Abstract: To obtain more accurate result of transverse natural vibration of barrel, a barrel was simplified to several segments of Timoshenko beams with variable cross-sections in consideration of the shear distortion and the moment of inertia, establishing the transverse vibration equations. The Chebyshev orthogonal polynomial was applied to deploy the differential equations. As a result, a set of transverse nature vibration equations of the barrel was obtained by assembling the boundary and collection equations. The natural vibration characteristic of barrel with variable cross-section was got by solving the equations. The results of numerical examples show that the method is effective, accurate, and could adapt to various boundary conditions.

Key words: oscillation and wave, barrel, Timoshenko beam, Chebyshev polynomial, eigenvalue, vibration