Small-Amplitude free vibrations of straight beams subjected to large displacements and rotation

Eroğlu, Uğurcan; Tüfekçi, Ekrem

doi:10.1016/j.apm.2017.08.028

Cited by 15 publications

(7 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Solutions of Eqs. (38)(39)(40) provide the critical buckling loads at k th order, , cr k P . The numerical results for different geometries with comparison are given in Table 4.…”

Section: Exponential Bending Rigiditymentioning

confidence: 99%

See 1 more Smart Citation

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Eroğlu

Tüfekçi

2018

International Journal of Engineering and Applied Sciences

Self Cite

View full text Add to dashboard Cite

This study aims to derive approximate closed-form solutions for critical loads of straight beams with variable cross-section. The governing equations are derived for purely flexible beam for small displacements and rotation and turned into non-dimensional form. Approximate solutions to the set of equations for stability problems are searched by Variational Iteration Method with Generalized Lagrange Multipliers. It turns out that highly accurate approximate buckling loads for cantilever beams with constant or variable section can be obtained in closed-form. Many novel closed-form solutions for critical load of such structures, which may serve as benchmark solutions, are presented.

show abstract

“…Solutions of Eqs. (38)(39)(40) provide the critical buckling loads at k th order, , cr k P . The numerical results for different geometries with comparison are given in Table 4.…”

Section: Exponential Bending Rigiditymentioning

confidence: 99%

“…Since the initiation of the method, there have been many modifications and improvements introduced to it [28][29][30][31][32], for the reviews of which we refer to the note by He [33]. VIM is recently used for solutions of many different structural problems, see for example [34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Eroğlu

Tüfekçi

2018

International Journal of Engineering and Applied Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The free vibration analysis of high-rise tower with different damper or spring coefficients, support frame stiffness and support positions is complicated and time consuming. Many research studies have simplified these long and tall structures with supports as single beam supported with elastic support or viscous damper to find the optimized design parameters (De Rosa et al , 2010; Farghaly and El-Sayed, 2016; Karimpour et al , 2016; Eroglu and Tufekci, 2018; Wang, 2014; Wu and Chen, 2000; Main and Krenk, 2005; Pierson et al , 2013; Chen et al , 2015). In this paper, HTFD will be simplified as a long cantilever beam connected by a short cantilever beam with a spring or damper attached at tip, as shown in Figure 2.…”

Section: Introductionmentioning

confidence: 99%

Dynamical shakedown analysis of high-rise tower structure

Hong-tao

Peng

Liu

2021

View full text Add to dashboard Cite

Purpose High-rise tower structures supported by side frame structure and viscous damper in chemical industry can produce plasticity under dynamic loads, such as wind and earthquake, which will heavily influence the long-term safety operation. This paper aims to systematically study the optimization design of these structures by free vibration and dynamic shakedown analysis. Design/methodology/approach The transfer matrix method and Euler–Bernoulli beam vibration are used to study the free vibration characteristic of the simplified high-rise tower structure. Then the extended stress compensation method is used to construct the self-equilibrated stress by using the dynamic load vertexes and the lower bound dynamic shakedown analysis for the structure with viscous damper. Using the proposed method, comprehensive parametric studies and optimization are performed to examine the shakedown load of high-rise tower with various supported conditions. Findings The numerical results show that the supported frame stiffness, attached damper or spring parameters influence the free vibration and shakedown characters of high-rise tower very much. The dynamic shakedown load is lowered down quickly with external load frequency increasing to the fundamental natural frequency of the structure under spring supported condition, while changed little with the damping connection. The optimized location and parameter of support are obtained under dynamical excitations. Research limitations/implications In this study, the high-rise tower structure is simplified as a cantilever beam supported by a short cantilever beam and a damper under repeated dynamic load, and linear elasticity for solid is assumed for free vibration analysis. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity. Originality/value This study provides a comprehensive method for the dynamical optimization of high-rise tower structure by combining free vibration and shakedown analysis.

show abstract

“…Large displacements and rotations lead to nonlinear terms in the equations of motion of the beams. Thus, only some limited cases are analytically solvable [39,40]. These nonlinearities are also considered for the analytical solutions of composite beams in the literature [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Composite Wind Turbine Blades as Beams: An Analytical and Numerical Study

et al. 2020

View full text Add to dashboard Cite

This study focuses on the dynamic modelling and analysis of the wind turbine blades made of multiple layers of fibre reinforced composites and core materials. For this purpose, a novel three-dimensional analytical straight beam model for blades is formulated. This model assumes that the beam is made of functionally graded material (FGM) and has a variable and asymmetrical cross section. In this model, the blades are assumed to be thin, slender and long with a relatively straight axis. They have two main parts, namely the core and the shell. The so-called core consists of a lightweight isotropic foam material, which also adds significant damping to the system. The core material is covered by the shell, which is modelled using homogenous and orthotropic material assumptions as the structure is reinforced with continuous fibres. Therefore, the blades are modelled under a straight beam with varying cross-section assumptions, in which the effective elastic properties are acquired by homogenizing the cross section. The beam formulation for modelling the system is performed both analytically and numerically with the finite element method. The results of both methods are in well agreement. The maximum deviation between the results is found below 4%.

show abstract

Small-Amplitude free vibrations of straight beams subjected to large displacements and rotation

Cited by 15 publications

References 65 publications

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Dynamical shakedown analysis of high-rise tower structure

Dynamic Analysis of Composite Wind Turbine Blades as Beams: An Analytical and Numerical Study

Contact Info

Product

Resources

About