Natural Frequencies of Composite Lattice Structure Surrounded by Winkler-Pasternak Ambient Using Galerkin Method (Advances in Applied Mathematics and Mechanics, 2024)
The present work contains an analytical expression and solution for freevibration problem of a composite lattice cylindrical shell surrounded by Winkler-Pasternak elastic foundation with clamped edges. The foundation is simulated usinga large number of linear, homogenous shear and radial springs with variable stiffness.An integrated formula for calculation of the natural frequency of lattice structure andits foundation is derived from the equations of motion of the shell implemented byWinkler-Pasternak terms based on Fourier decomposition and Galerkin method. Thefundamental frequency formula concerning the foundation elements and lattice parameters is an effective means of estimation frequency in earlier design phase and alsoa tool to assess the vibration analysis of composite lattice cylindrical shell surroundedby an elastic foundation in design analysis and numerical solutions. The results areverified and confirmed using finite element analysis which show a very good agreement.