ABSTRACT
This chapter discusses the vibrations of structural frameworks composed of prismatic members with and without superimposed masses. Members are considered to have bending deformation only, and structural joints are rigidly connected. The chapter presents formulations and numerical examples for eigensolutions, steady-state vibration, and response to general forcing functions with and without damping. The structures encountered are continuous beams and rigid frames that may have multiple degree-of-freedom in side-sway. Mathematical formulations are based on the dynamic stiffness method and the energy method. To formulate a structural stiffness matrix, the degree-of-freedom of the system must be known. A plane elastic structure has three generalized displacements at each node, including the supports; the restraints that are imposed on the displacements by the supports are three for a fixed support, two for a hinged support, and one for a roller support.
