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A new lumped-parameter matrix method is proposed to model the decoupled, in-plane longitudinal and transverse free undamped vibrations of a collinear system with fixed ends and formed of two end flexible and prismatic members linked by a middle rigid connector. The method calculates the natural frequencies associated with the system’s three degrees of freedom by solving a linear algebraic characteristic equation related to the dynamic matrix, which is obtained from the system compliance and mass matrices. The linear, small-displacement model characterizes either long or short beams by adequately formulating the compliance and mass matrices. The lumped-parameter model is comprehensively validated by two separate distributed-parameter models, which determine the system’s longitudinal-vibration and long-beam, bending-vibration natural frequencies. Numerical simulations are performed with the lumped-parameter model to identify the sensitivity of the natural frequencies to system parameters variations and model variants. The system’s matrices are also utilized to perform frequency-domain analysis of the three-member system in a displacement/acceleration sensing application. The method can be adapted and expanded to describe more complex configurations with multiple, non-collinear, and non-prismatic members.

2 February 2026

Schematic of a system with collinear straight-axis rigid and flexible members.

Editorial for the Special Issue of Vibration: Nonlinear Vibration of Mechanical Systems

  • Francesco Pellicano,
  • Yuri V. Mikhlin and
  • Antonio Zippo
  • + 1 author

Nonlinear vibration phenomena play a central role in modern engineering, spanning applications from large-scale civil infrastructure to microscale and nanoscale systems [...]

5 February 2026

With the development of aerospace technology, hypersonic flight vehicles are evolving towards larger size, lighter weight, and higher performance. Their cross-domain maneuverability and extreme flight environment led to the rigid–flexible coupling effect and became the core bottleneck restricting performance improvement, seriously affecting flight stability and control accuracy. This paper systematically reviews the research status in the field of control for high-speed rigid–flexible coupling aircraft and conducts a review focusing on two core aspects: dynamic modeling and control strategies. In terms of modeling, the modeling framework based on the average shafting, the nondeformed aircraft fixed-coordinate system, and the transient coordinate system is summarized. In addition, the dedicated modeling methods for key issues, such as elastic mode coupling and liquid sloshing in the fuel tank, are also presented. The research progress and challenges of multi-physical field (thermal–structure–control, fluid–structure–control) coupling modeling are analyzed. In terms of control strategies, the development and application of linear control, nonlinear control (robust control, sliding mode variable structure control), and intelligent control (model predictive control, neural network control, prescribed performance control) are elaborated. Meanwhile, it is pointed out that the current research has limitations, such as insufficient characterization of multi-physical field coupling, neglect of the closed-loop coupling characteristics of elastic vibration, and lack of adaptability to special working conditions. Finally, the relevant research directions are prospected according to the priority of “near-term engineering requirements–long-term frontier exploration”, providing Refs. for the breakthrough of the rigid–flexible coupling control technology of the new-generation high-speed aircraft.

27 January 2026

Construction of precast reinforced concrete (PRC) industrial halls in seismically active areas has been increasing in recent decades. As connections are one of the most sensitive and vulnerable zones of PRC structures, there is a need to pay special attention to their investigation and modeling in seismic analysis. Knowing that each PRC system is specific and unique, this study aims to evaluate the actual seismic performances of PRC industrial halls built in the AMONT system, which represent a significant portion of the existing industrial building stock in Italy, the Balkans, and Turkey. As there is a lack of published research data on its specific joints, the results of the quasi-static full-scale experiments carried out up to failure on the models of four characteristic connections are presented. Since the implementation of nonlinear dynamic analysis in everyday engineering practice can be demanding, a simplified model of the structure considering the effects of the connections’ stiffness is proposed in this paper. The differences in the roof top displacements between the proposed model and the model with the rigid joints of the analyzed frames are in the range from 16.53% to 66.93%. The values of inter-story drift ratios are larger by 10–100% when the real stiffness of connections is considered, which is above the limit value provided by standard EN 1998-1. These results confirm the necessity of considering the nonlinear behavior and stiffness of connections in precast frame structures when determining displacements, which is particularly important for the verification of the serviceability limit state of structures in seismic regions.

23 January 2026

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Vibration - ISSN 2571-631X