FREE-VIBRATIONS OF TIMOSHENKO BEAMS CARRYING ELASTICALLY MOUNTED, CONCENTRATED MASSES

An exact solution of the title problem is presented. The overall situation is of great interest in many engineering applications. Three combinations of boundary conditions for the structural element are considered: simply supported, simply supported - clamped and clamped at both ends. An analysis of the situation where the spring-mass system acts as a dynamic absorber cancelling out the motion at the point of attachment for certain modes of vibration is presented. An independent solution has also been obtained by means of a finite element code in order to ascertain the validity and accuracy of the results predicted by the exact solution of Timoshenko’s dynamic differential system. © 1993 Academic Press Limited.