedback is formed for practical consideration.
Species specific annualized static and dynamic equations were developed using the available data and the system was evaluated for long term behavior.
The dynamic equations are discretized using trigonometric expansion through the circumferential direction and harmonic differential quadrature (HDQ) method through the meridional direction.
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