Response suppression of FGM plate using piezoelectric layers under parametric uncertainty conditions with Markovian jump approach. (English) Zbl 07488889
Summary: It should be noted that in addition to the geometry, constituent material also affects the strength and rigidity of the cylindrical shell, some factors that determine the transient response are its geometry and the constituent material. The capability of piezoelectric materials to adept their properties in reaction to environmental factors including electricity and loading is one of the major reasons for using in this work. Therefore, in this study, the transient response of a symmetric annular sandwich plate incorporating functionally graded core and piezoelectric layers under external harmonic force and electrical voltage is investigated. The properties of the core material vary along its thickness according to a power law model. The displacement field is represented by the third-order shear deformation theory. With the aid of Hamilton’s principle, the structural equations are obtained in terms of displacement components, then solved using the differential quadrature method. In addition, the time response is evaluated with respect to effective parameters including the internal radius, power law index, core thickness, and external voltage. According to the simulation results, the oscillation amplitude decreases as the internal radius of the plate increases over the desired time interval. Also, a higher index parameter is associated with a wider time response range. Moreover, the stability analysis of a piezoelectric system with \(H\infty\) performance is considered based on the theory of Markovian jump systems. To this end, a Markovian jump state-space model of the piezoelectric system obtained using system identification under the effect of external disturbance is presented. The \(H\infty\) stability index is selected based on a candidate Lyapunov function that leads to a set of linear matrix inequalities for each region. The uncontrolled and controlled transient responses of the coupled system under external disturbance are calculated and compared, indicating the satisfactory controller performance in the presence of external disturbance and jump in the sensor and system dynamics.
Keywords:
transient time response; electro-mechanical loading; annular sandwich plate; functionally graded material; piezoelectric layers; differential quadrature method; active piezo-control; Markovian jump systemReferences:
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