Active vibration control of smart porous conical shell with elastic boundary under impact loadings using GDQM and IQM

In this paper, the active damping control of the porous metal foam truncated conical shell with smart material macro fiber composite (MFC) is studied. Suppose the shell has arbitrary elastic supported edges, and is subjected to the impact loadings. The elastic supported edges can be achieved by virtual spring technique. Adopting the elastic constraint boundary condition, various classical boundaries can be easily realized by varying the value of the spring stiffnesses. Along the thickness direction, there are three types of porosity distributions of truncated conical shell being considered, and they are nonuniform symmetric, uniform and nonuniform asymmetric distribution, respectively. The sensor layer MFC-d31 and the actuator layer MFC-d33 are applied in the vibration control system. According to the first order shear deformation theory (FSDT) and energy principle, the dynamic equation of the system under electrostatic–mechanical​ coupling is derived. Then it is discretized into ordinary differential equation by generalized differential quadrature method (GDQM). The output charge applied to the sensor can be solved by integral quadrature method (IQM). The convergence and validation of the formulation and numerical calculation are studied by the comparisons between the present solutions and those from the literatures, ANSYS and COMSOL for the truncate conical shell with classical boundary conditions, respectively. Suppose the impact loadings acting on the porous truncated conical shell are step loading and decreasing loading, respectively. The velocity negative feedback approach is employed to diminish the amplitude of the transient response and achieve the active damping control. Then the effects of control gain, external excitation, semi-vertex angle and spring stiffness on the transient response control of the conical shell are studied in detail.