Effective Modal Derivatives Based Reduction Method for Geometrically Nonlinear Structures

2011 ◽  
Author(s):  
Paolo Tiso
Keyword(s):  
Reduction Method ◽  
Order Reduction ◽  
Second Order ◽  
Geometrically Nonlinear ◽  
Vibration Modes ◽  
Model Order ◽  
Modal Derivatives ◽  
Dynamics Problems ◽  
Modal Truncation ◽  
Selection Of

Effective Model Order Reduction (MOR) for geometrically nonlinear structural dynamics problems can be achieved by projecting the Finite Element (FE) equations on a basis constituted by a set of vibration modes and associated second order modal derivatives. However, the number of modal derivatives generated by such approach is quadratic with respect to the number of chosen vibration modes, thus quickly making the dimension of the reduction basis large. We show that the selection of the most important second order modes can be based on the convergence of the underlying linear modal truncation approximation. Given a certain time dependency of the load, this method allows to select the most significant modal derivatives set before computing it.

scholarly journals Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

Vibration ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 175-204
Author(s):  
Yichang Shen ◽  
Alessandra Vizzaccaro ◽  
Nassim Kesmia ◽  
Ting Yu ◽  
Loïc Salles ◽  
...  
Keyword(s):  
Finite Element ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Model Order ◽  
Nonlinear Beam ◽  
Quadratic Nonlinearities ◽  
Reduction Methods ◽  
Modal Derivatives

The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).

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