12.1. Introduction

The response-spectrum analysis (RSA) is a widely used method for studying seismic responses of structures such as nuclear power plants, boilers, and pressure vessels. The current practice is to calculate only the responses of the modes having a frequency within the frequency range of the input spectrum.

In some cases, however, the responses of the higher modes may not be negligible. The missing-mass method is a convenient, computationally efficient, and accurate method used to account for:

  • The contribution of all modes with frequencies above fZPA, at which the response spectrum returns to the Zero Period Acceleration (ZPA).

  • The contribution to support reactions of mass apportioned to system-support points.

Terms Used

The following terms are used in this example problem:

Zero Period Acceleration (ZPA) -- The acceleration value (peak) at zero period (or infinite frequency) of an input spectrum. It corresponds to the response of a rigid system.

ZPA frequency (fZPA) -- The minimum frequency beyond which the input spectrum curves for various damping ratios converge towards the same ZPA acceleration.

For frequencies occurring in the amplified region of the response spectrum (f < fZPA), the mode responses generally have both in-phase (periodic) and out-of phase (rigid-response) components.[2]

To separate and combine the response components, the methods proposed by Gupta and Lindley-Yow are applied and the results are compared.[3] The in-phase modal response components and the missing-mass contributions are combined algebraically to produce the total in-phase response component. For the combination of the out-of-phase modal response components, either the Square Root of the Sum of the Squares (SRSS) method or the Der Kiureghian CQC method is applied.

For more information, see the following resources (in the Mechanical APDL Theory Reference):