Actuator nonlinearities can significantly affect control systems, leading to performance degradation and even loss of stability. Physical constraints such as rate and acceleration limits are particularly detrimental in applications where rapid actuation is required, yet their combined effects remain largely unexplored. This paper investigates the nonlinear dynamic behaviour induced by rate and acceleration limits in closed-loop systems, focusing on their steady-state response to sinusoidal excitation. The saturation regimes associated with these nonlinearities are fully characterised, and their analytical boundaries are represented in a two-dimensional parameter space defined by normalised rate and acceleration limits. Sinusoidal describing functions are derived for each regime, providing a unified frequency-domain representation of the actuator dynamics. These formulations are employed to analyse the impact of actuator nonlinearities on closed-loop dynamics, including the onset of nonlinear behaviour, phase lag and gain reduction. Analytical conditions for the occurrence of jump resonance are derived, along with the lowest frequency where multiple steady-state solutions appear, leading to potential abrupt changes in system response. The applicability of the proposed framework is demonstrated through both an illustrative first-order system and a realistic high-order aeroservoelastic model for gust load alleviation, where the interaction between actuator nonlinearities and closed-loop dynamics is shown to produce multiple jump resonance scenarios and isolated nonlinear response branches. The results highlight the critical role of actuator rate and acceleration limits in high-bandwidth control applications and provide practical insights for frequency-domain stability assessment and preliminary feedback control system design.

This paper investigates the impact of introducing a switchable vortex generator (SVG), acting as a minitab, on the aerodynamic performance of a high-aspect-ratio wing’s outer section in transonic regime. A parametric study is conducted employing computational fluid dynamics two-dimensional simulations, focusing on the aerodynamic effects of changing the chordwise position and height of the vane of a SVG located on the airfoil upper surface in both nominal cruise conditions and for varying angles of attack. The analysis reveals that minitabs can strongly affect the aerodynamic forces produced by the wing section, showing great potential for load alleviation and control, but also emphasizing the need for a careful parameter selection to reduce undesirable effects such as the generation of shock waves. In cruise conditions, lift reduction increases with the vane height and has its maximum for chordwise positions at 60% of the chord length. However, SVGs located in the first half of the chord length yield more robust performance for varying angle of attack, without sharp lift variations or generated shock waves, and a delayed stall onset. High SVGs (greater than or equal to 3% chord length) can also lead to strong shock waves on the airfoil lower surface at small or negative angle of attack, while small SVGs (less than 1% chord length) can generate normal shock waves on the upper surface, with limited lift reduction in cruise conditions and at higher incidence.

This study aims at assessing the predictive performance of the Amontons–Coulomb law to reliably predict the cyclic response, inclusive of stick–slip, of a single degree of freedom system in contact with the ground through two versions (steady-state and rate-and-state) of a regularized Dieterich–Ruina law. The assessment is carried out by defining a cost function and a physics-based constraint that enable the identification of the corresponding optimal coefficients of the Amontons–Coulomb law through a multi-start constrained non-linear optimization. The comparative study starts with a sensitivity analysis, aimed at first identifying the most meaningful model parameters for the Dieterich–Ruina law. Subsequently, the cyclic dynamic responses provided by both friction laws are analysed for varying model parameters, and characteristic features are observed within the dynamic forcing–displacement graph and the friction force–velocity plot, that could be directly linked to one friction model or the other. The sensitivity analysis led to the definition of a cost function expressed in terms of the displacement and velocity response differences and a constraint based on the phase difference. The optimization study identified areas of the Dieterich–Ruina's parameter space for which the Amontons–Coulomb law can reliably be used to predict a cyclic stick–slip response. The relevance of these results with respect to problems of modelling and identification of friction are discussed.

This paper proposes an approach for the determination of the analytical boundaries of continuous, stick-slip and no motion regimes for the steady-state response of a multi-degree-of-freedom (MDOF) system with a single Coulomb contact to harmonic excitation. While these boundaries have been previously investigated for single-degree-of-freedom (SDOF) systems, they are mostly unexplored for MDOF systems. Closed-form expressions of the boundaries of motion regimes are derived and validated numerically for two-degree-of-freedom (2DOF) systems. Different configurations are observed by changing the mass in contact and by connecting the rubbing wall to: (i) the ground, (ii) the base or (iii) the other mass. A procedure for extending these results to systems with more than 2DOFs is also proposed for (i)–(ii) and validated numerically in the case of a 5DOF system with a ground-fixed contact. The boundary between continuous and stick-slip regimes is obtained as an extension of Den Hartog’s formulation for SDOF systems with Coulomb damping (Trans Am Soc Mech Eng 53: 107–115, 1931). The boundary between motion and no motion regimes is derived with an ad hoc procedure, based on the comparison between the overall dynamic load and the friction force acting on the mass in contact. The boundaries are finally represented in a two-dimensional parameter space, showing that the shape and the extension of the regions associated with the three motion regimes can change significantly when different physical parameters and contact configurations are considered.

This paper investigates the steady-state response of a harmonically excited multi-degree-of-freedom (MDOF) system with a Coulomb contact between: (1) a mass and a fixed wall; (2) two different masses; (3) a mass and an oscillating base. Although discrete MDOF models are commonly used at early design stages to analyse the dynamic performances of engineering structures, the current understanding of the friction damping effects on MDOF behaviour is still limited due to the absence of analytical solutions. In this contribution, closed-form expressions of the continuous time response, the displacement transmissibility and the phase angle of each mass of the system are derived and validated numerically for 2DOF and 5DOF systems. Moreover, the features of the analytical response are investigated, obtaining the following results: (i) the determination of the minimum amounts of friction for which the resonant peaks become finite and (ii) for which stick-slip motion can be observed at high frequencies; (iii) an equation for the evaluation of invariant points for the displacement transmissibilities; (iv) a better understanding of phenomena such as the inversions of the transmissibility curves and the onset of additional resonant peaks due to the permanent sticking of the mass in contact. All these results show that MDOF systems exhibit significantly different dynamic behaviours depending on whether the friction contact and the harmonic excitation are applied to the same or different masses.

This paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.

This study investigates the displacement transmissibility of single-degree-of-freedom systems with a Coulomb friction contact between a mass and a fixed or oscillating wall. While forced vibration and base motion problems have been extensively investigated, little work has been conducted on the joined base-wall problem. Based on the work of Den Hartog (Trans Am Soc Mech Eng 53:107–115, 1930), analytical expressions of the displacement transmissibility are derived and validated numerically. The mass absolute motion was analysed in the joined base-wall motion case with a new technique, with results such as: (1) the development of a method for motion regime determination; (2) the existence of an inversion point in transmissibility curves, after which friction damping amplifies the mass response; (3) the gradual disappearing of the resonant peak when the ratio between friction and elastic forces is increased. Moreover, numerical analysis provides further insight into the frequency region where mass sticking occurs in the base motion problem.