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

2013 ◽  
pp. 283-298
Author(s):  
Tiberiu Colosi ◽  
Mihail-Ioan Abrudean ◽  
Mihaela-Ligia Unguresan ◽  
Vlad Muresan
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
And Control

Modeling and Control of a Thermoelastic Beam

2013 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Javier Gonzalez-Rocha
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Displacement ◽  
Linear Quadratic ◽  
Partial Differential ◽  
Numerical Application ◽  
Modeling And Control ◽  
Thermoelastic Beam ◽  
And Control

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.

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

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.

scholarly journals Numerical Simulation of Partial Differential Equations via Local Meshless Method

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 257 ◽  
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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