Monoharmonic Approach to Investigation of Heat Generation in The Viscoplastic Solids under Harmonic Loading

Intensive forced vibration of structural elements can be accompanied with significant temperature rise (heating) caused by internal dissipation of mechanical energy. Therefore, the thermomechanical coupling can cause the degradation in material properties, high strains and stresses and results in fracture of various engineering structures. In studying the nonstationary, in particular resonant, processes, it is important to take into account inelastic deformation and heat emission [

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]. Indeed, the thermoviscoplastic behavior of the material and the coupling of the mechanical and thermal fields may affect substantially the characteristics of vibration dampers for engineering structures. An approach to the solution of coupled problems of vibrations and dissipative heating of viscoplastic bodies is developed. Two problem statements are elaborated: “exact” and “approximate” ones. The former statement consists of universal balance equations of thermodynamics and constitutive equations derived from the general thermodynamic theory of viscoplastic bodies with internal state variables. For this aim the theory version that corresponds to the Bodner-Partom generalized flow theory is used. The approximate or monoharmonic problem statement for the case of steady-state vibrations under the harmonic loading is obtained by the application of modified harmonic linearizing technique to the initial system of equations. Thereby the subsystem of mechanical equations is formulated in the complex-value form and material properties are described by means of amplitudedependent complex-value moduli.

Numerical technique for the solution of the problems of vibration and dissipative heating of spatial and thin-wall elements of structures are developed. They are based on the iterative linearization procedures in association with FEM. The capabilities of the monoharmonic approach are studied by the example of the resonant and quasistatic vibrations and dissipative heating of a viscoplastic disk excited by a harmonic load [2].Additional attention is paid to the case of inhomogeneous (layered) solids. Physical and mechanical behavior of such systems is very complex because of the heterogeneity of the stress-strain state. Modeling such a behavior is additionally complicated by the necessity of allowing for the coupling of the mechanical and thermal fields when cyclic loading is intensive and for dynamic effects, in particular, when intensive vibrations occur in the quasistatic or resonant domain. Comparing the solutions obtained in the frame of the exact and approximate statements demonstrates high accuracy of the monoharmonic model for the problems investigated (axisymmetric vibrations and heating of layered or homogeneous viscoplastic disk and rectangle).