Internal Resonance of a Beam/Traveling-Mass System

2000 ◽  
Author(s):  
S. Siddiqui ◽  
F. Golnaraghi ◽  
G. R. Heppler
Keyword(s):  
Differential Equations ◽  
Nonlinear Interaction ◽  
Internal Resonance ◽  
Series Expansions ◽  
Nonlinear Ordinary Differential Equations ◽  
Mass System ◽  
Weighted Residuals ◽  
Average Acceleration ◽  
Acceleration Method ◽  
Traveling Mass

Abstract The dynamics of a cantilever beam undergoing large amplitude oscillations while experiencing a nonlinear interaction with an attached lumped spring/mass system are investigated. The resulting partial differential equations contain trigonometric non-linearities that are treated using methods of weighted residuals and do not require series expansions about the equilibrium positions. The resulting nonlinear ordinary differential equations are solved using a formulation of the average acceleration method.

Dynamic Stability of Free Piston Stirling Engines

1993 ◽  
Author(s):  
Necati Ulusoy ◽  
Frances McCaughan
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Periodic Motion ◽  
Nonlinear Ordinary Differential Equations ◽  
Work Output ◽  
Free Piston ◽  
Mass System ◽  
Nonlinear Load ◽  
Stirling Engines ◽  
Stable Periodic

Abstract A Stirling engine develops work output from a thermal input. It is a quiet pollution free engine, which can use any heat source, including solar power. The piston-displacer mechanism is essentially a vibrating spring mass system and can be dynamically modelled, leading to a set of coupled nonlinear ordinary differential equations. The inadequacies of previous linear approaches are discussed and it is shown that the inclusion of a nonlinear load will lead to stable periodic motion as desired.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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