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• A parametrically excited energy harvester with a resonant attachment is proposed. • Interactions with the attachment expanded the harvesting frequency range. • Intentionally introduced perturbations facilitated entry into the unstable region. • Resonant energy transfer rapidly induced a high-amplitude steady-state response. Drawing inspiration from the enhancement of sensing capabilities in Micro-electro-Mechanical Systems (MEMS), the utilization of parametric resonance with nonlinear amplification features shows promise in vibration energy harvesting. However, harnessing parametric resonance for vibration energy harvesting presents several challenges. Initiating the resonant regime under low-energy conditions can be challenging, and the periodic modulation of system parameters requires additional time to accumulate the vibration amplitude. The range of modulation frequencies needs to trigger parametric resonance is notably narrow, especially when employing piezoelectric transducers for energy harvesting. To address these concerns, a parametrically excited piezoelectric energy harvester incorporating with a movable resonant attachment is proposed. The governing equations of this system were derived using the extended Hamilton principle and then numerically solved. Experimental testing was performed based on the design, and it displayed good agreement with numerical predictions. System parametric studies were carried out, revealing the mutual influence among critical system parameters. The findings demonstrate that the proposed device exhibited hardening dynamic responses and achieved more than a fivefold increase in overall bandwidth compared to a conventional parametrically excited counterpart. [ABSTRACT FROM AUTHOR]

• Dynamics of a planar curved beam subjected to moving loads or masses. • Arbitrary Lagrangian-Eulerian formulation for a corotational curved beam element. • Treatment of geometric nonlinearity and viscoelasticity of the beam. • Driving force for a prescribed motion of a mass along the beam. This paper presents an arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for the geometric nonlinear dynamic analysis of planar curved viscoelastic beams subjected to moving loads. In the ALE description, the beam nodes can be moved in arbitrarily specified ways to describe the moving loads' material positions accurately. The pure deformation and the deformation rate of the element are measured in a curvilinear coordinate system fixed on a curved reference configuration that follows the rotation and translation of a corotational frame. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. Then, a standard element can be embedded within the element-independent framework. An accurate two-node curved element and the Kelvin-Voigt model are introduced in this framework to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational efficiency, and versatility of the presented formulation. The effect of internal damping, external damping, the inertia force of a moving mass, and the moment of inertia of the mass on the dynamic response of the beam are investigated. Moreover, the driving force for a prescribed motion of a mass along the beam is investigated. [ABSTRACT FROM AUTHOR]

• A nonlinear dynamic analysis of a hydraulic arresting gear system is performed. • A sliding flexible structure with multiple non-material supports is investigated. • A 2D non-material variable-domain corotational element is developed. • The propagation mechanism of longitudinal waves and kink waves is investigated. In this paper, a 2D non-material variable-domain corotational element (NVCE) is developed to perform a nonlinear dynamic analysis of arresting gears. In the arresting process, the impact of the carrier aircraft will result in the arresting cable sliding out of the deck sheaves and undergoing large deformation. The positions of the sheaves relative to the material points of the cable depend on the current configuration of the cable. Considering this type of non-material boundary condition, we model the cable as a sliding flexible structure with multiple non-material supports. Every part between the supports can be discretized using a suitable number of the NVCEs. Based on the corotational method, a 'standard element' can be embedded within the dynamic formulation. To consider the shear deformation and rotary inertia, the interdependent interpolation element is introduced, and three examples are presented to demonstrate the validity, accuracy and effectiveness of the formulation. For the dynamic analysis of the arresting cable, the cable element is introduced to improve the computational efficiency. In the numerical examples, the propagation mechanism of longitudinal waves and kink waves and the dynamic characteristics of the arresting system are investigated. [ABSTRACT FROM AUTHOR]

This paper presents a consistent corotational formulation for the geometric nonlinear dynamic analysis of 2D sliding beams. Compared with the works of previously published papers, the same cubic shape functions are used to derive the elastic force vector and the inertia force vector. Consequently, the consistency of the element is ensured. The shape functions are used to describe the local displacements to establish an element-independent framework. Moreover, all kinds of standard elements can be embedded within this framework. Therefore, the presented method is more versatile than previous approaches. To consider the shear deformation, the sliding beam (a system of changing mass) is discretized using a fixed number of variable-domain interdependent interpolation elements (IIE). In addition, the nonlinear axial strain and the rotary inertia are also considered in this paper. The nonlinear motion equations are derived by using the extended Hamilton's principle and solved by combining the Newton-Raphson method and the Hilber-Hughes-Taylor (HHT) method. Furthermore, the closed-form expressions of the iterative tangent matrix and the residual force vector are obtained. Three classic examples are given to verify the high accuracy and efficiency of this formulation by comparing the results with those of commercial software and published papers. The simulation results also show that the shear deformation and the rotary inertia cannot be neglected for the large-rotation and high-frequency problem. [ABSTRACT FROM AUTHOR]