Numerical Simulation Using Partial Differential Equations, for Propagation and Control in Discontinuous Structures Processes

The objective of this paper is to model a thermoelastic beam and use thermoelectric heat actuators dispersed over the beam to control not only its vibration, but also its temperature. The model is represented by two coupled partial differential equations governing the elastic bending displacement and temperature variation over the length of the beam. The partial differential equations are replaced by a set of ordinary differential equations through discretization. The first-order ordinary differential equations are cast in the compact state-space form to be used in the thermoelastic analysis and control. The Linear Quadratic Gaussian (LQG) is used for control design. An numerical application to a uniform cantilever beam demonstrates the coupling between the temperature and the elastic displacement and feasibility of using thermoelectric actuators in controlling the vibration and temperature simultaneously.

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Modeling and Control of a Manufacturing Flow Line Using Partial Differential Equations

IEEE Transactions on Control Systems Technology ◽

10.1109/tcst.2007.903085 ◽

2008 ◽

Vol 16 (1) ◽

pp. 130-136 ◽

Cited By ~ 24

Author(s):

Roel van den Berg ◽

Erjen Lefeber ◽

Koos Rooda

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Flow Line ◽

Partial Differential ◽

Modeling And Control ◽

And Control

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Modeling and Control of Flexible Transporter System With Arbitrarily Time-Varying Cable Lengths

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2003/vib-48345 ◽

2003 ◽

Author(s):

Yuhong Zhang ◽

Sunil K. Agrawal ◽

Peter Hagedorn

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Ritz Method ◽

Nonlinear Partial Differential Equations ◽

Time Varying ◽

Governing Equations ◽

Partial Differential ◽

Modeling And Control ◽

Lyapunov Controller ◽

And Control

A systematic procedure for deriving the system model of a cable transporter system with arbitrarily time-varying lengths is presented. Two different approaches are used to develop the model, namely, Newton’s Law and Hamilton’s Principle. The derived governing equations are nonlinear partial differential equations. The same results are obtained using the two methods. The Rayleigh-Ritz method is used to obtain an approximate numerical solution of the governing equations by transforming the infinite order partial differential equations into a finite order discretized system. A Lyapunov controller which can both dissipate the vibratory energy and assure the attainment of the desired goal is derived. The validity of the proposed controller is verified by numerical simulation.

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Numerical Simulation of Partial Differential Equations via Local Meshless Method

Symmetry ◽

10.3390/sym11020257 ◽

2019 ◽

Vol 11 (2) ◽

pp. 257 ◽

Cited By ~ 6

Author(s):

Imtiaz Ahmad ◽

Muhammad Riaz ◽

Muhammad Ayaz ◽

Muhammad Arif ◽

Saeed Islam ◽

...

Keyword(s):

Numerical Simulation ◽

Partial Differential Equations ◽

Differential Equations ◽

Meshless Method ◽

Three Dimensional ◽

Salient Feature ◽

Test Problems ◽

Spatial Discretization ◽

Partial Differential ◽

Meshless Collocation

In this paper, numerical simulation of one, two and three dimensional partial differential equations (PDEs) are obtained by local meshless method using radial basis functions (RBFs). Both local and global meshless collocation procedures are used for spatial discretization, which convert the given PDEs into a system of ODEs. Multiquadric, Gaussian and inverse quadratic RBFs are used for spatial discretization. The obtained system of ODEs has been solved by different time integrators. The salient feature of the local meshless method (LMM) is that it does not require mesh in the problem domain and also far less sensitive to the variation of shape parameter as compared to the global meshless method (GMM). Both rectangular and non rectangular domains with uniform and scattered nodal points are considered. Accuracy, efficacy and ease implementation of the proposed method are shown via test problems.

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