Derivation of the equations of motion and boundary conditions of a thin plate via the variational method

Pachas, V. S.; Paredes, A. D.; Beltrán, J.

doi:10.1590/1806-9126-rbef-2021-0387

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…Theoretical studies on the vibration of basic plate and shell structures have been developed in various directions, including different shape classes, differences in boundary conditions and changes in load states [20][21][22][23]. Kim et al proposed a frequency-domain spectral element method for the vibration analysis of thin plate structures under the action of moving point forces [24].…”

Section: Introductionmentioning

confidence: 99%

Vibration Response of Metal Plate and Shell Structure under Multi-Source Excitation with Welding and Bolt Connection

Ding,

Tang,

Zhang

et al. 2024

Agriculture

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There are many excitation sources and complex vibration environments in combine harvesters. The coupling and superposition of different vibration signals on the plate and shell seriously affect the working parts of the body. This also reduces the reliability of the whole machine. At present, domestic and foreign research on existing harvesters mainly focuses on harvesting performance, with less research on vibration characteristics. Therefore, in this paper, the vibration response of the metal plate–shell under the two connection modes of bolt connection and welding is studied, in order to optimize the design and structure of the plate–shell structure of the combine harvester and improve the overall performance. First, the welded and bolted plates are numerically modeled using Hypermesh pre-processing functions. Then, the boundary conditions are simulated by continuous variable stiffness elastic constraint experiments. Finally, the intrinsic vibration dynamic model of the four-sided simply supported plate and four-sided solidly supported plate is established using the modal superposition method. By analyzing the modal frequencies and vibration patterns, the following results are obtained. The connection method between the plate and the frame has a significant impact on the inherent vibration characteristics of the plate. The bolt connection will make the plate’s intrinsic vibration frequency higher than that of the welding method, but the effect on the plate’s intrinsic vibration pattern is more minor. At the same time, in order to verify the accuracy of the model, the actual modal vibration patterns and frequencies of the same proportion of plates in the modal test are compared with the results of modal vibration patterns and frequencies obtained by Ansys. The errors of the two dynamic model analytical methods are within 1% and 3%, respectively. This result verifies the accuracy of the dynamic model of the metal plate and shell structure under different connection methods.

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Section: Introductionmentioning

confidence: 99%

Vibration Response of Metal Plate and Shell Structure under Multi-Source Excitation with Welding and Bolt Connection

Ding,

Tang,

Zhang

et al. 2024

Agriculture

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Differential equations of oscillation of thin plates with point bonding

Berikkhanova

Zholymbayev

Aniyarov

2023

Zeitschrift Für Naturforschung A

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The relevance of the research results presented in this article lies in the general concept of elasticity theory, which integrates the bases of theoretical-empirical physics, practical mathematics and the natural implementation of modelling results in the fields of industrial (to a large extent in the design and manufacture of aircraft and naval aircraft shells and fuselages), construction (more so in the design and formation of multi-layer building structures), electronics and other areas of the science and industry complex. The aim of the study is to form a mathematical model of thin plate vibration based on a system of differential equations for the computational case of point bonding. The method of scientific search (Multilocal Literature Review) is used to achieve the set goal, which made it possible to establish the actual scientific-theoretical basis of the investigated problem, the method of mathematical modelling allowing to systematize the systems of differential equations developed earlier and formed in the framework of the present study, both for the general concept of the theory of elasticity of thin plates and for a selected calculation situation with partial constraints in the form of point bond imposing. As a result of the investigations conducted in the framework of this study, a mathematical model of the oscillations of thin plates bounded by special point-coupling conditions has been obtained, consisting of a system of differential equations obtained by successive iterations of mathematical transformations for the generated local boundary conditions. The mathematical model obtained is of practical scientific interest. The developed model environment forms a complete mathematical theory of elasticity for the formulated problem of the oscillatory process of thin plates with bounding point couplings. This problem has not received a satisfactory mathematical apparatus because of the complexity and cumbersomeness of analytical methods to describe the investigated elastic object.

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Derivation of the equations of motion and boundary conditions of a thin plate via the variational method

Cited by 2 publications

References 12 publications

Vibration Response of Metal Plate and Shell Structure under Multi-Source Excitation with Welding and Bolt Connection

Vibration Response of Metal Plate and Shell Structure under Multi-Source Excitation with Welding and Bolt Connection

Differential equations of oscillation of thin plates with point bonding

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