Damping described by fading memory—analysis and application to fractional derivative models
✍ Scribed by Mikael Enelund; Peter Olsson
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 488 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0020-7683
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✦ Synopsis
Some damping models where the actual stress does not depend on the actual strain but also on the entire strain history are studied[ Basic requirements in the frequency and time domain signi_cant for the choice of damping model are outlined[ A one!dimensional linear constitutive viscoelastic equation is considered[ Three di}erent equivalent constitutive equations describing the viscoelastic model are presented[ The constitutive relation on the convolution integral form is studied in particular[ A closed form expression for the memory kernel corresponding to the fractional derivative model of viscoelasticity is given[ The memory kernel is examined with respect to its regularity and asymptotic behavior[ The memory kernel|s relation to the fractional derivative operator is discussed in particular and the fractional derivative of the convolution term is derived[ The fractional derivative model is also given by two coupled equations using an {{internal variable||[ The inclusion of the fractional derivative constitutive equation in the equations of motion for a viscoelastic structure is discussed[ We suggest a formulation of the structural equations that involves the convolution integral description of the fractional derivative model of viscoelasticity[ This form is shown to possess several mathematical advantages compared to an often used formulation that involves a fractional derivative operator form of constitutive relation[ An e.cient time discretization algorithm\ based on New! mark|s method\ for solving the structural equations is presented and some numerical examples are given[ A simpli_cation of the fractional derivative of the memory kernel\ derived in the present study\ is then employed\ which avoids the actual evaluation of the memory kernel[