There are several parameters required for viscoelastic material modeling to describe the material behavior. On the other hand, the parameter identification of viscoelastic materials often leads to difficult experimental procedures. Since the fractional controllers are robust to parameter uncertainties in the plant model, in this paper, this type of controller is proposed to avoid the difficulties of parameters identification in viscoelastic materials. As a prototype, a viscoelastic beam covered by piezoelectric patches is modeled for suppressing vibrations arising from transient excitations of viscoelastic materials. Different fractional-order PIλDμ controllers are used to illustrate the effect of fractional integral and fractional derivative orders separately. The results show that the fractional-order controllers are successful and effective for vibration suppression of viscoelastic beams.
In this work, an inverse forced convection-radiation boundary design problem for a two-dimensional channel with a forward and a backward-facing step is solved. In design problems, it is desired to provide uniform temperature and heat flux distribution over a design surface by obtaining the unknown temperature distribution over a heater surface. The flow is laminar, and the high-temperature gas is treated as an absorbing, emitting and isotropic scattering medium. The channel walls are considered to be diffuse-gray absorbers and emitters. The radiative transfer equation is solved by the discrete ordinates method. The conjugate gradient method which is based on an optimization technique is applied to solve the inverse problem. By the applied numerical method, the desired heat flux distribution over the design surface is very well reconstructed. Also, the effects of step inclination angle, scattering albedo and optical thickness on the solution of the present inverse problem are explored. It is found that by increasing in step inclination angle, scattering albedo and decreasing in the optical thickness, the total heat flux over the heater surface increases.
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