A unified vibration modeling and dynamic analysis of FRP-FGPGP cylindrical shells under arbitrary boundary conditions

Li, Hui; Liu, Dongming; Li, Pengchao; Zhao, Jing; Han, Qingkai; Wang, Qingshan

doi:10.1016/j.apm.2021.03.054

Cited by 21 publications

(2 citation statements)

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“…Besides the dynamical modeling and dynamical properties of beam structures with complex boundary conditions [19], the dynamical modeling and dynamical properties of plate structures [20][21][22][23][24], shell structures [25][26][27][28][29][30][31], and other types of structures [32][33][34] with complex boundary conditions have also been investigated [35][36][37][38][39]. For example, Xue et al [20] developed and solved a dynamics model for medium-thick composite laminates with arbitrary boundary conditions based on Mindlin's theory, Hamilton's principle, a modified Fourier series method, and the spring technique, with parametric studies on the effects of several key parameters, such as thickness-to-width ratio, number of plies, and lay-up angle between two plies.…”

Section: Introductionmentioning

confidence: 99%

“…The extensive research results show that a variation of the boundary conditions can have a profound effect on the dynamic behavior of the structure. Li et al [25] indicated that the effects of classical and elastic boundary conditions on the vibration characteristics of the cylindrical shell of functionally graded porous graphene platelets (FGPGP) are unavoidable via study. As the circumferential wave number increased, the natural frequency decreased first and then increased.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

2023

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The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures.

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