Dynamic Effects

Abstract

The strains in an elastic body may be computed from a specified displacement field using the equations of compatibility, regardless of whether the displacements arise from static or dynamic excitation. The corresponding stresses and, indeed, the displacements themselves may be dependent on the rate characteristics of the loading function. Therefore, the time derivatives of the displacements, i.e., velocities and accelerations, enter into these equations. In this Chapter, the field equations of linear elasticity are generalized to include rate-dependent terms. Further, in the case of dynamic excitation, two important system characteristics are the natural frequencies, or their reciprocal the periods of vibration, and the corresponding mode shapes. A related quantity, which is dependent only on the material properties, is the velocity at which an elastic wave propagates through a medium or a body. Damping, which represents internal energy dissipation, is also an important consideration in dynamic response computations and may be dependent on the displacement, the velocity, or other rate quantities.