Chaotic vibration control of a composite cantilever beam

Abstract

In this research, an adaptive control strategy adapted from fuzzy sliding mode control is established and applied in chaotic vibration control of a multiple-dimension nonlinear dynamic system of a laminated composite cantilever beam. The third order shearing effect on the vibration of the beam is considered in the nonlinear dynamic model establishment, and the Hamilton principle as well as the Galerkin method is employed. It is discovered that a multi-dimensional nonlinear dynamic system of the cantilever beam needs to be considered for accurate vibration estimation. Therefore, the control strategy appropriate for the chaotic vibration control of a multiple-dimension system of the laminated composite beam is necessary, and then proves to be effective in chaotic vibration control in numerical simulation.

Control of large amplitude limit cycle of a multi-dimensional nonlinear dynamic system of a composite cantilever beam

“…In 2022, Liu 14 established a two-dimensional system of an axially moving composite laminated cantilever beam and discussed the influence of different axially moving rates on the tip amplitude of the axially translating structure. In the following year, Liu and Sun 15 analyzed the chaotic responses of a composite cantilever beam in a two-dimensional form. Furthermore, in recent years, some scholars have attempted high www.nature.com/scientificreports/ dimensional nonlinear dynamic systems of composite cantilever structures.…”

“…( 14) l 0 = 0.5m, b = 0.02m, h = 0.01m, (15) q = 3000sin(14πt)Pa, c = 0.01N/ (m/s)m 2 , (16) w 1,1 (0) = 0.3, w 1,2 (0) = 0, w 2,1 (0) = 0.07, w 2,2 (0) = 0. www.nature.com/scientificreports/ Then, considering the large amplitude limit cycle in Fig. 2, a control strategy available for vibration control of multi-dimensional nonlinear dynamic systems is required 15 .…”

“…Following the latest study 15 , if a nonlinear dynamic equation is presented below (such as Eq. ( 10))…”