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The development process of mechanical systems involves the evaluation of its modes of vibrations in the frequency range of interest. In general, a linear modal analysis is sufficient to determine whether the system can operate in dynamic conditions. However, in some cases the assembly is composed of many subsystems connected through nonlinear connections which make the response depend on the amplitude and frequency of the excitation. In those cases, Linear Normal Modes (LNMs) are not sufficient to fully describe the dynamics of the system and Nonlinear Normal Modes (NNMs) must be used. Using substructuring techniques it is possible to treat nonlinear joints as independent subsystems. However, a reliable nonlinear model is needed to use this approach. The experimental characterization is the only way to correctly estimate the nonlinear behavior of the connection. Thus, the aim of this work is to develop and validate the experimental characterization to build an experimental nonlinear modal model of a strongly nonlinear element that can be used to connect different linear subsystems and can be regarded as a localized source of nonlinearity. The NNMs identification is performed using the single-point single-harmonic phase resonance method, and the experimental nonlinear modal model of the NLCE is obtained by retaining only the first harmonic term of each NNM in order to get nearly uncoupled modal equations. • Experimental identification of nonlinear normal modes of strongly nonlinear elements. • New concept design of a nonlinear connecting element. • Quantification of super-harmonics contributions of the response around resonance. • Validation of the identified model of the strongly nonlinear element. [ABSTRACT FROM AUTHOR]

Mechanical joints play a critical role in many engineering structures, but identifying their characteristics can be challenging, particularly when the joint interface (coupling DoFs) cannot be directly measured. In these cases, an existing iterative procedure based on the use of the System Equivalent Model Mixing (SEMM) expansion technique and substructure decoupling can be used to identify the joint properties by taking measurement on other accessible DoFs (internal DoFs). Despite the potential of this procedure, it is prone to large error propagation. In addition, in the SEMM expansion a weighted pseudo-inverse operation is needed to ensure the convergence of the iterative procedure when both coupling and internal DoFs (extended interface) are involved in the decoupling. This paper focuses on the detection of the error sources in the process and on the definition of some strategies to limit error propagation. The use of internal DoFs only (pseudo-interface) in the decoupling is proposed. This avoids the use of coupling DoFs affected by the expansion error. Furthermore, two strategies are proposed to improve the conditioning of the procedure when using the extended interface. Both strategies are based on the Truncated Singular Values Decomposition (TSVD). It is shown that the weights clearly indicate the number of singular values to be retained in the matrices to be inverted. The proposed improvements are validated on a laboratory benchmark. Measurements on the benchmark are performed to validate the strategies with experimental data. In addition, the Monte Carlo method is applied using noise-polluted numerical data to evaluate the potential of the proposed strategies to mitigate the error propagation in the SEMM-based joint identification procedure. • This paper highlights and discusses the error propagation in SEMM-based joint identification procedure. • The use of the pseudo-interface in decoupling step and a fitting procedure are proposed to limit the error propagation. • Two strategies based on the TSVD are introduced to improve the quality of the joint identification when using the extended interface in decoupling. • Numerical and experimental examples are used to evaluate the proposed improvements. [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]

This work wants to provide insights on the coupling between contact behaviour (local scale) and vibrational response (global scale) which brings to different contact scenarios arising in dry frictional systems. A newer setup, named TriboWave, has been developed in order to reproduce and investigate the system response to frictional contact, under well-controlled boundary conditions. The experimental results highlighted how a simple frictional system can switch from stable friction-induced vibrations to unstable vibrations, i.e. either macroscopic stick–slip instabilities or mode coupling instabilities. The effect of the contact surface roughness on the reproduced frictional scenario has been investigated too. [ABSTRACT FROM AUTHOR]