Rotatory Inertia Influence on the highly prestressed orthotropic rectangular plates under travelling loads

Oni, ST; Tolorunsagba, J M

doi:10.4314/jonamp.v9i1.40038

Cited by 2 publications

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“…𝑢 4 (𝑛, 𝑘, 𝜋) = ± √ 𝐻 2 (𝑛,𝑘,𝜋)±√𝐻 2 2 (𝑛,𝑘,𝜋)−4𝐻 1 (𝑘)𝐻 3 (𝑛,𝑘,𝜋) 2𝐻 2 (𝑘) (65) where 𝐻 2 (𝑘) = 𝑘 4…”

Section: Remarks On Theorymentioning

confidence: 99%

“…After an earlier work by Oni [64] where he studied the dynamic response to a moving load (using the method of matched Asymptotic Expansion MMAE) of a fully clamped pre-stressed orthotropic rectangular plate, Oni and Tolorunsagba [65] took up the problem of assessing the rotatory inertia influence on the highly prestressed orthotropic rectangular plate when it is under the action of moving load. The method of composite expansion (MCE), an alternate singular perturbation technique is employed in conjunction with the method of integral transformation and Cauchy residue theorem to obtain an approx-imately uniformly valid solution in the entire domain of definition of the rectangular plate.…”

Section: Introductionmentioning

confidence: 99%

“…Also, for high values of rotatory inertia correction factor, the critical velocity approaches a constant value indicating that resonant effect is remote for higher values of rotatory inertia correction factor. However, in the work of Oni [64] and Oni and Tolorunsagba [65], only plates not resting on foundation and under moving forces were considered. For practical application, it is pertinent to considered plates supported by an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

“…For practical application, it is pertinent to considered plates supported by an elastic foundation. Also, in the moving load model, only the force effect of the moving load is considered in [64] and [65] and the inertia effect of the moving load was neglected. However, it has been found that the inertia of the moving load contribute effectively to the deflection of the dynamical structure.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Behaviour of Highly Prestressed Orthotropic Rectangular Plate Under a Concentrated Moving Mass

Tolorunshagba

Oni²

2022

JPS

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In this paper the dynamic response to concentrated moving masses of highly prestressed orthotropic rectangular plate-structure is examined. When the ratio of the bending rigidity to the in-plane loading is small, a small parameter multiplies the highest derivatives in the equation governing the motion of the plate under the action of moving masses. Such vibrational problems defile conventional methods of solution. An approach suitable for the solution of this type of problem is the singular perturbation. To this end, a choice is made of the method of matched asymptotic expansions (MMAE) among others. The application of the singular perturbation scheme in conjunction with the finite Fourier sine transform produces two different but complementary approximations to the solution for small parameter - one being valid in the region where the other fails. One is valid away from the boundary called the outer solution while the other is valid near and at the boundary called the inner solution. Thereof, the Van Dyke asymptotic matching principle which produces the unknown integration constants in the outer and inner expansions is applied. Thereafter, the inverse Laplace transformation of the obtained results is carried out using the Cauchy residue theorem. This process produces the leading order solution, and the first order correction, to the uniformly valid solution of the plate dynamical problem. The addition of the two results above produces the sought uniformly valid solution in the entire domain of definition of the plate problem. Similarly, the resonant states and the corresponding critical speeds are obtained. The analysis of this result is then shown in plotted curves. Graphical interpretation of the results show that the critical speeds at the respective resonant states increase as the value of prestress increase thus the risk of resonance is remote as prestress is increased for any choice of value of rotatory inertia correction factor. Also, lower values of rotatory inertia show variation in the value of critical speed hence the possibility of resonance. Similarly, the critical speed increases with shear modulus for various values of prestress. However, as the value of shear modulus increases, critical speed approaches more or less constant value. Thus, a design incorporating high value of shear modulus is more stable and reliable. The critical speed increases with material orthotropy for lower values of rotatory inertia correction factor.

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“…𝑢 4 (𝑛, 𝑘, 𝜋) = ± √ 𝐻 2 (𝑛,𝑘,𝜋)±√𝐻 2 2 (𝑛,𝑘,𝜋)−4𝐻 1 (𝑘)𝐻 3 (𝑛,𝑘,𝜋) 2𝐻 2 (𝑘) (65) where 𝐻 2 (𝑘) = 𝑘 4…”

Section: Remarks On Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Behaviour of Highly Prestressed Orthotropic Rectangular Plate Under a Concentrated Moving Mass

Tolorunshagba

Oni²

2022

JPS

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“…The dynamic behavior of flexible structures (such as plate and beam) position on supple foundation under the travelling has been the center of attention of major researchers in the fields of structural Engineering, Physics and Applied Mathematics (Timoshenko, 1921;Oni, 2004;Oni, & Adedowole, 2008). For decades, numerous researchers have carried out diverse studies on this subject matter.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Variable Cross Section Timoshenko Beams Resting on Flexible Foundation Under Two Travelling Loads

Adedowole

2023

ejtas

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Dynamic behavior of variable cross section Timoshenko beams resting on elastic foundation and subjected to two travelling loads is investigated. The vibrating system of beam structure and the simultaneous equations were treated using Galerkin and integral transform techniques. Closed form solution was obtained for both the transverse displacement response and the rotation the variable cross section Timoshenko beams under the travelling loads. From the analytical and numerical results, as the magnitude of foundation stiffness increases, the deflection profile of the Timoshenko beam decreases. Likewise, amplitude of deflection diminishes as the distance between the loads increases. The state at which the structure-load system experience resonance condition is established.

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Rotatory Inertia Influence on the highly prestressed orthotropic rectangular plates under travelling loads

Cited by 2 publications

References 0 publications

Dynamic Behaviour of Highly Prestressed Orthotropic Rectangular Plate Under a Concentrated Moving Mass

Dynamic Behaviour of Highly Prestressed Orthotropic Rectangular Plate Under a Concentrated Moving Mass

Vibration Analysis of Variable Cross Section Timoshenko Beams Resting on Flexible Foundation Under Two Travelling Loads

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