Stochastic response analysis techniques for “unconventionally modeled” engineering dynamical systems

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The efficient and rigorous handling of uncertainties in engineering systems constitutes a key element in providing with solution frameworks to study their behavior and assess their reliability. One of the main challenges associated with uncertainty quantification in the field of stochastic dynamics of structural/mechanical systems relates to “unconventional” system modeling. This equivalently translates to the need for modeling the system governing equations in a more efficient manner, taking into account its nonlinear/hysteretic behavior, as well as the evolutionary characteristics of the excitations. In addition, the modeler should also consider employing fractional calculus to better model the system characteristics, and multi-body system-based techniques to facilitate the complex system modeling. Moreover, considering another main challenge in the field of stochastic dynamics, namely the efficient propagation of uncertainties, contemporary system modeling necessitates the development of analytical methods, to bypass the frequently computational expensive MCS based schemes.Directing attention to addressing the above challenges and also aiming at an efficient stochastic response analysis, the research objective of this proposal constitutes a groundbreaking effort to adapt and extend random vibration theoretical tools for treating in a straightforward manner “unconventionally modeled” dynamical systems.The academic impact of the project will be broad and multifaceted, since it lies in the intersection of engineering stochastic dynamics and applied/computational mathematics. Specifically, from a fundamental research point of view, an efficient framework for conducting joint time-frequency response analyses of “unconventionally modeled” dynamical systems will be developed. This will be complemented by a framework for conducting stochastic response analyses for classes of systems endowed with fractional derivative terms. From an applied research and applications point of view, the methodology will have a major impact on the analysis and design of diverse dynamical systems, and will contribute to a number of emerging technologies such as in nano-mechanics and vibration energy harvesting. Further, treating systems endowed with fractional derivative elements becomes especially important, considering the extensive use of fractional calculus modeling in a plethora of emerging technologies.Overall, the proposed cross-disciplinary project will contribute to diverse research fields, such as (linear/nonlinear) stochastic (structural/multibody) dynamics, and computational methods for solving (approximately) linear and nonlinear systems of stochastic differential equations.