In recent papers the author has shown that when determining optimum parameters for an absorber which minimizes the vibration response of a complex system, the latter may be treated as an equivalent single degree-of-freedom system if its natural frequencies are well separated. Emphasis was on minimizing the displacement response when the excitation was a harmonic force. In the present paper simple expressions for optimum absorber parameters are derived for undamped one degree-of-freedom main systems for harmonic and white noise random excitations with force and frame acceleration as input and minimization of various response parameters. These expressions can be used to obtain optimum parameters for absorbers attached to complex systems provided that optimization is with respect to an absolute, rather than a relative, quantity. The requirement that the natural frequencies should be well separated is investigated numerically for the different cases. The effect of damping in the main system on optimum absorber parameters is investigated also.

Optimum absorber parameters for various combinations of response and excitation parameters

Parametric study and simplified design of tuned mass dampers

In the classical problem a damped one degree-of-freedom absorber system is attached to a main system, which has one degree of freedom and is undamped The optimum values of absorber stiffness and damping, which will minimize the resonant response of the main mass, are well known In this paper the effect on these optimum conditions of light damping in the main system is studied The authors show that optimum parameters for absorbers, which are attached to beams and plates, can be obtained simply and accurately from those for an equivalent one degree-of-freedom main system This depends upon the concept of an effective mass for the elastic body and the representation of its response by the single relevant mode It will be shown in a later paper that for more complex elastic bodies such as cylindrical shells, for which the natural frequencies are more closely spaced, these simple concepts do not predict accurately optimum absorber parameters

Optimum absorber parameters for simple systems

H∞ and H 2 optimization problems of the Voigt type dynamic vibration absorber (DVA) are classical optimization problems, which have been already solved for a special case when the primary system has no damping. However, for the general case including a damped primary system, no one has solved these problems by algebraic approaches. Only the numerical solutions have been proposed until now. This paper presents the analytical solutions for the H∞and H 2 optimization of the DVA attached to the damped primary systems. In the H∞ optimization the DVA is designed such that the maximum amplitude magnification factor of the primary system is minimized; whereas in the H 2 optimization the DVA is designed such that the squared area under the response curve of the primary system is minimized. We found a series solution for the H∞ optimization and a closed-form algebraic solution for the H 2 optimization. The series solution is then compared with the numerical solution in order to check the accuracy in connection with the truncation error of the series. The exact solution presented in this paper is too complicated to handle by a hand-held calculator, so we proposed an approximate solution for the practical object.

D. L. Taylor

Papers

Optimum Vibration Absorbers for Linear Damped Systems