Effect of Preloading on the Resonant Vibrations and Dissipative Heating of a Rectangular Thermoviscoelastic Plate*
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International Applied Mechanics, Vol. 56, No. 4, July, 2020
EFFECT OF PRELOADING ON THE RESONANT VIBRATIONS AND DISSIPATIVE HEATING OF A RECTANGULAR THERMOVISCOELASTIC PLATE* Ya. A. Zhuk1,2 and A. Kh. Ostos1
The problem of forced resonant vibrations and dissipative heating of a hinged viscoelastic elastomeric plate under membrane preloads is given. The case of square and rectangular plates is considered. The effect of elastomer properties, preload, and heat exchange conditions on the amplitude- and temperature–frequency characteristics of the forced vibrations of the plate and the achievement of critical temperature at which the material softens is studied. Keywords: resonant vibration, dissipative heating, viscoelastic material, prestressed rectangular plate Introduction. Structural members such as beams, plates, and shells made of elastomeric materials with specific properties are widely used as the main bearing or functional components of modern technology structures [1, 2, 14, 17]. The main features of the deformation behavior of elastomers include the ability to deform reversibly, small tensile, compressive, shear moduli; relaxation properties; the ability to change the mechanical properties over time and under external factors, either mechanical or non-mechanical; significant mechanical losses under cyclic strains, etc. In particular, hysteresis (internal friction) for elastomers is manifested as the phase lag between the load and the strains and the irreversible dissipation of some of the mechanical energy [9, 14–16, 19]. The features of structural members made of such materials are most manifested under dynamic loading and harmonic load as its typical case. In this case, some of the mechanical energy due to internal friction is converted into heat, and the phenomenon of self-heating or dissipative heating is observed [2, 4, 11]. This feature and the low thermal conductivity of elastomers that prevents rapid heat removal lead to the non-isothermal conditions of structural members during deformation, andtemperature field is generated in them [7, 8, 11]. The energy dissipated over a period is usually low, so that the temperature can be considered a slowly varying function [4, 6]. In this case, temperature fluctuations having a thermoelastic or dissipative nature during the period are neglected. The available experimental data [15, 16] indicate their negligible smallness in most practically important problems. A characteristic feature of the process is that it consists of four interrelated subprocesses. The first process corresponds to a non-stationary wave process of the superposition of traveling reflected waves. This process generates a certain vibration mode. The second subprocess is damped beats in a certain vibration mode. This phase ends with the formation of a quasi-stationary vibration mode. The third subprocess described by the averaged components of the motion is associated with the response to the averaged components of external loads or initial strains. The last subprocess is an increase in the s
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