Analytical solutions for free and forced vibrations of a multiple cracked Timoshenko beam subject to a concentrated moving load

AbstractA composite beam with single delamination under the action of moving load has been modeled accounting for the Poisson’s effect, shear deformation, and rotary inertia. The existence of the delamination changes the stiffness of the structure, and this affects the dynamic response of the structure. We have used a constrained mode to simulate the behavior between the delaminated surfaces. Based on this mode, eigensolution technique is used to obtain the natural frequencies and their corresponding mode shapes for the delaminated beam. Then, the Ritz method is adopted to derive the dynamic response of the beam subjected to a moving load. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literature. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the size, depth, and spanwise location of the delamination, the load velocity, the different ply configurations, and the Poisson’s effect on the dynamic response of the beam are studied.

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Vibrations of a Timoshenko beam on an inertial foundation under a moving load

MATEC Web of Conferences ◽

10.1051/matecconf/201819601056 ◽

2018 ◽

Vol 196 ◽

pp. 01056

Author(s):

Magdalena Ataman

Keyword(s):

Timoshenko Beam ◽

Moving Load ◽

Equations Of Motion ◽

Free Vibrations ◽

Forced Vibrations ◽

Governing Equations ◽

Concentrated Load ◽

Numerical Example ◽

Moving Force ◽

Speed Response

In the paper vibrations of the Timoshenko beam on an inertial foundation subjected to a moving force are discussed. Considered model of the inertial foundation is described by three parameters. They take into account elasticity, shear and inertia of the subgrade. In the literature such model of the subgrade is called Vlasov or Vlasov-Leontiev model. The Timoshenko beam is traversed by a concentrated load, moving with uniform speed. Response of the beam is found from the governing equations of motion of the problem. Problem of forced vibrations and problem of free vibrations of the beam are solved. Damping of the system is taken into consideration. Solution of the problem is illustrated by numerical example.

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FREE AND FORCED VIBRATIONS OF THICK-WALLED LAMINATED ANISOTROPIC CYLINDRICAL SHELLS WITH ACCOUNT FOR ENERGY DISSIPATION AT FREQUENCIES CLOSE TO RESONANCE ONES

Composites Mechanics Computations Applications An International Journal ◽

10.1615/compmechcomputapplintj.v8.i3.40 ◽

2017 ◽

Vol 8 (3) ◽

pp. 239-265

Author(s):

Aleksandr V. Marchuk ◽

S.V. Gnedash ◽

D. O. Shandyba

Keyword(s):

Energy Dissipation ◽

Cylindrical Shells ◽

Forced Vibrations ◽

Free And Forced Vibrations

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Numerical Simulation of Turbulent Flows for Free and Forced Vibrations of Bodies in a Flow

Heat Transfer Research ◽

10.1615/heattransres.v39.i8.20 ◽

2008 ◽

Vol 39 (8) ◽

pp. 661-670

Author(s):

N. A. Shchur ◽

D. K. Zaitsev

Keyword(s):

Numerical Simulation ◽

Turbulent Flows ◽

Forced Vibrations ◽

Free And Forced Vibrations

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Nonlinear Free and Forced Vibrations of Symmetric Laminated Panels

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.471-472.616 ◽

2011 ◽

Vol 471-472 ◽

pp. 616-621 ◽

Cited By ~ 1

Author(s):

Alireza Shooshtari ◽

Soheil Razavi ◽

Hadi Ghashochi Bargh ◽

Mohammad Homayoun Sadr-Lahidjani

Keyword(s):

Perturbation Method ◽

External Force ◽

Laminated Composite ◽

Composite Plates ◽

Forced Vibrations ◽

Numerical Results ◽

Transverse Displacement ◽

Laminated Composite Plates ◽

Free And Forced Vibrations ◽

Laminated Panels

In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.

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