# Nonlinear Vibrations of Low Pressure Turbine Bladed Disks: Tests and Simulations
## 1 Introduction  
In modern engineering, the efficient operation of turbomachinery is crucial for numerous industrial processes, including power generation, aviation, water, oil and gas exploitation, and chemical processing. The performance of turbomachinery is vital for productivity, safety, and sustainability. Central to this machinery are complex interactions of forces, materials, and dynamic phenomena, with vibrations being a critical aspect. These vibrations, stemming from rotor unbalance, aerodynamic forces, mechanical resonance, and fluid-structure interactions, can range from benign to harmful. Understanding and mitigating these vibrations is essential to prevent accelerated wear, fatigue, and potential catastrophic failure, making it a key focus of research and engineering. Friction damping devices are commonly employed in turbomachinery to minimize vibration amplitudes and improve the longevity and reliability of bladed disks. These dampers work by dissipating vibrational energy, thereby protecting the machinery from excessive wear and potential failure [1]. The study of the performance of dampers has attracted both academic and practical attention. Some techniques [2; 3; 4; 5; 6; 7] have investigated the performance of so-called ring dampers to reduce vibration amplitude through energy dissipation at the friction contact in the rim interface. In particular, ref. [4] presenteda design of a new passive damper coupling the energy-dissipative mechanisms of dry friction and a piezoelectric shunting circuit for integrally bladed disks. Other studies [8; 9] have focused on the impacts of a dissipative mechanism in reducing blade vibration. However, there is a study [10] that developed semi-active dry friction dampers which allow the control of the normal force for a reduction in steady-state vibration. Concerning conventional underplatform dampers, numerous studies [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22] have been performed to study their dynamic properties and damping efficiency. Specifically, ref. [12] proposed a new numerical tool to analyze the dynamic behavior of bladed disk systems with UPDs. This tool utilizes time-marching algorithms to perform individual time domain simulations under the harmonic excitation of certain frequencies. [PERSON] et al. [11] investigated the effect of frictional heat on the performance of UPDs. The results revealed a significant influence which may lead to a strong misprediction of the optimal centrifugal force and underestimation of the resonant peak in the presence of frictional heat. While some works have put a focus on the experimental or the numerical analysis of UPDs [14; 19], others have performed both [13; 15; 18; 20; 21; 22]. [PERSON] et al. [19] presented a new approach to evaluate damper-blade interaction. This resulted in a more insightful and less uncertain experimental investigation of damper behavior. [PERSON] et al. [13] numerically and experimentally investigated the nonlinear response variability in turbine bladed disks coupled with UPDs. They proposed a method which is able to predict the experimentally measured variability range with numerically calculated limits. [PERSON] et al. [21] developed a blade vibration test system for capturing damping characteristic curves through frequency sweep excitation and damping-free vibration methods. [PERSON] et al. [22] compared the experimental and numerical nonlinear dynamic responses of a bladed disk with UPD. As a result, the guidelines were proposed to enhance the nonlinear dynamic modeling approaches. On the other hand, there is a study by [PERSON] et al. [16] which tried to modify the geometric properties of UPD to improve the damping efficiency. This geometry was based on a conical shape, which prevented the pure rolling motion of the damper and ensured a high kinematic slip. The results revealed that this geometry has a high damping capacity and is more robust than conventional ones. Additionally, [PERSON] et al. explored the multiphase vortex-induced vibration (MVIV) in hydropower systems.