Natural vibration of an elastically supported porous truncated joined conical-conical shells using artificial spring technology and generalized differential quadrature method

In this paper, the natural vibration of an elastically supported porous truncated joined conical-conical shell (JCCS) is studied. The elastic support is achieved by using artificial spring technology. Four types of the metal foam porous distribution are presented, i.e. the uniform distribution along the radial direction and three other types of the gradient distribution. By applying Hamilton principle and the first order shear deformation theory (FSDT), dynamic equations of motion of the JCCS in the form of partial differential are derived. Considering the elastically supported boundary conditions, displacements continuity conditions and forces continuity conditions at the joining section of the coupling conical shell, partial differential equations used to describe this dynamic system are simplified into a set of algebraic equations by utilizing the generalized differential quadrature method (GDQM), in which the trigonometric function is used in the circumferential direction, while in meridian direction the DQ is applied. To obtain the natural vibration characteristic of the JCCS, the eigenvalue solving technology is utilized. The validation and convergence of the theoretical formulation are confirmed by comparison studies. Influences of boundary conditions, the spring stiffness, the geometric and material parameters on natural frequencies and mode shapes of the JCCS with two particular elastic boundary conditions are studied in detail.