A variational formulation for vibration analysis of curved beams with arbitrary eccentric concentrated elements

Su, Jinpeng; Zhou, Kai; Qu, Yegao; Hu, Hua

doi:10.1007/s00419-018-1360-3

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…Su et al [40] studied the free and forced vibrations of bending beams with different boundary conditions based on a modified variational method. He et al [41] proposed a new energy method to solve the fluid-solid coupling problem for a functional gradient porous fluid-filled cylindrical shell with arbitrary boundary conditions using a modified variational principle.…”

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%

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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“…To solve this problem, Qu [24] proposed a modified variational method, which is based on the modified variational principle and the weighted residual method to solve the internal interface and boundary constraints of the structure, thereby relaxing the requirements for the selection of structural allowable functions. Subsequently, Su et al [25] used this method to solve the in-plane vibration problem of curved beams and used the advantages of flexible application range to study the influence of concentrated mass points on the vibration characteristics of curved beams. Also, Li [26] proposed an improved Fourier series, which is a combination of traditional Fourier series and auxiliary functions and used it to analyse the lateral vibration characteristics of a straight beam under arbitrary supports.…”

Section: Introductionmentioning

confidence: 99%

A General Fourier Formulation for In‐Plane and Out‐of‐Plane Vibration Analysis of Curved Beams

Nie

Zhu

et al. 2021

Shock and Vibration

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Based on the principle of energy variation, an improved Fourier series is introduced as an allowable displacement function. This paper constructs a calculation model that can study the in-plane and out-of-plane free and forced vibrations of curved beam structures under different boundary conditions. Firstly, based on the generalized shell theory, considering the shear and inertial effects of curved beam structures, as well as the coupling effects of displacement components, the kinetic energy and strain potential energy of the curved beam are obtained. Subsequently, an artificial spring system is introduced to satisfy the constraint condition of the displacement at the boundary of the curved beam, obtain its elastic potential energy, and add it to the system energy functional. Any concentrated mass point or concentrated external load can also be added to the energy function of the entire system with a corresponding energy term. In various situations including classical boundary conditions, the accuracy and efficiency of the method in this paper are proved by comparing with the calculation results of FEM. Besides, by accurately calculating the vibration characteristics of common engineering structures like slow curvature (whirl line), the wide application prospects of this method are shown.

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In-plane vibration of a circular ring with arbitrary concentrated elements by an analytical method

Niu

Zhang

et al. 2019

Arch Appl Mech

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A variational formulation for vibration analysis of curved beams with arbitrary eccentric concentrated elements

Cited by 10 publications

References 22 publications

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

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

A General Fourier Formulation for In‐Plane and Out‐of‐Plane Vibration Analysis of Curved Beams

In-plane vibration of a circular ring with arbitrary concentrated elements by an analytical method

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