**5.1. Problem statement**

Given a desired fundamental frequency, construct a brace–plate system as described by a mass matrix *M* and a stiffness matrix *K*. All dimensional (geometric) properties of the brace–plate system are assumed to be specified and fixed except for the thickness of the brace *hc* and the

design variable, which must be found. The plate and brace material properties are also assumed to be known.

It is known from vibrations theory that the natural frequencies of a system specified by stiffness matrix *K* and mass matrix *M* are the square roots of the generalized eigenvalues of the matrices (*K*, *M*). Hence, a specified fundamental frequency of the system is the same as specifying the smallest generalized eigenvalue of (*K*, *M*).
