Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

Gao, Kang; Gao, Wei; Wu, Di; Song, Chongmin

doi:10.1007/s11071-017-3811-8

Cited by 21 publications

(7 citation statements)

References 35 publications

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“…Consider P as a variable and analyze the stability of the variable stepped column [22]. From the displacement expression (48) at the top of the column, the column will get unstable when the value of tan [23].…”

Section: Stability Analysismentioning

confidence: 99%

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

Wang

Weng

et al. 2020

Metals

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The steel bent frame structure of single-story factory buildings is actually a spatial structure system. Different bent frame columns are connected with the roof of bent frame structure, making the columns work and bearing the load together. In the steel frame of the factory building with bridge cranes below 20 t, variable-section columns with corbels are used to bear the crane load. In this article, the steel bent frame column of single-story factory buildings was taken as the research object. The bent frame column was simplified as a cantilever variable stepped column bearing a transverse concentrated force at the top. After simplifying the model, the theoretical formula of deflection, rotating angle, and bending moment of the compression rod was put forward. Moreover, bending deformation and stability of variable stepped columns were analyzed in order to obtain the theoretical and practical formula, then the ANSYS software was used to simulate the bent column.

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Section: Stability Analysismentioning

confidence: 99%

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

Wang

Weng

et al. 2020

Metals

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“…The dynamical stability of Euler–Bernoulli beam columns under the longitudinal constant rates of loading was presented by Gao et al. 31 in a thermal environment. Gao et al.…”

Section: Introductionmentioning

confidence: 97%

Nonlinear dynamic stability of an imperfect shear deformable orthotropic functionally graded material toroidal shell segments under the longitudinal constant velocity

Ali

Hasan

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study investigates the nonlinear dynamic buckling of the exponentially functionally graded orthotropic toroidal shell segments under constant loading rates under the shear deformation theory with the damping influence. The properties of the shell material are assumed to be graded according to the exponential distribution function through the shell thickness direction. The shear deformation theory with von Karman nonlinearity, Stein and McElman assumption, initial imperfection, and damping effect are adopted to create the theoretical formulations. Nonlinear dynamic stability equation is solved using Galerkin's procedure and the fourth-order Runge–Kutta technique. The dynamic buckling loads are evaluated by using Budiansky–Roth criterion. Moreover, different parameter influences such as geometrical parameters, velocity, imperfections, damping ratios, and nonhomogeneous parameters on the dynamic buckling are examined in detail. The obtained results are validated with the previous publications and the good agreements are shown.

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“…Elishakoff and Soize [16] comprehensively elaborated stochastic models for vibration problems, when there is a random excitation such as earthquake load. Gao et al [18][19][20] made the stochastic analysis of beam-type structures and showed the importance of stochastic analysis. There are papers about the stochastic analysis on the Euler-Bernoulli beams (see [21,22]).…”

Section: Introductionmentioning

confidence: 99%

Stochastic analysis of lattice, nonlocal continuous beams in vibration

Challamel

Elishakoff

2021

Vietnam J. Mech.

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In this paper, we study the stochastic behavior of some lattice beams, called Hencky bar-chain model and their non-local continuous beam approximations. Hencky bar-chain model is a beam lattice composed of rigid segments, connected by some homogeneous rotational elastic links. In the present stochastic analysis, the stiffness of these elastic links is treated as a continuous random variable, with given probability density function. The fundamental eigenfrequency of the linear difference eigenvalue problem is also a random variable in this context. The reliability is defined as the probability that this fundamental frequency is less than an excitation frequency. This reliability function is exactly calculated for the lattice beam in conjunction with various boundary conditions. An exponential distribution is considered for the random stiffness of the elastic links. The stochastic lattice model is then compared to a stochastic nonlocal beam model, based on the continualization of the difference equation of the lattice model. The efficiency of the nonlocal beam model to approximate the lattice beam model is shown in presence of rotational elastic link randomness. We also compare such stochastic function with the one of a continuous local Euler-Bernoulli beam, with a special emphasis on scale effect in presence of randomness. Scale effect is captured both in deterministic and non-deterministic frameworks.

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Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

Cited by 21 publications

References 35 publications

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

Nonlinear dynamic stability of an imperfect shear deformable orthotropic functionally graded material toroidal shell segments under the longitudinal constant velocity

Stochastic analysis of lattice, nonlocal continuous beams in vibration

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