Integration of Base Excitation With Non‐Linear Coupling Within the Multiharmonic Balance Method
Tido Kubatschek, Tomke Julia Albers, Sebastian Tatzko, Jörg Wallaschek
Source abstract
ABSTRACT This study presents the implementation of linear and nonlinear base excitation within the Multiharmonic Balance framework. Two nonlinear approaches are explored: the introduction of relative coordinates and the direct inclusion of nonlinear base excitation as a nonlinear force. This is complemented by the derivation of the analytical Jacobian. The methodologies are then tested on a single degree of freedom base‐excited Duffing oscillator, revealing unbounded response amplitude growth beyond a certain excitation amplitude. This phenomenon is analytically explored using a mono‐harmonic approach, confirming the behavior through the frequency response functions. Furthermore, the method is tested on a system with a Van‐der‐Pol nonlinearity for different types of base excitation. In the end, the method is applied to a two‐degree‐of‐freedom system with nonlinear base excitation via a cubic spring, which shows a similar phenomenon as the base‐excited Duffing oscillator. The insights gained offer significant implications for understanding and predicting system behavior when nonlinear base excitation is present.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.