论文信息 - Dynamic analysis of thin‐walled and variable open section beams with shear flexibility

Dynamic analysis of thin‐walled and variable open section beams with shear flexibility

The equations of motion of thin-walled beams with open cross-section, considering the effects of shear flexibility and rotatory inertia in the stress resultants, as well as variable cross-sectional properties are presented using a state variables approach. These equations are based on Vlasov's theory of thin-walled beams, which is modified to include the effects indicated above. The resulting equations are used in the determination of the natural frequencies of an open cross-section prestressed concrete beam. Comparisons with other formulations are also presented employing the waves dispersion equation.

[1] G. Cowper. The Shear Coefficient in Timoshenko’s Beam Theory , 1966 .

[2] Giuseppe Andrea Ferro,et al. Shear deformability of thin‐walled beams with arbitrary cross sections , 1992 .

[3] S. Timoshenko,et al. LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[4] R. Courant,et al. Methods of Mathematical Physics , 1962 .

[5] H. R. Aggarwal,et al. A Theory of Torsional and Coupled Bending Torsional Waves in Thin-Walled Open Section Beams , 1967 .

[6] Atef F. Saleeb,et al. Shear-flexible models for spatial buckling of thin-walled curved beams , 1991 .

[7] E. F. Kurtz,et al. Matrix methods in elastomechanics , 1963 .

[8] A.D.S. Barr,et al. Linear vibration of thin-walled beams of equal angle-section , 1974 .

[9] S. Timoshenko,et al. X. On the transverse vibrations of bars of uniform cross-section , 1922 .

[10] P. Muller,et al. Torsional-flexural waves in thin-walled open beams , 1983 .

[11] N. G. Stephen. On the Variation of Timoshenko’s Shear Coefficient With Frequency , 1978 .