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Extracting Frequency of an Autonomous System by Harmonic Balance
Journal of Circuits, Systems and Computers, 1997Some considerations on initial partitioning of the circuit within harmonic balance analysis are presented. Instead of linear and nonlinear, it is divided into resistive and reactive parts. Following the procedure presented, frequency as a parameter appears no more than once inside each equation, and most of the unknowns are expressed explicitly.
Bostjan Persic, Igor Medic
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1990
Harmonic balance differs from traditional transient analysis in two fundamental ways. These differences allow harmonic balance to compute periodic and quasiperiodic solutions directly and in certain circumstances give the method significant advantages in terms of accuracy and efficiency.
Kenneth S. Kundert +2 more
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Harmonic balance differs from traditional transient analysis in two fundamental ways. These differences allow harmonic balance to compute periodic and quasiperiodic solutions directly and in certain circumstances give the method significant advantages in terms of accuracy and efficiency.
Kenneth S. Kundert +2 more
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Scalable parallelization of harmonic balance simulation
1999A new approach to parallelizing harmonic balance simulation is presented. The technique leverages circuit substructure to expose potential parallelism in the form of a directed, acyclic graph (dag) of computations. This dag is then allocated and scheduled using various linear clustering techniques. The result is a highly scalable and efficient approach
David L. Rhodes, Apostolos Gerasoulis
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Solution of a Duffing-harmonic oscillator by the method of harmonic balance
Journal of Sound and Vibration, 2006Abstract The first-order harmonic balance method via first Fourier coefficient is used to construct an approximate frequency–amplitude relation for a Duffing-harmonic oscillator. This relation is in agreement with the result obtained by the Ritz procedure.
H. Hu, J.H. Tang
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Harmonically forced Cavendish balance
American Journal of Physics, 1983The Cavendish balance, when driven into resonance by swinging the external mass, provides an interesting corridor demonstration of gravity. It is, moreover, a suitable means of demonstrating properties of driven harmonic systems.
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Proceedings of CICC 97 - Custom Integrated Circuits Conference, 2002
Fast and accurate computation of the steady-state response of large nonlinear networks under periodic and quasi-periodic drive is a key simulation problem for integrated RF designs. In this paper we describe recent work which extends the method of Harmonic Balance to networks containing several million unknowns. A new implementation is described, which
D. Long +3 more
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Fast and accurate computation of the steady-state response of large nonlinear networks under periodic and quasi-periodic drive is a key simulation problem for integrated RF designs. In this paper we describe recent work which extends the method of Harmonic Balance to networks containing several million unknowns. A new implementation is described, which
D. Long +3 more
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Harmonic balance and the Hopf bifurcation
Mathematical Proceedings of the Cambridge Philosophical Society, 1977SummaryA form of the Hopf bifurcation theorem specially suited to systems in block-diagram form has been developed, which allows one to deal with high or infinite order linear elements solely in terms of their transfer functions. The results are proved by the method of harmonic balance, and, for general non-linear systems, lead to criteria for the ...
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Solving the Harmonic Balance Equations
2019Harmonic Balance leaves us with a problem to be solved: a nonlinear algebraic equation system with respect to the Fourier coefficients of the approximation. In this chapter, we categorize the fundamentally different strategies suited for solving such equation systems. We then focus on local numerical methods, in particular on Newton-type methods. These
Malte Krack, Johann Gross
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A generalization of the method of harmonic balance
Journal of Sound and Vibration, 1986A procedure is provided for generalizing the method of harmonic balance to obtain higher-order approximations to the periodic solutions of differential equations for two systems, one a conservative system and the other nonconservative. The procedure is currently being applied to investigate the possible solution behaviors of singular, nonlinear ...
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Computation of periodic orbits for piecewise linear oscillator by Harmonic Balance Methods
Communications in Nonlinear Science and Numerical Simulation, 2022Ekaterina Pavlovskaia +2 more
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