scholarly journals Application of the finite difference method for modeling cantilever bar vibrations

2020 ◽  
Vol 224 ◽  
pp. 02002
Author(s):  
M I Volnikov
Keyword(s):  
Mathematical Modeling ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Structural Mechanics ◽  
Forced Vibrations ◽  
Cantilever Beams ◽  
System Parameters ◽  
Free And Forced Vibrations ◽  
The Finite Difference Method

The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.

scholarly journals Mathematical modeling of air duct heater using the finite difference method

2011 ◽  
Vol 13 (4) ◽  
pp. 47-52
Author(s):  
M. Sarafraz ◽  
S. Peyghambarzadeh ◽  
A. Marahel
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Design And Optimization ◽  
The Finite Difference Method

Mathematical modeling of air duct heater using the finite difference method In this research, mathematical modeling of a duct heater has been performed using energy conservation law, Stefan-Boltzman law in thermal radiation, Fourier's law in conduction heat transfer, and Newton's law of cooling in convection heat transfer. The duct was divided to some elements with equal length. Each element has been studied separately and air physical properties in each element have been used based on its temperature. The derived equations have been solved using the finite difference method and consequently air temperature, internal and external temperatures of the wall, internal and external convection heat transfer coefficients, and the quantity of heat transferred have been calculated in each element and effects of the variation of heat transfer parameters have been surveyed. The results of modelling presented in this paper can be used for the design and optimization of heat exchangers.

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