Interaction Between Coriolis Forces and Mistuning on a Cyclic Symmetric Structure With Geometrical Nonlinearity

Abstract

An investigation of the interaction between Coriolis forces and mistuning on a cyclic symmetric structure is presented in this paper. The sensitivity of the eigenvalues and eigenvectors to mistuning is first studied with the perturbation method. A lumped parameter model is used to perform a modal analysis using a numerical approach after which geometrical nonlinearity is added to compare behavior with the linear case. Two different modes are thoroughly investigated for different rotational speeds, the first with an eigenvalue isolated from the others and the second presenting a frequency veering zone. The evolution from a standing wave domination at low speeds to a travelling wave domination at high speeds is observed for the isolated mode, whereas a standing wave domination remains around the veering zone for the second mode studied. It is also shown that the geometrical nonlinearity reinforces the mistuning effect versus the Coriolis forces.

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [68,138,250], piezoelectric material nonlinearities [62,139,299], non-local models for nanostructures [238,239], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,267] with applications to blades [79,224,226,271], large strain elastic nonlinear constitutive laws [187], fluid-structure interaction [107,165] and coupling with nonlinear aeroelastic forces [48]; or thermal effects [99,219], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization, could be also used with such tools [65,291,308,309].…”

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [66,137,251], piezoelectric material nonlinearities [60,138,299], non-local models for nanostructures [239,240], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,268] with applications to blades [77,225,227,272], large strain elastic nonlinear constitutive laws [188], fluid-structure interaction [105,166] and coupling with nonlinear aeroelastic forces [46]; or thermal effects [97,220], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization could be also used with such tools [63,292,308,309].…”