Bounds for natural frequencies, Dunkerley's formula and application to soil–structure interaction

A new expression for a lower bound for the fundamental natural frequency of a structure is presented and its relationship with Dunkerley's formula is examined. A related improved estimate for the fundamental frequency is also obtained and applied to obtain an approximate expression for the fundamental frequency of a soil–structure system including a 1-DOF structure, a flat rigid foundation, and an elastic soil. The resulting approximation is then compared with the now standard result first obtained by Jennings and Bielak [6]

► A new expression for a lower bound fundamental natural frequency of a structure is presented.
► Its relationship with Dunkerley's formula is examined.
► A related improved estimate for the fundamental frequency is also obtained.
► An approximate fundamental frequency expression of a 1-DOF SSI system is obtained.
► The approximation is compared with the now standard result first obtained by Jennings and Bielak.