Periodicity in the response of nonlinear plate, under moving mass

Shadnam, Mohammad Reza; Rofooei, Fayaz R.; Mofid, Massood; Mehri, B.

doi:10.1016/s0263-8231(01)00041-6

Cited by 21 publications

(16 citation statements)

References 13 publications

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“…Equation 11 [3] is employed to simplify and reduce (11) to a sequence of second-order ordinary differential equations called Galerkin equations. This technique requires that solution to (11) be written in the following form:…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Various structures ranging from bridges and roads to space vehicles and submarines are constantly acted upon by moving masses and hence the problem of analyzing the dynamic response of these structures under the action of moving masses continues to motivate a variety of investigations. In most of the studies available in literature, such as the works of Sadiku and Leipholz in [2], Oni in [3], Gbadeyan and Oni in [4], Huang and Thambiratnam in [5], Lee and Ng in [6], Adams in [7], Chen and Li in [8], Savin in [9], Rao in [10], Shadnam et al in [11], and Oni and Awodola in [12], the scope has been restricted to structural members having uniform crosssection whether the inertia of the moving load is considered or not and the load modelled as moving concentrated load.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions

Andi

Oni

2014

Chinese Journal of Mathematics

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This paper investigates the flexural vibration of a finite nonuniform Rayleigh beam resting on an elastic foundation and under travelling distributed loads. For the solution of this problem, in the first instance, the generalized Galerkin method was used. The resulting Galerkin’s equations were then simplified using the modified asymptotic method of Struble. The simplified second-order ordinary differential equation was then solved using the method of integral transformation. The closed form solution obtained was analyzed and results show that, an increase in the values of foundation moduli K and rotatory inertia correction factor R0 reduces the response amplitudes of both the clamped-clamped nonuniform Rayleigh beam and the clamped-free nonuniform Rayleigh beam. Also for the same natural frequency, the critical speed for the moving distributed mass problem is smaller than that for the moving distributed force problem. Hence resonance is reached earlier in the former. Furthermore, resonance conditions for the dynamical system are attained significantly by both R0 and K for the illustrative end conditions considered.

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Section: Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions

Andi

Oni

2014

Chinese Journal of Mathematics

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“…Nosier and Reddy [22] presented the nonlinear dynamic equations of composite laminated rectangular plates using the first-order and the third-order shear deformation plate theory, respectively. Shadnam et al [23] considered the nonlinear dynamics of thin plates under the influence of relatively heavy moving masses. Awrejcewicz et al [24] utilized the BubnovGalerkin approach with high-order approximations and finite difference method to investigate the complex nonlinear vibrations and bifurcations of a transversally and axially excited thin plate strip.…”

Section: Introductionmentioning

confidence: 99%

Subharmonic Melnikov method of four-dimensional non-autonomous systems and application to a rectangular thin plate

et al. 2015

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The existence and bifurcations of the subharmonic orbits for four-dimensional non-autonomous nonlinear systems are investigated in this paper. The improved subharmonic Melnikov method is presented by using the periodic transformations and Poincaré map. The theoretical results and the formulas are obtained, which can be used to analyze the subharmonic dynamic responses of four-dimensional nonautonomous nonlinear systems. The improved subharmonic Melnikov method is used to investigate the subharmonic orbits of a simply supported rectangular thin plate under combined parametric and external excitations for verifying the validity and applicability of the method. The theoretical results indicate that the subharmonic orbits can occur in the rectangular thin plate with 1:1 and 1:2 internal resonances. The results of numerical simulation also indicate the existence of the subharmonic orbits for the rectangular thin plate, which can verify the analytical predictions.

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“…Cifuentes and Lalapet [15] exploited an adaptive discretization to simulate the plate dynamics under an orbiting mass. Shadnam et al [16] studied the response of the nonlinear plates traversed by relatively heavy masses.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response analysis of a thin rectangular plate of varying thickness to a traveling inertial load

Ghazvini

Nikkhoo

Allahyari

et al. 2015

J Braz. Soc. Mech. Sci. Eng.

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Periodicity in the response of nonlinear plate, under moving mass

Cited by 21 publications

References 13 publications

Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions

Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions

Subharmonic Melnikov method of four-dimensional non-autonomous systems and application to a rectangular thin plate

Dynamic response analysis of a thin rectangular plate of varying thickness to a traveling inertial load

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