Large amplitude vibration analysis of a non-uniform beam under arbitrary boundary conditions based on a constrained variational modeling method

Zhou, Zi-Xuan; Huang, Xiuchang; Hu, Hua

doi:10.1007/s00707-021-03094-2

Cited by 4 publications

(1 citation statement)

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“…Both the solutions corresponding to the general elastic boundary conditions and the conventional boundary conditions were presented explicitly. Zhou et al [16] proposed a constrained variational modeling method for predicting the static and dynamic behaviors of the large deflection non-uniform beam under arbitrary boundary conditions on the basis of a geometrically exact formulation. Peng et al [17] presented an analysis model of the imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams with arbitrary boundary conditions based on the first-order shear theory using the boundary spring technique and simulated the relaxation degree by adjusting the spring stiffness, derived the governing equations using the Rayleigh-Ritz method of solving the frequencies of beams with geometric imperfections, and relaxed boundaries.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%