NONLINEAR NORMAL MODES

By Alexander F. Vakakis. 2001

155 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/b160328f95141f57e385e18d9fb44376892b3a60

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Ocean Engineering

Citations in the corpus

A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes (2018, methodology): “Thus, the major effort has been spent to make time-domain methods for MDOF nonlinear systems computationally more efficient [5, 6].”
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist (2009, methodology): “An alternative method is to discretize the governing nonlinear partial differential equations into an infinite set of ordinary differential equations that is truncated to a finite number of equations [20].”
Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction (2016, background): “[33], and Avramov and Mikhlin [3,4] for reviews).”
Numerical computation of nonlinear normal modes in mechanical engineering (2016, unknown): “Since then, it was used in various applications including nonlinear beams [44,64], vibration absorbers [39, 65, 66], structures with cyclic symmetry [67], and granular chains [68].”
Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases (2015, background): “Some nonlinear systems [1] can even have a countable infinity of periodic solutions, which makes the search for all solutions very difficult, if not impossible.”
A harmonic-based method for computing the stability of periodic solutions of dynamical systems (2010, methodology): “In the second technique, the monodromy matrix is simply a by-product of a shooting continuation method [2].”
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques (2009, background): “To provide an extension of the NNM concept to damped systems, Shaw and Pierre defined an NNM as a two-dimensional invariant manifold in phase space.”
Nonlinear Generalization of Den Hartog's Equal-Peak Method (2015, methodology): “The algorithm is similar to that used in [32]”