Thermoelastic-induced vibrations on an elliptical disk with internal heat sources

Bhad, Pravin; Varghese, Vinod; Khalsa, Lalsingh

doi:10.1080/01495739.2016.1254075

Cited by 5 publications

(7 citation statements)

References 6 publications

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“…In this article, we have described the theoretical treatment of temperature distribution and the deflection in the form of ordinary and modified Mathieu functions used to determine thermal stresses by proposed new operational methods inline with other integral transform developed by authors [16][17][18]. The analytical technique proposed here is relatively straightforward and widely applicable compared to the methods proposed by other researchers.…”

Section: Numerical Results Discussion and Remarksmentioning

confidence: 99%

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

Bhad¹

2017

International Journal of Thermodynamics

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In this paper, we consider a transient thermal stress investigation into an annulus thin elliptical plate in which edges are fixed and clamped. The realistic problem of the plate is supposed with mixed-type boundary conditions subjected to arbitrary initial temperature on the upper face, and the lower face is kept at zero temperature. Things get further complicated when internal heat generation persists in the object and further becomes unpredictable when sectional heat supply is impacted on the body. The solution to conductivity equation and the corresponding initial and boundary conditions is solved by employing a new integral transform technique. The governing equation for small deflection is found and utilized to preserve the intensities of thermal bending moments and twisting moments, involving the Mathieu and modified functions and their derivatives. It was found that the deflection result nearly agrees with the previously given result. Thus, the numerical results obtained are accurate enough for practical purposes. Conclusions emphasize the importance of better understanding the underlying elliptic structure, improved understanding of its relationship to circular object profile, and better estimates of the thermal effect of the thermoelastic problem.

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Section: Numerical Results Discussion and Remarksmentioning

confidence: 99%

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

Bhad¹

2017

International Journal of Thermodynamics

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“…Substituting equation (26) into equations (20) and (21), differential equations of the rotating plate are obtained as…”

Section: Dimensionless Differential Equation and Boundary Conditionsmentioning

confidence: 99%

“…Kumar et al 20 studied a two-dimensional axisymmetric vibration in a homogeneous isotropic micropolar porous thermoelastic circular plate by using the eigenvalue approach and analyzed the displacements, microrotations, volume fraction fields, temperature distributions and stresses in the transformed domain subjected to thermomechanical sources. Bhada et al 21 used integral transform technique to investigate the thermally induced vibration of an elliptical disk and discussed the thermal moment, normal stresses and normal deflection of disk. The above research works on the thermoelastic coupling vibration of circular plates are mainly focused on the analysis of the coupled term and dynamic term, but the research on the differential equation of thermoelastic coupling vibration is not that much.…”

Section: Introductionmentioning

confidence: 99%

“…Bhada et al. 21 used integral transform technique to investigate the thermally induced vibration of an elliptical disk and discussed the thermal moment, normal stresses and normal deflection of disk. The above research works on the thermoelastic coupling vibration of circular plates are mainly focused on the analysis of the coupled term and dynamic term, but the research on the differential equation of thermoelastic coupling vibration is not that much.…”

Section: Introductionmentioning

confidence: 99%

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Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

Yang

Wang

2018

Journal of Low Frequency Noise, Vibration and Active Control

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Rotating friction circular plates are the main components of a friction clutch. The vibration and temperature field of these friction circular plates in high speed affect the clutch operation. This study investigates the thermoelastic coupling vibration and stability of rotating friction circular plates. Firstly, based on the middle internal forces resulting from the action of normal inertial force, the differential equation of transverse vibration with variable coefficients for an axisymmetric rotating circular plate is established by thin plate theory and thermal conduction equation considering deformation effect. Secondly, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the thermoelastic coupling transverse vibrations with three different boundary conditions are calculated. In this case, the change curve of the first two-order dimensionless complex frequencies of the rotating circular plate with the dimensionless angular speed and thermoelastic coupling coefficient are analyzed. The effects of the critical dimensionless thermoelastic coupling coefficient and the critical angular speed on the stability of the rotating circular plate with simply supported and clamped edges are discussed. Finally, the relation between the critical divergence speed and the dimensionless thermoelastic coupling coefficient is obtained. The results provide the theoretical basis for optimizing the structure and improving the dynamic stability of friction clutches.

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“…Roy Choudhary [3], Khobragade and Deshmukh [4], Varghese and Khalsa [5] and many others. Similarly, the present author [6][7][8][9][10][11][12][13] have investigated various thermoelastic problems in elliptical objects of simple materials due to interior heat generation or sectional heat supply with different solid objects. Even one-dimensional thermoelastic problems made up of non-simple elastic material due to heat sources has been studied by various authors, viz.…”

Section: Introductionmentioning

confidence: 99%

Temperature and stress distribution in a non-simple elastic elliptical plate due to point impulsive heat sources

Varghese¹,

Bhad²,

Mahakalkar³

2019

International Journal of Thermodynamics

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The paper attempts to determine the thermoelastic stresses in a thin elliptical plate made up of non-simple elastic material subjected to point impulsive time-dependent source of heat moving with constant velocity over the specified finite portion. The temperature field in the plate has been considered when the sectional heat supply is continuously distributed along the circumference of an ellipse over the upper face with zero temperature on the lower face, and thermally insulated curved edge. The solution is formulated involving the Mathieu and modified functions by employing the Laplace transform technique. The analytical solution for the thermal stress components is obtained using Airy's stress function with mechanical boundary conditions as stress-free. Numerical results are also obtained.

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Thermoelastic-induced vibrations on an elliptical disk with internal heat sources

Cited by 5 publications

References 6 publications

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

Temperature and stress distribution in a non-simple elastic elliptical plate due to point impulsive heat sources

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