Journal Article

Nonlinear dynamic response and bifurcation of variable thickness sandwich conical shell with internal resonance

Ma, W. S., Niu, Y., Yang, S. W., Zhang, W., Wang, Z. Q., Hao, Y. X.

2024

Overview

This paper explores the nonlinear dynamic responses and bifurcations of the truncated sandwich simply supported porous conical shell with varying thickness under 1:1 internal resonance. Two skins with carbon fiber and a core with porous aluminum foam, which has an exponentially variable thickness along the generator and various porosity distribution types along the core thickness, make up the sandwich shell structure with varying stiffness. The porous shell structure is affected by a combination of the in-plane load, transverse excitation, thermal stress and aerodynamic force, which is formulated by employing first-order piston theory with a modified term for curvature. By way of FSDT, von-Karman geometrical formulations, Hamilton’s principle and Galerkin procedure, the nonlinear dynamic formulations in ordinary differential form for the variable stiffness porous sandwich shell structure are identified. The averaged equations in polar and Cartesian coordinate forms for the sandwich structure under the combined circumstance of 1:1 internal resonance, first-order main resonance and 1/2 subharmonic resonance are determined by multiple-scale technique. The frequency-amplitude and force–amplitude characteristic curves, phase portraits, time history and bifurcation diagrams are exhibited by numerical simulation. The impacts of the damping coefficient, detuning parameters, temperature increment, transverse and in-plane excitations on the nonlinear dynamics and bifurcation behaviors of variable thickness sandwich porous conical shell are demonstrated.

• Publisher: Springer Netherlands,Springer Nature B.V
• Subject: Aerodynamic forces / Aluminum / Amplitudes / Automotive Engineering / Behavior / Bifurcations / Carbon fibers / Cartesian coordinates / Classical Mechanics / Conical shells / Control / Damping / Dynamic response / Dynamical Systems / Engineering / Excitation / Hamilton's principle / Load / Mechanical Engineering / Metal foams / Nonlinear dynamics / Nonlinear response / Piston theory / Resonance / Sandwich structures / Stiffness / Thermal stress / Variable thickness / Vibration