Base Excitation Terminology

Core terms

• Base excitation: seismic ground motion applied as displacement, velocity or acceleration at the supports of a structure
• Support motion formulation: the equations of motion expressed in relative coordinates (displacement relative to the supports), which separates the inertial response from the rigid body motion
• Influence vector (r): a vector that defines the displacement of each degree of freedom due to a unit support displacement in a given direction; for a horizontal earthquake, r has ones at horizontal DOFs and zeros elsewhere
• Effective earthquake force: the equivalent force vector representing the inertial effect of base excitation, given by F_eff = M * r * x_ground_ddot
• Rigid body mode: a mode (or component of a mode) where the structure moves as a rigid body with the ground; occurs at frequencies above the rigid boundary

Relative vs absolute response

In base excitation analysis, the total displacement is the sum of the support displacement and the relative displacement. The relative displacement is what produces internal forces and stresses. Spectral acceleration from a response spectrum is the absolute acceleration of the oscillator; the relative acceleration is obtained by subtracting the ground acceleration. For design, the relative quantities (forces, stresses) are typically of interest, while the absolute acceleration is relevant for equipment qualification.