Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method

Kiani, Keivan; Nikkhoo, Ali; Mehri, B.

doi:10.1007/s10409-010-0365-0

Cited by 33 publications

(19 citation statements)

References 17 publications

(26 reference statements)

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“…For interpolation, several powerful methods exist such as generalized moving least square method [4,26,27], in which coefficients of basis functions vary on each data point in order to interpolate local values. On the other hand, reconstruction aims to find systems that globally hold, and one can obtain relations between variables including their degree and coefficients from the results.…”

Section: Using the Order Ideal To Create A Reduced Projection Of Polymentioning

confidence: 99%

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Kera

Hasegawa

2016

Nonlinear Dyn

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Reconstruction of nonlinear dynamical systems from noisy time series data has attracted much attention in recent years, and it has broad applications in many fields, especially in theoretical biology. Here, we propose a reconstruction algorithm based on the noise-tolerant algebraic approach that can infer underlying continuous-time polynomial dynamical systems from the observed time series data. The advantages of our approach are that it can handle nonlinearity, and it can be applied to noisy systems. Our approach reduces the range of monomials to be considered without any a priori knowledge as many other studies does. We apply the proposed method to two oscillatory systems (the FitzHugh-Nagumo and the Oregonator) subject to noise, where the conventional fitting methods based on L 1 and L 2 regularizations often fail. Our numerical experiments show that the proposed method accurately reconstructs the continuous-time polynomial dynamical systems. We also apply the method to a chaotic system and show the effectiveness of our approach.

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Section: Using the Order Ideal To Create A Reduced Projection Of Polymentioning

confidence: 99%

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Kera

Hasegawa

2016

Nonlinear Dyn

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“…According to the inherent complexities of the moving mass problems in the linear beams, some studies have been carried out using different numerical schemes, e.g., [5][6][7][8][9][10]. As a nonlinear moving mass problem, Xu et al [11] derived the nonlinear equations of motion for a finite elastic beam traversed by a moving mass.…”

Section: Introductionmentioning

confidence: 99%

On the limitations of linear beams for the problems of moving mass-beam interaction using a meshfree method

Kiani

Nikkhoo

2012

Acta Mech Sin

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This paper deals with the capabilities of linear and nonlinear beam theories in predicting the dynamic response of an elastically supported thin beam traversed by a moving mass. To this end, the discrete equations of motion are developed based on Lagrange's equations via reproducing kernel particle method (RKPM). For a particular case of a simply supported beam, Galerkin method is also employed to verify the results obtained by RKPM, and a reasonably good agreement is achieved. Variations of the maximum dynamic deflection and bending moment associated with the linear and nonlinear beam theories are investigated in terms of moving mass weight and velocity for various beam boundary conditions. It is demonstrated that for majority of the moving mass velocities, the differences between the results of linear and nonlinear analyses become remarkable as the moving mass weight increases, particularly for high levels of moving mass velocity. Except for the cantilever beam, the nonlinear beam theory predicts higher possibility of moving mass separation from the base beam compared to the linear one. Furthermore, the accuracy levels of the linear beam theory are determined for thin beams under large deflections and small rotations as a function of moving mass weight and velocity in various boundary conditions. Keywords Nonlinear beam theory · Moving mass-beam interaction · Euler-Bernoulli beam theory · Reproducing kernel particle method (RKPM) · Galerkin method (GM)

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“…ey demonstrated the efficiency and simplicity of their method using several numerical examples. Kiani et al [21,22] reported a numerical parametric investigation into the design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via the generalized moving least squares method and another comprehensive parametric investigation on the evaluation of design parameters, where the maximum deflection and bending moment of beams were analyzed. Regarding the problem of moving loads acting on thin beams with geometric nonlinearity, they also employed an efficient meshless method and the reproducing kernel particle method for a spatial discretization nonlinear beam [23].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of a Casting Crane Rigid‐Flexible Coupling System to High Temperature

Xin

Dong

et al. 2020

Advances in Civil Engineering

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To determine the influence of temperature on the mechanical properties of crane metal structures, three Q355 alloy steel samples were processed and their elastic moduli were tested at different temperatures using a metal tension test bed. The constitutive equation for the elastic modulus of Q355 alloy steel at different temperatures was predicted using test data and a neural network algorithm. Based on crane structural characteristics and the principle of system dynamics, a coupling vibration model was established that included the crane flexible girder, cabin, trolley, crane, and temperature. System motion equations were established according to the Lagrange equation, and the approximate solution of nonlinear system vibration was solved by the direct integration method (the Newmark method). The dynamic characteristics of the main beam and cabin were analyzed at different temperatures, as well as safety during service. The results show that, with increasing temperature, the maximum midspan displacement of the main beam increases gradually, by 14.3%, 21.4%, and 57.1% at temperatures of 300°C, 400°C, and 600°C, respectively. The cabin vibration displacement increases with temperature, by up to 32.5% at 600°C, but the influence of temperature on cabin vibration acceleration is not obvious. It was concluded that the influence of temperature on the dynamic characteristics of the main beam must be considered during the design stage of cranes. The proposed model and analysis method provide a theoretical basis for the design of casting cranes according to temperature.

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Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method

Cited by 33 publications

References 17 publications

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

On the limitations of linear beams for the problems of moving mass-beam interaction using a meshfree method

Dynamic Response of a Casting Crane Rigid‐Flexible Coupling System to High Temperature

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