Search results for "Variation of parameters"
showing 5 items of 5 documents
A procedure to achieve fine control in MW processing of foods
2007
Abstract A two-dimensional analytical model for predicting the unsteady temperature field in a cylindrical shaped body affected by spatially varying heat generation is presented. The dimensionless problem is solved analytically by using both partial solutions and the variation of parameters techniques. Having in mind industrial microwave heating for food pasteurization, the easy-to-handle solution is used to confirm the intrinsic lack of spatial uniformity of such a treatment in comparison to the traditional one. From an experimental point of view, a batch pasteurization treatment was realized to compare the effect of two different control techniques both based on IR thermography readout: t…
Implicit analytic solutions for a nonlinear fractional partial differential beam equation
2020
Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and u…
Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach)
2004
Structures involving uncertainties in material and/or in geometrical parameters are referred to as uncertain structures. Reliability analysis of such structures strongly depends on variation of parameters and probabilistic approach is often used to characterize structural uncertainties. In this paper dynamic analysis of linearly elastic system in presence of random parameter variations will be performed. In detail parameter fluctuations have been considered as inelastic, stress and parameter dependent superimposed strains. Analysis is then carried out via superposition principle accounting for response to external agencies and parameter dependent strains. Proposed method yields asymptotic s…
Fractional-Order System Identification of Viscoelastic Behavior: A Frequency Domain Based Experimental Study
2020
In this work, the fractional-order modeling of viscoelastic behavior is investigated based on measurement data in the frequency domain. For the results of two different test setups we apply existing parameter estimation algorithms designed for fractional-order transfer functions. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. An iterative procedure is used to evaluate the influence of the unknown structure. The measured polymer samples show a viscoelastic stress response. We can show that integer-order models are not capable of capturing this behavior. For a set of predefined structures, the best obtained fractional-o…
Wronskian Addition Formula and Darboux-Pöschl-Teller Potentials
2013
For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant.