On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: instability and resonance analysis

Pirmoradian, Mostafa; Keshmiri, Mehdi; Karimpour, Hossein

doi:10.1007/s00707-014-1240-z

Cited by 27 publications

(7 citation statements)

References 29 publications

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“…To obtain the boundary frequency equations the Fourier series with period 2T (12) or T (21) can be used, assuming that     …”

Section: Harmonic Balance Methodmentioning

confidence: 99%

“…To obtain the boundary frequency equations the Fourier series with period 2T (12) or T (21) can be used, assuming that     where M, M R , K and K G are respectively the mass matrix, the rotatory inertia matrix, the stiffness matrix and the incremental (or geometric) stiffness matrix. These matrices include effects of the shear deformation and are developed based on physical shape functions [29].…”

Section: Harmonic Balance Methodmentioning

confidence: 99%

“…The first approach is used for slender rods (straight lines or planes normal to the neutral beam axis remain straight and normal after deformation) [5][6][7][8] and the latter for stocky rods (the rods with small length-to-depth ratio) in which the transverse shear deformation and the rotatory inertia are involved [9,10]. Various aspects for Timoshenko beam theory have been investigated, for example, beams with asymmetric cross-section [11], beams excited by a sequence of moving masses [12], twisted beams [13,14], beams with damping [14] and beams under tangential follower forces [15][16][17]. The Timoshenko beam theory can also be used to study dynamic stability of sandwich beams [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

Obara

Gilewski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The objective of this paper is to determine dynamic instability areas of moderately thick beams and frames. The effect of moderate thickness on resonance frequencies is considered, with transverse shear deformation and rotatory inertia taken into account. These relationships are investigated using the Timoshenko beam theory. Two methods, the harmonic balance method (HBM) and the perturbation method (PM) are used for analysis. This study also examines the influence of linear dumping on induced parametric vibration. Symbolic calculations are performed in the Mathematica programme environment. The majority of studies reported in the literature use numerical analysis for determining resonance areas. Only a few researchers have adopted an analytical approach.The purpose of this article is to propose two methods for determining parametric resonance areas for moderately thick beams and frames under various support conditions. These methods, never before used for this purpose, are the harmonic balance method (HBM) and the perturbation method (PM). The latter of these two methods represents a surprisingly simple tool for achieving the goal, as its results are very close to those obtained from the standard harmonic balance method which is far more troublesome in application.An analytical approach is used to analyze simply supported moderately thick beams, and a numerical technique, based on the finite element method with the use of physical shape functions [32] is applied to other beams and frames. The analysis covers the effect of moderate thickness on resonance frequencies and the influence of type of fixing used in the beams and frames on the instability areas. For this purpose, shear deformation and rotatory inertia are taken into account. The Timoshenko beam theory is applied to examine how these factors affect resonance frequency values. The results are compared with those obtained with the Bernoulli-Euler beam theory.In addition, the effect of linear dumping of induced parametric vibration is considered. Analysis of a simply supported beamThe following assumptions are adopted in physical and numerical modeling:• The beam is made of an isotropic homogenous linear elastic material with Young's modulus E, shear modulus G and Poisson's ratio v.

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“…To obtain the boundary frequency equations the Fourier series with period 2T (12) or T (21) can be used, assuming that     …”

Section: Harmonic Balance Methodmentioning

confidence: 99%

Section: Harmonic Balance Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

Obara

Gilewski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…At the macro-scale, there have been numerous studies on the moving load case [25][26][27][28][29]. However, several published articles have considered the inertia effects [30][31][32][33][34][35][36][37][38][39]. Unfortunately, the proposed methods in all of the aforementioned research required time-dependent complex mathematical calculations.…”

Section: Introductionmentioning

confidence: 99%

A simplified-nonlocal model for transverse vibration of nanotubes acted upon by a moving nanoparticle

Nikkhoo

Zolfaghari

Kiani

2017

J Braz. Soc. Mech. Sci. Eng.

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This study provides a simplified solution for estimating the dynamic response of a single-walled carbon nanotube when excited by a moving nanoparticle. At first, the strong form of the equation of motion for a nonlocal Rayleigh nanotube is deduced, and the inertia effect of a moving nanoparticle along a nanobeam is then considered. For obtaining a weak form of the above nonlocal model, we use the Galerkin method, where the test functions are a set of orthogonal polynomials generated from a polynomial satisfying given boundary conditions. This process leads to a second-order differential equation which for a moving load the matrix coefficients are time dependent. In the state-space formulation, the forced response depends upon a transition matrix that can be locally approximated by the matrix exponential by assuming that the coefficients are locally constant. The normalized frequencies for a moving force are calculated and compared to those obtained in previous studies, and good agreement between them was observed. After acquiring the dynamic responses of a nanotube for a wide range of velocities and weights of moving nanoparticles, as well as for the nonlocal effects on a nanobeam, a nonlinear regression analysis is adapted to estimate the response of a nanobeam according to an analogous classical Rayleigh beam. These equivalent results in three multipliers (a, b, and c) are functions of kinetic parameters and nonlocal effects. Due to the normalization of the variables, these multipliers can be used for various types of beam-like structures in both the nanoand macro-domains. The accuracy of these coefficients is evaluated using the results gained by the analytical solution. This paper offers a remedy for a time-consuming process by means of some simple substitutions. Keywords Single-walled carbon nanotube Á Nonlocal Rayleigh beam theory Á Moving load Á Moving mass Á Conversion coefficient

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“…However, to the authors' best knowledge, effects of closed natural frequencies and mode localization on the vehicle-induced vibration of the cable-stayed bridge have not been investigated. Dynamic analysis of a beam excited by a sequence of moving mass loads has attracted many researchers [21][22][23][24] since it has many practical applications such as a train traveling on a railroad track.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a cable-stayed bridge subjected to a continuous sequence of moving forces

Song

Cao

Zhu

2016

Advances in Mechanical Engineering

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In this work, an eigenfunction expansion approach is used to study the dynamic response of a cable-stayed bridge excited by a continuous sequence of identical, equally spaced moving forces. The nonlinear dynamic response of the cable-stayed bridge is obtained by simultaneously solving nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality conditions of exact mode shapes of the linearized cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is numerically solved. Convergence of the dynamic response from the Galerkin method is investigated. Effects of close natural frequencies, mode localization, the distance between any two neighboring forces, and geometric nonlinearities of stay cables on the forced dynamic response of the cable-stayed bridge are captured using a convergent modal truncation.

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On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: instability and resonance analysis

Cited by 27 publications

References 29 publications

Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

A simplified-nonlocal model for transverse vibration of nanotubes acted upon by a moving nanoparticle

Dynamic analysis of a cable-stayed bridge subjected to a continuous sequence of moving forces

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