Optimal vibration control of beams with total and partial MR-fluid treatments

Abstract

This study presents synthesis of full-state and limited state flexible mode shape (FMS)based controllers for suppression of free-and forced vibration of a cantilever beam fully and partially treated with the magneto-rheological (MR) fluid. The governing equations of motion of the three layer MR sandwich beam are expressed in the state variable form comprising a function of the control magnetic field. An optimal control strategy based on the linear quadratic regulator (LQR) and a full-state dynamic observer is formulated to suppress the vibration of the beam under a limited magnetic field intensity. The lower flexural mode shapes of the passive beam are used to obtain the estimates of the deflection states so as to formulate a limited state LQR control synthesis. The free-and forced vibration control performances of both the full-state observer-based and limited state FMS-based LQR control strategies are evaluated for the fully as well as partially treated MR-fluid sandwich beams. The results show that the full-state observer-based LQR control can substantially reduce the tip deflection responses and the settling time of the free vibration oscillations. The limited-state LQR control based on the mode shapes effectively adapts to the deflections of the closed-loop beams and thus yields vibration attenuation performance comparable to that of the full-state LQR controller. The partially-treated beam with MR-fluid concentration near the free end also yields vibration responses comparable to the fully treated beam, while the natural frequencies of the partially treated beams are considerably higher.

Dynamic characteristics and control of magnetorheological/electrorheological sandwich structures: A state-of-the-art review

“…Haiqing and King (1997) suggested less significant effect of partial treatments on the loss factor of partially treated ER beam compared to natural frequencies. Rajamohan et al (2011) investigated the effect of MR locations on the modal damping factors for five modes of partially treated sandwich beam, under SSB, clamp (CCB), and cantilever boundary conditions. They divided core layer into 12 portions and treated different portions.…”

“…Figure 21. Variations in modal loss factor of MR sandwich beams with MR location under different boundary conditions (Rajamohan et al, 2011). four-partitioned ER plate to investigate the effect of intensity and area of applied field on the natural frequencies and mode shapes of the structure. The sandwich plate was fully treated by ER fluid and each quarter of the core layer could be activated individually.…”

“…In view of uniform distributed variable damping properties of the sandwich structures, which are provided by MR/ER fluid core layers, proportional damping assumption can be employed in the vibration analysis of the structures. Employing modal coordinate system yields uncoupled governing equations of motion for the sandwich structure in the following form (Allahverdizadeh et al, 2013c;Rajamohan et al, 2011) f…”

“…However, the approximation is valid in a limited range of frequency and applied field. The field-dependent equation presented in equation (18) can be used to develop different semi-active controllers such as LQR (Rajamohan et al, 2011) and sliding mode (Allahverdizadeh et al, 2013c) for the sandwich structures. Sapin´ski and Snamina (2008) demonstrated the concept of switched stiffness in vibration analysis of a cantilever beam with MR fluid as the core layer.…”

“…Dyniewicz et al (2015) proposed a semi-active controller to minimize unwanted vibration of a partially treated MRE beam structure in a particular mode of vibration. Rajamohan et al (2011) presented full-state observer-based and limited state LQR controller to suppress free and forced vibration of a cantilever beam, comprising two elastic layers and MR fluid as the core layer. The FE models of the fully and partially treated beams were expressed in the state-space form, as f_ x s g = ½Afx s g + ½Bfgg + ff g and fy s g = ½Cfx s g…”