NATURAL FREQUENCIES AND MODE SHAPES OF BEAMS CARRYING A 2-DEGREE-OF-FREEDOM SPRING-MASS SYSTEM

An exact solution for the natural frequencies and mode shapes for a be am elastically constrained at its ends and to which a rigid mass is el astically mounted is obtained. The attached mass can both translate an d rotate. The general solution is obtained using the Laplace transform with respect to the spatial variable and yields the exact solutions t o several previously published simpler configurations that were obtain ed using approximate methods. Numerous numerical results are presented for the natural frequency coefficients that extend previously reporte d results and that show the transition between various limiting cases. In addition, values are presented for the lowest two natural frequenc y coefficients for a beam that is clamped at both ends and is carrying a two dof spring-mass system. Representative mode shapes at selected values of the system's parameters are also given.