Nonlinear forced vibrations analysis of imperfect stiffened FG doubly curved shallow shell in thermal environment using multiple scales method

This study investigates the non-linear vibrations of stiffened imperfect functionally graded double-curved shallow shells, as rested on nonlinear elastic foundations. The shells are exposed to external harmonic excitation and are placed in the thermal situations. The modeling of shells is derived according to the classical shell theory and the non-linear geometric von Karman relationships. It is considered that the distribution of material properties changes along the thickness direction based on a power law index. The smeared stiffener technique is considered to model the stiffened shells. An approximation, according to Galerkin's approach, is utilized to reduction of the shell governing equations into the non-linear coupled ordinary differential relations. The ODE equations are analytically solved and analyzed through the perturbation methodology for investigating the resonance behavior of shells. Simulation results are reported to examine the influences of stiffeners, initial imperfection, foundation coefficients, thermal environment, and geometrical characteristics on the non-linear primary resonance response of doubly curved shallow shells. Also, the nonlinear dynamic behaviors are analyzed by numerical methods through the bifurcation diagrams, and the nonlinear dynamical behaviors of the shell for different value of parameters are examined.

Automated summary

This study investigates the non-linear vibrations of stiffened imperfect functionally graded double-curved shallow shells, as rested on nonlinear elastic foundations. The shells are exposed to external harmonic excitation and thermal situations. The modeling of shells is derived according to the classical shell theory and the non-linear geometric von Karman relationships, considering material properties changes along the thickness direction based on a power law index. The study uses analytical and numerical methods to analyze the resonance behavior and nonlinear dynamic behaviors of the shells under various conditions.