Time Analysis of Dissipative Systems Elastic Response. Part 2

AbstractBased on common equations of response of dissipative system, which is presented in the form of Duhamel's integral, some particular cases of the application of this integral to the problems of dynamics of structures are considered. The calculated construction scheme is simulated by the system with n degrees of freedom; accountancy of damping is conducted in the limits of linear theory of viscous damping. The solution under dynamic effect from constant suddenly applied forces, acting both for a long period of time and during some fixed period of time, after which the forces suddenly disappear, is obtained. It is shown that the determination of the response of calculated model of the structure impacted by vibratory load is connected with the solution of Sylvester's continuous equation. Response equation is set in a general form for the case when the excitation parameters (angular frequencies, initial phases, amplitudes) are different in various nodes of discrete system. The response equation under the action of periodic pulse for the case of rectangular and sinusoidal form is provided. All the proposed solutions have been recorded in the analytical form. The results of the theoretical research are illustrated with the examples of vibrations of three-floored space frame of the building