Nonlinear free vibration of truncated conical shells has been investigated for three different
shell theories; Donnell, Sanders and Nemeth to investigate the effect of their simplifying
assumptions. The displacement field of a finite element model that was obtained from the
exact solution of equilibrium equations of Sander's improved first-approximation theory is
used to define the nonlinear strain energy of conical shells. Employing generalized
coordinates method the equations of motion are derived and subsequently the amplitude …