A condensation procedure for the coupled analysis of multidegree‐of‐freedom primary‐secondary (PS) structural systems is developed based on energy principles. It provides a simple and consistent approach to the response analysis of secondary systems in a vibrational environment for both tuned and detuned cases without explicit knowledge of the frequency characteristics associated with the combined PS system. In this method, a multidegree‐of‐freedom (larger than three degrees) P‐system is always substituted by a three‐degree‐of‐freedom system before condensing a 1S‐3P model to a 1S‐2P model based on the equivalence of the S‐system energy. All the energy parameters in the 1S‐2P and 1S‐3P models are analytically calculated from closed‐form expressions so that an increase in the number of degrees of freedom does not substantially increase the computational effort. Some of the solution properties such as its convergence as the mass ratio approaches a small value and the accuracy and efficiency of the solution ...

Energy-Based Dynamic Analysis of Secondary Systems

Exact solutions are presented for the mean-square responses of a class of complex structure-equipment systems under dynamic loads. The complex systems consist of an n -story building with each floor supporting a branch of an equipment system. The structure-equipment systems are precisely decomposed into n subsystems whose degrees-of-freedom are only dependent on the degrees-of-freedom in each branch equipment. These results can be used to evaluate the accuracy of existing approximate techniques, to better understand the dynamic characteristics of multituned structure-equipment systems, and to study the dynamic interaction between any two branches of the equipment system. Three illustrative examples indicate that there exists an optimum design damping of the equipment anchorage in such a complex system to suppress its vibration level. Advantage can also be taken of a nonuniform mass distribution in the equipment system to further reduce its vibration. The dynamic interaction between two branch equipment is...

Exact Solutions to A Class of Structure-Equipment Systems

Slightly slanting impact on an elastic cantilever column—an experimental study

In this technical note, power flow between two oscillators with spring and damping (nonconservative) couplings is introduced, and its relationship with energies stored in the two oscillators is established. It is shown analytically as well as through numerical examples that power flow and energies are appropriate response variables of a primary-secondary (PS) system, and that they both reflect the tuning characteristics of system and provide information on optimum design of the S-system.

L.X. Ren

Papers

Slightly slanting impact on an elastic cantilever column—an experimental study

Almost-axial impact on an elastic cantilever column—a theoretical study