Nonlinear vibrations of rotating rings and shells under the usage of the finite element method

Schmidt, R.; Ams, Alfons

doi:10.1002/pamm.202100154

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…For local FE discretization flat shell elements are used instead of curved ones. As already presented in [5], this type of elements has better convergence characteristics in comparison with curved shell elements. The curvature of the shell can be expressed with different element orientations.…”

Section: Local Discretizationmentioning

confidence: 70%

A comparison of different nonlinear shell theories for rotating fluid‐filled structures

Schmidt

Ams²

2023

Proc Appl Math and Mech

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Rotating fluid‐filled shell structures can be used for different applications in technique. Because of spin‐softening as well as stress‐stiffening it is essential to consider geometrical non‐linearities. Additionally, shear deformation is getting important in case of thick shells. At this point different theories from KIRCHHOFF‐LOVE (no shear deformation) and MINDLIN‐REISSNER (first order shear deformation) are compared with each other. For both theories the nonlinear kinematics are shown and therewith the HAMILTON's principle is evaluated to receive the equations of motion. The solution of the corresponding eigenvalue problem is done with a global RITZ approach on the one hand, on the other hand with local FE‐discretization. Different results of rotating and non‐rotating cylindrical shells with respect to their eigenfrequencies are presented and compared. Furthermore, experimental data is used for validation.

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Section: Local Discretizationmentioning

confidence: 70%

A comparison of different nonlinear shell theories for rotating fluid‐filled structures

Schmidt

Ams²

2023

Proc Appl Math and Mech

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“…After evaluation of Hamilton's principle (Equation ( 7)), the variational formulation can be solved under usage of global Ritz or local FE approaches. A detailed study of different finite shell elements is presented in [6].…”

Section: Kinematics Of Deformation and Variational Formulationmentioning

confidence: 99%

Various beam and shell models for long slender tools in the area of HSC milling

Schmidt,

Ams

2023

Proc Appl Math and Mech

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High‐speed‐cutting) milling is an extensively used production process in tool‐making and mold‐making industries. For the purpose of a self‐balancing tool, a hollow shaft is used and filled partially with a fluid. This talk presents different beam and shell models for the investigation of nonlinear vibrations. Therefore, different theories are compared with respect to the influence of geometrical nonlinearities, spin‐softening as well as stress‐stiffening, and also shear deformation. Additionally, a stochastic Wedig–Dimentberg approach is presented for the simulation of a spatial distributed unbalance. Starting with the nonlinear kinematics for the tool‐deformation Hamilton's principle is evaluated for the variational formulation of each model. Regarding to the shear deformation, the theories of Euler‐‐Bernoulli and Ehrenfest–Timoshenko (beam models) as well as Kirchhoff‐‐Love and Mindlin–Reissner (shell models) are used. In the following up, the variational formulation is discretized under usage of a global Ritz approach on the one hand, and on the other hand with a local finite element (FE) discretization. Afterward, the governing system of differential equations is solved and discussed. Different results of rotating and nonrotating tools are presented, which show the available options of each theory and also their limits. In particular, results of the eigenfrequencies including their stochastic distribution, stationary deformation, stability behavior, and various time solutions are shown.

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Nonlinear vibrations of rotating rings and shells under the usage of the finite element method

Cited by 2 publications

References 3 publications

A comparison of different nonlinear shell theories for rotating fluid‐filled structures

A comparison of different nonlinear shell theories for rotating fluid‐filled structures

Various beam and shell models for long slender tools in the area of HSC milling

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