The natural frequencies and modes of complex-shaped plates on an elastic base

Abstract When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated by certain additional wavenumbers in the presence of periodically spaced model features. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. A straightforward algebraic relation and a graphical checkerboard diagram are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.

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Effects of component interfacial boundary conditions on component mode synthesis estimates for natural frequencies and modes.

The Journal of the Acoustical Society of America ◽

10.1121/1.415306 ◽

1996 ◽

Vol 99 (4) ◽

pp. 2600-2603

Author(s):

Jerry E. Farstad ◽

Rajendra Singh

Keyword(s):

Boundary Conditions ◽

Natural Frequencies ◽

Component Mode Synthesis ◽

Natural Frequencies And Modes ◽

Interfacial Boundary

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Calculation of natural frequencies and modes of tires in road contact by utilizing Eigenvalues of the axisymmetric non-contacting tire

Journal of Sound and Vibration ◽

10.1016/0022-460x(80)90325-9 ◽

1980 ◽

Vol 70 (4) ◽

pp. 573-584 ◽

Cited By ~ 22

Author(s):

W. Soedel ◽

M.G. Prasad

Keyword(s):

Natural Frequencies ◽

Natural Frequencies And Modes

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Optimization Method of the Car Seat Rail Abnormal Noise Problem Based on the Finite Element Method

Shock and Vibration ◽

10.1155/2017/4132092 ◽

2017 ◽

Vol 2017 ◽

pp. 1-13

Author(s):

Huijie Yu ◽

Xinkan Zhang ◽

Chen Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Natural Frequencies ◽

Joint Probability ◽

Element Model ◽

Joint Probability Distribution ◽

Natural Frequencies And Modes ◽

Car Seat ◽

Finite Element Software ◽

Element Method

The finite element model of the seat rail is established with a spring-damping element to simulate the ball in the rail joint part. The stiffness and damping parameters of the joint part are determined by the combination of finite element method and experiment. Firstly, the natural frequencies and modes of the guide rail are obtained by modal experiment. The stiffness of the spring-damping element is optimized in the finite element software to make the natural frequencies and modes of the system consistent with the experimental ones. Secondly, the dynamic response curve of the key nodes is obtained through sweeping experiment, and the damping of the spring-damping element is optimized in the finite element software to make the nodal response of the system output consistent with the experiment. Then, the gap of the joint part of the car seat rail is studied considering the factors of load and structure randomness. The influence factors of the gap are selected by Hammersley experimental design method. The results show that the gap is normally distributed, and therefore the confidence interval of the gap is obtained. Finally, the joint probability distribution of the gap is obtained under the condition that the load and the structure are all random, which provides the theoretical guidance for determining the reasonable gap of the joint.

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