Nonlinear vibrations of beams and plates with fractional derivative elements subject to combined harmonic and random excitations

Fractional-Order Control Method Based on Twin-Delayed Deep Deterministic Policy Gradient Algorithm

“…Deriving Equation ( 23) and substituting the system state equation shown in (1) with the control law shown in (8) yield…”

“…Fractional-order calculus stands out for its flexible description of the behavior of nonlocal and non-Markovian dynamics, providing a rich mathematical tool for modeling complex systems. Its main applications include the modeling of nonlinear and nonsmooth system dynamics [1], the simulation of multiscale complex systems [2], the analysis of non-Markovian processes [3], as well as in the fields of signal processing, control systems and financial modeling [4]. In the field of control, fractional-order control has been combined with many traditional control schemes, such as fractional-order PID control [5], fractional-order robust control [6], and fractional-order sliding-mode control [7]; these fractional-order control methods have been developed in depth at the theoretical level to form a sound theoretical system and have achieved extensive and powerful results in practical applications.…”

On non-stationary response of cracked thin rectangular plates acted upon by a moving random force

“…Furthermore, the vibration of a rectangular-shaped system subjected to the white noise was studied by Jiao and Spanos [12]. Spanos and Malara [13] studied the nonlinear vibration of the simply-supported beams and plates subjected to the Brownian noise. A linearization of a nonlinear single degree of freedom system subjected to the deterministic and the White noise as a random load was presented by Zhang and Spanos [14].…”

Non-stationary response of nonlinear systems with singular parameter matrices subject to combined deterministic and stochastic excitation

“…Assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to combined deterministic and stochastic loading constitutes a persistent challenge in random vibration, which finds a plethora of applications in several engineering fields. Indicatively, these span from vibration energy harvesting (e.g., [1,2,3]) to the problem of turbine blades vibration under turbulent flow (e.g., [4,5]), or nonlinear vibration of beams and plates (e.g., [6]), and vibration of gear systems (e.g., [7]).…”

“…This has been done by utilizing and combining standard deterministic and stochastic analysis tools such as, indicatively, the harmonic balance and statistical linearization or Gaussian closure methods (e.g., [8,9,10,7,11,12]), the harmonic balance and stochastic averaging methods (e.g., [13]), and the equivalent linearization and deterministic or stochastic averaging methods (e.g., [14,15]). Further, the need for more accurate media behavior modeling dictated by recent advances in theoretical and applied mechanics (e.g., [16]) has propelled the use of fractional calculus which, in turn, resulted to the development of pertinent frameworks (e.g., [6,17]). Yet, most of the approaches available in the literature to-date treat systems whose stochastic excitation component is modeled as a stationary stochastic process.…”