Numerical computation of nonlinear normal modes in mechanical engineering

On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems

Numerical computation of Nonlinear Normal Modes (NNMs) for conservative vibratory systems is addressed, with the aim of deriving accurate reduced-order models up to large amplitudes. A numerical method is developed, based on the center manifold approach for NNMs, which uses an interpretation of the equations as a transport problem, coupled to a periodicity condition for ensuring manifold’s cont...

Nonlinear Normal Modes, Part II: Practical Computation Using Numerical Continuation Techniques

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the NNM computation is possible with limited implementation effort, which paves the way to a practical...

Nonlinear Normal Modes of Vibrating Mechanical Systems and Their Applications

Numerical Computation of Normal

In this paper we introduce a general methodology for computing (numerically) the normal form around a periodic orbit of an autonomous analytic Hamiltonian system. The process follows two steps. First, we expand the Hamiltonian in suitable coordinates around the orbit and second, we perform a standard normal form scheme, based on the Lie series method. This scheme is carried out up to some nite ...

A finite element framework for computation of protein normal modes and mechanical response.

A computational framework based on the Finite Element Method is presented to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by elastic network models, proteins are treated as continuum elastic solids with molecular volume defined by their solvent-excluded surface. The discretized Finite Element representation is obtained using a sur...