On the three‐dimensional vibration analysis of simultaneously skewed and twisted cantilevered parallelepipeds

The natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the Ritz method. The present work is the first known three‐dimensional study of the problem. Assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. Reasonably accurate natural frequencies are calculated for low aspect ratio, thick parallelepipeds having arbitrary degrees of twist and skewness. Detailed numerical studies show that a three‐dimensional analysis is essential in monitoring complicated coupled‐mode sensitivities in the variation of non‐dimensional natural frequencies with increasing skew and twist angles and thickness ratio. Results obtained using the present method are compared with those obtained in a detailed three‐dimensional finite element analysis, where the suitability and limitations of s‐version solid element discretizations are clearly brought out.