Dynamic buckling active control of FGM spherical shell with piezoelectric sensor and actuator layers

The mechanical snap-through phenomenon represents one of the buckling modes inherent in shallow shells, exemplifying the shell's reaction to external loads, which can potentially have detrimental effects on structural performance. This article delves into the study of this phenomenon within the context of spherical shells. Leveraging functionally graded material (FGM) in the main layer of this structure proves instrumental in enhancing the shell's performance against rapid mechanical loads. Furthermore, the strategic placement of piezoelectric layers, both symmetrically and asymmetrically, coupled with the implementation of a proportional and derivative control system, facilitates the control of the shell's response. The formulation of displacement field and electric potential is grounded in the first-order shear deformation theory (FSDT) and second-order distribution, respectively. The strong form of nonlinear dynamic and electrostatic equations is derived using Hamilton's principle. Solving these equations is achieved through the implementation of the generalized differential quadrature (GDQ) method in the spatial domain and Newmark in the time domain. Additionally, the Newton-Raphson method is employed to tackle the inherent nonlinearity of the problem. The Budiansky's criterion is employed for the assessment of the load necessary for the buckling of the shell. Following the validation of results against numerical, analytical, and laboratory outcomes, a set of parametric results is presented. These results underscore the remarkable impact of the control system in mitigating shell deformation under time- dependent mechanical loads, as well as in postponing the occurrence of the snap-through phenomenon and damping the vibrations.