In this chapter, we shall study the dynamic behavior of structures designated as beams, that is, structures which carry loads which are mainly transverse to the longitudinal direction, thus producing flexural stresses and lateral displacements. We begin by establishing the static characteristics for a beam segment; we then introduce the dynamic effects produced by the inertial forces. Two approximate methods are presented to take into account the inertial effect in the structure: (1) the lumped mass method in which the distributed mass is assigned to point masses, and (2) the consistent mass method in which the assignment to point masses includes rotational effects. The latter method is consistent with the static elastic deflections of the beam. In Chapters 20 and 21, the exact theory for dynamics of beams considering the elastic and inertial distributed properties will be presented. In these chapters, the mathematical relationship between the exact solution and the stiffness and the consistent mass coefficients will be shown.
KeywordsStiffness Matrix Modal Shape Mass Matrix Axial Force Cantilever Beam
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