Structural modification. Part 1: rotational receptances

The inverse problem of assigning natural frequencies and antiresonances by a modification to the stiffness, mass and damping of a structure is addressed. Very simple modifications such as the addition of masses and grounded springs can be easily accommodated and require the measurement of translational receptances at the connection coordinates. Realistic modifications of practical usefulness, such as a modification by an added beam, require the measurement of rotational as well as translational receptances. Such data are difficult to obtain because of the practical problems of applying a pure moment. One method, the so-called ‘T-block’ approach, has received considerable attention in the literature, but the accompanying problem of ill-conditioning has not been fully addressed until now. The T-block is attached to the structure at the modification point, so that a force applied to the T-block generates a moment together with a force at the connection point between the T-block and the parent structure. Forces and linear displacements measured on the T-block, together with a mass and stiffness model of the T-block itself, allow the problem to be cast as a special case of excitation by multiple inputs. The resulting equations are generally ill-conditioned, but can be regularized by using a small number of independent measurements. The methodology and signal processing techniques required to estimate the rotational receptances are described. An experimental example is used to demonstrate the practical application of the method.