Research Projects

The nonlinear damping behavior of a dynamical system can be efficiently modeled by using fractional derivative representation. The efficient mathematical modeling of the time-dependent nonlinear stress-strain relationship of viscoelastic damping materials is possible by fewer terms of fractional derivatives; however, while using integer-order derivatives, a larger series is required. Though viscous, viscoelastic, and friction dampers with semi-active control are extensively used to mitigate the undesirable dynamic response of civil structures, their mathematical modeling requires improvements, especially for maximizing dynamic response reduction. Conventionally, integer-order derivatives are used for mathematical modeling of semi-active dampers to a certain level of accuracy, wherein the effect of nonlinearity is often ignored. Hence, this research proposal is aiming to develop an analytical solution methodology of semi-active dampers for a generalized dynamical system using the fractional derivative approach to overcome the existing research gap, thereby, obtain realistic dynamic response by means of the optimized damping parameters and fractional-order. With successful accomplishment of this research work, the extensive application of the fractional derivative in realistic modeling of the highly nonlinear semi-active dampers for effective mitigation of dynamic response for complex structural systems is achieved. Furthermore, through this research activity, mathematical understanding on the fractional derivative driven semi-active damping devices will improve and can be applied for the dynamical system with active damping devices, as it advances.