TY - GEN

T1 - Free vibrations of general elastically restrained nonuniform Timoshenko beams

AU - Lee, Sen-Yung

AU - Lin, Shueei Muh

PY - 1992/12/1

Y1 - 1992/12/1

N2 - The free vibration of a general elastically restrained symmetric nonuniform Timoshenko beam resting on a nonuniform elastic foundation and subjected to axial loads is studied. The relation between the flexural displacement and the angle of rotation due to bending is derived. The two coupled governing characteristic differential equations are reduced into one complete fourth-order ordinary differential equation with variable coefficients in the angle of rotation due to bending. The frequency equation is expressed in terms of the four normalized fundamental solutions of the differential equation. If the closed form fundamental solutions of the governing characteristic differential equation are not available, then the approximate fundamental solutions can be obtained through a simple and efficient algorithm. The limiting cases such as uniform Timoshenko beams, nonuniform Rayleigh and Bernoulli-Euler beams are examined. Several examples are given to illustrate the validity and accuracy of the analysis.

AB - The free vibration of a general elastically restrained symmetric nonuniform Timoshenko beam resting on a nonuniform elastic foundation and subjected to axial loads is studied. The relation between the flexural displacement and the angle of rotation due to bending is derived. The two coupled governing characteristic differential equations are reduced into one complete fourth-order ordinary differential equation with variable coefficients in the angle of rotation due to bending. The frequency equation is expressed in terms of the four normalized fundamental solutions of the differential equation. If the closed form fundamental solutions of the governing characteristic differential equation are not available, then the approximate fundamental solutions can be obtained through a simple and efficient algorithm. The limiting cases such as uniform Timoshenko beams, nonuniform Rayleigh and Bernoulli-Euler beams are examined. Several examples are given to illustrate the validity and accuracy of the analysis.

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M3 - Conference contribution

AN - SCOPUS:0026962712

SN - 079181131X

T3 - American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

SP - 101

EP - 109

BT - Recent Advances in Structural Mechanics - 1992

PB - Publ by ASME

T2 - Winter Annual Meeting of the American Society of Mechanical Engineers

Y2 - 8 November 1992 through 13 November 1992

ER -