Identification of complex non-linear modes of mechanical systems using the Hilbert-Huang transform from free decay responses

Modal analysis is a well-established method for of linear systems, but its extension to non-linear structures has proven be much more problematic. Several competitive definitions modes and variety experimental methods have been introduced. In this paper, the definition complex (CNMs) mechanical systems adopted possibility their identification from free decay responses using Hilbert-Huang transform (HHT) explored. It firstly discussed that since there are similarities in intrinsic mode functions obtained HHT reduced order model slow-flow dynamics based on CNMs, reason believe can indeed extract CNMs. This however, presents new insight into use by showing amplitude-dependent frequency damping extracted response only suitable detection characterisation non-linearities, they cannot used quantify behaviour fitting CNMs even if system known. The analytical proof currently formulated due limited understanding empirical nature. Instead, unconventional conclusion supported series numerical studies conservative non-conservative with wide range parameters. all cases, special care taken apply basic such signals which separation possible (no mode-mixing occurs). eliminates need sophisticated versions clearly demonstrates inability simplest cases. addition studies, several demonstrated experimentally ECL benchmark. shown able successfully whose character correspond reference, parameters conclusions made paper. findings highlight ability severely limited, while non-parametric manner feasible.