Vibration studies on completely free shallow shells having triangular and trapezoidal planforms

Abstract The first known vibration study on completely free shallow shells having triangular and trapezoidal planforms is conducted. The Ritz method with algebraic polynomials is used. Detailed convergence studies are made and showed that relatively accurate results can be obtained. The lowest six natural frequencies for completely free shallow shells with triangular and trapezoidal planforms are listed. Both right and symmetrical triangular and trapezoidal shell configurations are considered. The methods can be used for generally shaped planforms.