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Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena. [ABSTRACT FROM AUTHOR]

The vibrations produced by an agricultural machine are transmitted to the seat of the tractor operator and must comply with the limitations imposed by international and national regulations. An agricultural machine is generally composed of a tractor that can be linked to different machines required to perform a large number of agricultural tasks. In this paper, substructuring techniques are proposed to investigate the dynamics of the agricultural machine and to evaluate the resulting vibration exposure to the tractor driver in different configurations of the machine. These techniques allow one to couple reduced-order models or experimental models of the component subsystems to obtain the response of the whole system. In the results, the vibration exposure of the tractor operator is evaluated for different configurations of the agricultural machine, by observing the frequency response function (inertance and transmissibility) and the transient response to a given excitation. In conclusion, these techniques allow one to investigate a large number of different configurations and a wide range of operating conditions with a light computational burden and without asking the manufacturers to share sensitive design details. [ABSTRACT FROM AUTHOR]

• Dynamic substructuring is extended to time-variant interfaces due to a sliding contact. • Time dependent compatibility and equilibrium conditions are considered • The problem is solved in the time domain using primal and dual assembly. • Time Dependent Frequency Response Functions (TD-FRFs) are defined. • A lumped parameter model and to a discretized continuous system are studied. The study of complex systems composed by substructures connected together by frictional interfaces can benefit of the framework developed for dynamic substructuring. These systems are generally composed by time-invariant substructures in relative motion, implying time variant contact interfaces. Although the classical formulations of dynamic substructuring deal with time-invariant systems, they can be extended to include time-invariant component subsystems subjected to time-variant coupling conditions. The problem can be tackled in time domain using both primal and dual assembly, and in time-frequency domain using dual assembly to obtain the Time Dependent Frequency Response Functions (TD-FRFs). The equilibrium and the compatibility conditions are time-dependent and have to be defined under the assumption that the relative sliding motion at the contact interfaces is known a priori, at least approximately. The proposed method is applied to a lumped parameter model in order to evaluate its feasibility, and to a finite element model to verify its effectiveness. [ABSTRACT FROM AUTHOR]