| Title |
Free Vibrations of Timoshenko Beam with Elastomeric Bearings at Two Far Ends |
| Keywords |
free vibration;Timoshenko beam;elastomeric bearing;rotatory inertia;shear deformation;자유진동;Timoshenko 보;탄성받침;회전관성;전단변형 |
| Abstract |
This paper deals with free vibrations of the Timoshenko beam supported by two elastomeric bearings at two far ends. The ordinary differential equation governing free vibrations of such beam is derived, in which both effects of rotatory inertia and shear deformation are included as the Timoshenko beam theory. Also, boundary conditions of the free end are derived based on the Timoshenko beam theory. The ordinary differential equation is solved by the numerical methods for calculating natural frequencies and mode shapes. Both effects of the rotatory inertia and shear deformation on natural frequencies are extensively discussed. Also, relationships between natural frequencies and slenderness ratio, foundation modulus and bearing length are presented. Typical mode shapes of bending moment and shear force as well as deflection are given in figures which show the positions of maximum amplitudes and nodal points. |