Vibrations of Elastically Restrained Nonuniform Beams with Arbitrary Pretwist

Abstract

The coupled governing differential equations with general elastic boundary conditions for coupled bending ‐ bending vibration of a pretwisted nonuniform beam are derived by using Hamilton’ s principle. The e eld transfer matrix for the general system is expressed in integration form. As the elements of the matrix can be integrated analytically, the exact e eld matrix is, therefore, obtained. The transfer matrix method is presented to study the vibrations of any nonuniform cross-sectional beam with arbitrary variation of pretwist angle. The frequency equation is derived and expressed in terms of the transfer matrix. Several limiting cases are examined. The corresponding results are compared with previous work in the literature. Finally, the ine uence of elastically restrained boundary conditions and uniform and nonuniform pretwists on the natural frequencies is investigated.