Free in-plane vibration of curved beam structures: A tutorial and the state of the art

Yang, Fan; Esmailzadeh, Ebrahim

doi:10.1177/1077546317728148

Cited by 35 publications

(13 citation statements)

References 148 publications

(195 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Before using the variational principle to obtain the final vibration equation of the system, the displacement tolerance function needs to be clarified. e differential equation of motion for the in-plane vibration of a curved beam [7] is as follows:…”

Section: Variational Formulation Model Of the Curved Beammentioning

confidence: 99%

“…To simplify the calculation, the axial tensile deformation, shear deformation, and rotational inertia are sometimes ignored [1][2][3][4][5], but this may result in a large error in calculating the high-order natural frequency of the curved beam [6]. Besides, since the vibration of the plane-curved beam is not coupled between the in-plane and out-of-plane, most scholars discuss it as two relatively independent issues [7,8], and few documents have studied both at the same time [9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Nie

Zhu

et al. 2021

Shock and Vibration

View full text Add to dashboard Cite

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.

show abstract

Section: Variational Formulation Model Of the Curved Beammentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…The angular transformation matrix and global dynamic stiffness matrix of the arch are given in Eqs. (8)(9), respectively:…”

Section: Application Of Dsmmentioning

confidence: 99%

“…A limited number of analytical studies consider the aforementioned aspects [4][5][6][7]. More specifically, these studies carry out free vibration analysis of circular beams having various boundary conditions using the DSM [4,6,8,9].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of arch-frames using the dynamic stiffness approach

Bozyiğit¹,

Yeşilce²,

Acikgoz³

2020

Vib. proced.

View full text Add to dashboard Cite

The aim of this study is to investigate free vibration characteristics of arch-frames which consist of two columns and an arch. Firstly, an exact formulation of the problem is presented using the Dynamic Stiffness Method (DSM). The end forces and displacements of column elements are obtained analytically using Timoshenko beam theory (TBT). These are then combined with the end forces and displacements of the semi-circular arch, which is modeled with exact curved beam elements that consider axial and shear deformations and rotational inertia. By employing standard assembly and bisection based root finding procedures, exact free vibration analysis of the whole vibrating system is carried out. Then, in an effort to simplify the formulations, an approach based on approximating the arch as assembly of linear straight beam segments is presented. The calculated natural frequencies using DSM for both exact and approximate results are then tabulated for comparison purposes. The mode shapes are also compared. The results show that the proposed model simplification is effective and produces accurate mode frequency and shape estimations.

show abstract

“…13 Observations and incorporation of stretching, rotary inertia, and shear deformation in curved beam dynamic models have become one major research area for the last few decades. 14…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of large deformed curved beam incorporating rotary inertia and shear deformation effects and its experimental validation

Ghuku

Saha

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

The paper theoretically and experimentally analyzes free vibration characteristics of statically loaded moving boundary type curved beam considering rotary inertia and shear deformation effects. Effects of rotary inertia and shear deformation are observed for different thickness to span ratios of curved beam. The subject problem is decoupled into two interrelated problems: determining equilibrium configuration under static load and finding the corresponding free vibration frequency. The static problem is analyzed incrementally in body fitted curvilinear frame as it involves geometric nonlinearity due to generalized curvature, large deformation, and moving boundaries. Variational energy principle is employed to derive governing equation. The nonlinear governing equation associated with complicated boundary conditions is solved through iterative geometry updation. Once static problem is solved for current load step, governing equation for dynamic characteristics is derived using Hamilton’s principle. The governing equation gets linearized by using the static configuration, which finally yields a linear eigenvalue problem. Experiment is performed in a dedicated setup with two master leafs having different thickness to span ratios. The roller supported specimens are excited with an instrumented hammer and response signals are captured by accelerometers. The excitation and response signals are recorded using HBM-MX840B data acquisition system. Frequency response functions of the curved beam systems under different static loads are obtained from postprocessing of the dynamic signals in MATLAB®. First two natural frequencies of the specimens are noted from the experimental results and the corresponding theoretical results are generated. The specimens are also modeled in ABAQUS® CAE and finite element results are computed. Comparison between the theoretical, experimental, and finite element results validates the present model. The study also provides some meaningful observations on effects of rotary inertia and shear deformation. Based on the observations, more results are generated for different thickness to span ratios and findings are reported suitably.

show abstract

Free in-plane vibration of curved beam structures: A tutorial and the state of the art

Cited by 35 publications

References 148 publications

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

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

Free vibration analysis of arch-frames using the dynamic stiffness approach

Free vibration analysis of large deformed curved beam incorporating rotary inertia and shear deformation effects and its experimental validation

Contact Info

Product

Resources

About