Reciprocal Relations in Oscillations of Dissipative Systems

The equations of the dynamic response of discrete dissipative systems at arbitrary load are considered within the theory of time analysis. The structure of the kinematic parameters of a reaction is analyzed and it is shown that the constituent matrices of movements, velocities and accelerations of the nodes of the system are symmetrical which is considered as a specific case of reciprocal relations in an elastic dissipative system. On the basis of the properties of matrices, the more general reciprocal relations are proved, where in addition to the familiar principle of reciprocity of virtual work there are reciprocal relations in the form of a product of mass forces and velocities and in the form of a product of mass forces and accelerations. The theoretical calculations are illustrated by the example.