Impulse response functions for elastic structures with rigid-body degrees of freedom

Abstract

A procedure based on the theory of generalized functions is developed which allows the calculation of impulse response functions for discrete and continuous elastic systems with structural damping and rigid-body degrees of freedom. For any degree of freedom the procedure divides the Fourier transform of the impulse response function into two parts. The first part contains the singularity due to the rigid-body degree of freedom. Its time-domain counterpart is obtained in closed form. The second part exhibits no singularities, and its time-domain counterpart is obtained by numerical integration using a Fast Fourier Transform routine. The procedure is applied to two systems for which closed form solutions are also obtained: a system consisting of two point masses connected by an elastic spring which slide without friction on a horizontal plane, and a non-dispersive mechanical slider with elastic deformations due to shear strain. The agreement between the results yielded by the proposed procedure and the closed form solutions is shown to be excellent. The procedure is then used to calculate the impulse response function for the tip displacement of a dispersive medium consisting of a flexible robot manipulator with the mechanical properties of a Timoshenko beam.