Stochastic Optimal Bounded Parametric Control of Periodic Viscoelastomer Sandwich Plate with Supported Mass Based on Dynamical Programming Principle

Abstract

The sandwich plate (SP) with supported mass can model structural systems such as platform or floor with installed vibration-sensitive apparatus under random loading. The stochastic optimal control (in time domain) of periodic (in space) viscoelastomer (VE) SP with supported mass subjected to random excitation is an important research subject, which can fully use VE controllability, but it is a challenging problem on optimal bounded parametric control (OBPC). In this paper, a stochastic OBPC for periodic VESP with supported mass subjected to random base loading is proposed according to the stochastic dynamical programming (SDP) principle. Response-reduction capability using the proposed OBPC is studied to demonstrate further control effectiveness of periodic SP via SDP. Controllable VE core modulus of SP is distributed periodically in space. Differential equations for coupling vibration of periodic SP with supported mass are derived and transformed into multi-dimensional system equations with parameters as nonlinear functions of bounded control. The OBPC problem is established by the system equations and performance index with bound constraint. Then, an SDP equation is derived according to the SDP principle. The OBPC law is obtained from the SDP equation under bound constraint. Optimally controlled responses are calculated and compared with passively controlled responses to evaluate control effectiveness. Numerical results on responses and statistics of SP via the proposed OBPC show further remarkable control effectiveness.