Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

Карнаухов, В. Г.; Revenko, Yu. V.

doi:10.1007/s10778-005-0106-4

Int Appl Mech

2005

DOI: 10.1007/s10778-005-0106-4

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Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

В. Г. Карнаухов

Yu. V. Revenko

Abstract: An analytic solution is obtained to describe the vibrations and dissipative heating of a simply supported infinite cylindrical panel under periodic normal loads moving over its surface with a constant velocity. Special attention is focused on resonant vibrations, which result in the most intensive dissipative heating. It is additionally assumed that the material of the panel is viscoelastic, its properties are independent of temperature, and Poisson's ratio is real. The influence of thickness, radius of curvat… Show more

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Cited by 6 publications

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“…Methods to solve thermoelastic problems for inhomogeneous bodies under various loading conditions are outlined in [4,6,[17][18][19][20][21]. Thus, the law of time variation in the temperature of the boundary surface r = k 1 is unknown, i.e., the function t…”

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Identification of the thermal and thermostressed states of a two-layer cylinder from surface displacements

Yasinskii

2008

Int Appl Mech

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The problem of identifying the law of time variation in the temperature of one boundary surface of a two-layer cylinder and its thermal and thermostressed state from the temperature and radial displacement of the other surface is formulated and solved. The inverse problem of thermoelasticity to which the problem posed is reduced is analyzed for well-posedness. The solution of the direct problem of thermoelasticity is used to numerically test the technique of solving the inverse problem Keywords: two-layer cylinder, identification, inverse problem of thermoelasticity, well-posedness, numerical testingIntroduction. The experimental analysis of the thermal and thermostressed states of parts of operating heat-and-power equipment is often complicated by the fact that the thermal load on a part can only be determined on some portion of its boundary surface for design, technological, or methodical reasons [11,12]. Therefore, the problems of heat transfer and thermoelasticity are ill-posed, and additional data are needed to solve them. If the original problem is supplemented with information on the behavior of thermal parameters (temperature, heat flow) at some point(s) of a part, then the thermal load can be identified by solving ill-posed inverse problems of heat transfer. The studies based on such an approach are systematized in the monographs [5,11,12,23]. Most algorithms used in these studies to construct regularized solutions to inverse heat-transfer problems assume that additional data are obtained (measured) at an internal point(s) of the body. However, it is not always justified to disturb an operative part to make such measurements. Moreover, it may even be impossible to determine all the characteristics of thermal load in the inverse heat-transfer problem [13]. In this connection, the recent studies [13,14,16,24] identified the thermal and thermostressed states of a body using data on the behavior of mechanical parameters (displacements, strains, stresses) at some point as additional information. The temperature of the boundary surface of a thick layer was determined in [14,16] within the framework of a one-dimensional dynamic problem of thermoelasticity. The heat flow on the inside surface of a long hollow cylinder was determined in [13,22] from the temperature and strains on the outside surface. It was shown in [9, 10] that the use of additional information on the behavior of the displacements of the boundary surface to reduce the identification problem to the inverse problem of thermoelasticity leads to a qualitatively new result-the resulting inverse problems of thermoelasticity are under certain conditions well-posed in the sense of Tikhonov [7] and, hence, can be solved using methods intended for well-posed problems. It was proved in [22] that the problem of identifying the thermostressed state of an elastic body from displacements and temperature on a portion of its boundary surface has a unique solution.The present paper addresses the inverse problem of thermoelasticity to which we reduce the problem o...

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Identification of the thermal and thermostressed states of a two-layer cylinder from surface displacements

Yasinskii

2008

Int Appl Mech

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“…Also, vibrational heating is a crucial factor for some high-intensity processes such as ultrasonic plastic welding [7][8][9]. The stationary vibrations and vibrational heating of linear viscoelastic bodies were studied and associated models were validated in [20][21][22]. The results obtained there were generalized in [2,11,[16][17][18][19]25].…”

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Vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion

2007

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The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined Keywords: viscoelastic material, vibrations heating, rectangular prism, cylindrical inclusion Introduction. Intensive vibrations of viscoelastic bodies are generally accompanied by vibrational heating, which is because of the conversion of mechanical energy into heat. Heating can noticeably reduce the performance and life of structural members such as rubber shock absorbers, solid-propellant engines [11,26], etc. Also, vibrational heating is a crucial factor for some high-intensity processes such as ultrasonic plastic welding [7][8][9]. The stationary vibrations and vibrational heating of linear viscoelastic bodies were studied and associated models were validated in [20][21][22]. The results obtained there were generalized in [2,11,[16][17][18][19]25]. The cited publications employed the concept of complex moduli, which was convincingly substantiated, both experimentally and theoretically, during the early development of the theory of linear thermoviscoelasticity in [1, 12, 14, 15, etc.].One of the special features of vibrational heating is the effect of thermal instability. It manifests itself as abrupt increase in temperature and leads to thermal fatigue failure of structural members [6,14,15,26]. Relevant results are reviewed in [3,4,16,18,19,23].Fracture usually sets in near stress concentrators. It is these areas that become sources of vibrational heating. Such processes in bodies with cylindrical inclusions under compressive and shear loading of kinematic type were studied in [8,9]. Vibrational heating in laminated prisms acted upon by a vibrating punch was addressed in [13,16].Intensive high-frequency loading of a rectangular prism with an inclusion produces a number of specific effects. The major effect is concentration of stress, dissipation rate, and temperature. It was established that the level of vibrational heating is strongly dependent on the type of loading and the stiffness of the inclusion.The present paper studies the kinetics of vibrational heating and thermal instability of a rectangular prism with an inclusion under harmonic compressive loading of mechanical type. We will compare the mechanical and kinematic types of excitation and examine the cases of rigid and soft inclusion.

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“…It may affect the performance of the structure, even to the point of thermal failure [8]. Studies of this phenomenon under monoharmonic loading are reviewed in [4][5][6][11][12][13][14]. In such problems, the load can be either preset or determined from the solution of a contact problem [3].…”

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confidence: 99%

“…When loads are moving, polyharmonic deformation occurs in both cases. A dissipative-heating problem was solved in [12] for a viscoelastic cylinder subjected to a moving surface load with normal and tangential components and in [11,13] for thin-walled structural members.…”

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Dissipative heating of a viscoelastic cylinder steadily rolling over a rigid foundation

Карнаухов

Revenko

2006

Int Appl Mech

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Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

Cited by 6 publications

References 4 publications

Identification of the thermal and thermostressed states of a two-layer cylinder from surface displacements

Identification of the thermal and thermostressed states of a two-layer cylinder from surface displacements

Vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion

Dissipative heating of a viscoelastic cylinder steadily rolling over a rigid foundation

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