Modeling of the cyclic deformation of viscoelastic materials as the key aspects of analysis of the structural behavior is performed. The approach that uses the complex-value amplitude relations is preferred rather than direct numerical integration of the complete set of constitutive equation for the material. Time dependent transient inelastic response of polymer materials to monoharmonic kinematic loading is simulated by the Goldberg constitutive model. To predict the steady-state response in terms of amplitudes, the relations between the amplitudes of main field variables are established with making use of complex moduli concept. It is performed by making use of equivalent linearization technique. It is shown that this technique leads to overestimation of stress amplitude. To avoid this, the modified equivalent linearization technique is applied. Characterization of the complex moduli dependence on frequency and temperature as well as amplitude of strain intensity is performed. Results demonstrate a weak dependence of loss moduli on the frequency of the loading within the wide interval of it, while variation of storage moduli with increasing temperature is more pronounced.
W pracy przedstawiono zależności określające gęstość energii rozpraszanej w zadanym czasie w sprężystolepkim pręcie przy jego harmonicznym rozciąganiu-ściskaniu i skręcaniu, z uwzględnieniem udziału odkształceń objętościowych i postaciowych. Wyliczono również całkowitą ilość energii rozproszonej w określonym czasie, z zaznaczeniem dominującej roli warstw zewnętrznych pręta przy jego skręcaniu.
EN
The paper presents formulae for density of energy dissipated in a viscoelastic rod subjected to harmonic tension-compression and torsion with the shares of volume changes and distortions taken into account. The total dissipation energy during a given period of time is also calculated with the dominant role of outer layers of the twisting rod indicated.
An elastic slab having periodic breaks across its cross-section is loaded by space-harmonic forces applied to its surfaces. Due to the breaks, the slab displacement response to the load includes a series of space-harmonics. A method is proposed for evaluation of the slab harmonic response within a presumed spectral domain.
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