An artificial damping method for the determination of the steady state of harmonically excited non-linear systems

1988 ◽  
Vol 120 (3) ◽  
pp. 597-608 ◽  
Author(s):  
A.E. Kanarachos ◽  
C.N. Spentzas
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Artificial Damping ◽  
Non Linear ◽  
Non Linear Systems

Effects of Suspension Design on the Attitudes of a Car during Braking and Acceleration

1973 ◽  
Vol 187 (1) ◽  
pp. 787-794
Author(s):  
J. R. Ellis
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
Coupled Systems ◽  
Two Degrees Of Freedom ◽  
Simulation Techniques ◽  
Non Linear ◽  
Non Linear Systems ◽  
Effort Distribution

Two degrees of freedom models of a car are employed to demonstrate the effects of the suspension derivative ∂ x/∂ z on the pitch and bounce attitudes during braking or accelerating. The work equation is employed to show that brake effort distribution between the axles has a significant effect on the attitudes when anti-dive suspension characteristics are utilized. The steady-state positions in both pitch and bounce are developed for linear systems of typical suspensions that may be either standard or coupled systems. Non-linear systems are considered using simulation techniques. A description of some simulation circuits is contained in an appendix.

Algorithm for the Determination of the Resonances of Anharmonic Damped Oscillators

1987 ◽  
Vol 42 (8) ◽  
pp. 803-807 ◽  
Author(s):  
G. Reiser ◽  
A. Hübler ◽  
E. Lüscher
Keyword(s):  
Linear Systems ◽  
New Method ◽  
Resonance Spectroscopy ◽  
Driving Mechanism ◽  
Non Linear ◽  
Non Linear Systems ◽  
Damped Oscillators ◽  
The Way

Non-linear damped oscillators can be resonantly driven by an aperiodic force. An algorithm is described which shows how such a driving mechanism can be calculated. This new method paves the way for resonance spectroscopy in non-linear systems.

scholarly journals Dynamic Catalysis Fundamentals: I. Fast calculation of limit cycles in dynamic catalysis

2021 ◽  
Author(s):  
Brandon Foley ◽  
Neil Razdan
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Closed Form ◽  
Linear Systems ◽  
Computational Cost ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Closed Form Solutions ◽  
Non Linear ◽  
Non Linear Systems

Dynamic catalysis—the forced oscillation of catalytic reaction coordinate potential energy surfaces (PES)—has recently emerged as a promising method for the acceleration of heterogeneously-catalyzed reactions. Theoretical study of enhancement of rates and supra-equilibrium product yield via dynamic catalysis has, to-date, been severely limited by onerous computational demands of forward integration of stiff, coupled ordinary differential equations (ODEs) that are necessary to quantitatively describe periodic cycling between PESs. We establish a new approach that reduces, by ≳108×, the computational cost of finding the time-averaged rate at dynamic steady state (i.e. the limit cycle for linear and nonlinear systems of kinetic equations). Our developments are motivated by and conceived from physical and mathematical insight drawn from examination of a simple, didactic case study for which closed-form solutions of rate enhancement are derived in explicit terms of periods of oscillation and elementary step rate constants. Generalization of such closed-form solutions to more complex catalytic systems is achieved by introducing a periodic boundary condition requiring the dynamic steady state solution to have the same periodicity as the kinetic oscillations and solving the corresponding differential equations by linear algebra or Newton-Raphson-based approaches. The methodology is well-suited to extension to non-linear systems for which we detail the potential for multiple solutions or solutions with different periodicities. For linear and non-linear systems alike, the acute decrement in computational expense enables rapid optimization of oscillation waveforms and, consequently, accelerates understanding of the key catalyst properties that enable maximization of reaction rates, conversions, and selectivities during dynamic catalysis.

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