An analytical investigation of nonlinear response and stability characteristics of beam with three-dimensional tip mass

Kumar, Pravesh

doi:10.1007/s11012-023-01710-0

Meccanica

2023

DOI: 10.1007/s11012-023-01710-0

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An analytical investigation of nonlinear response and stability characteristics of beam with three-dimensional tip mass

Pravesh Kumar

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2024

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Cited by 2 publications

References 38 publications

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A generalized Bouc–Wen model for simulating the quasi-static and dynamic shear responses of helical wire rope isolators

Capuano,

Vaiana,

Carboni

2024

Nonlinear Dyn

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This research investigates the mechanical behavior of a helical wire rope isolator deforming along its shear direction. In particular, we present the results of an extensive experimental campaign including both quasi-static and dynamic tests. The former provide hysteresis loops characterizing the device quasi-static behavior; the latter, performed by using an electro-mechanical shaker, furnish frequency response curves describing the dynamic behavior of a rigid block supported by the tested device. To simulate such a complex behavior, we adopt a generalized Bouc–Wen model and identify its parameters on the basis of the quasi-static test results. Subsequently, such a model is employed to reproduce the frequency response curves of the isolated rigid block. Since the results of the dynamic tests suggest the presence of rate-dependent hysteresis phenomena in the isolated system, the generalized Bouc–Wen model is enhanced by introducing a linear viscous component. Finally, to substantiate the model validation, the experimental results obtained by applying a series of white noise signals are compared with those obtained numerically to demonstrate the model capability of reproducing the device behavior in non-stationary response conditions.

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A generalized Bouc–Wen model for simulating the quasi-static and dynamic shear responses of helical wire rope isolators

Capuano,

Vaiana,

Carboni

2024

Nonlinear Dyn

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Vibrational and stability analysis of planar double pendulum dynamics near resonance

Amer,

Moatimid,

Zakria

et al. 2024

Nonlinear Dyn

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The focus of this paper is to examine the motion of a novel double pendulum (DP) system with two degrees of freedom (DOF). This system operates under specific constraints to follow a Lissajous curve, with its pivot point moving along this path in a plane. The nonlinear differential equations governing this system are derived using Lagrange's equations. Their analytical solutions (AS) are subsequently calculated using the multiple-scales method (MSM), which provides higher-order approximations. These solutions are considered new, as the traditional MSM has been applied to this novel system for the first time. Additionally, the accuracy of these solutions is validated through numerical results obtained using the fourth-order Runge–Kutta method. The solvability conditions and characteristic exponents are determined based on resonance cases. The Routh–Hurwitz criteria (RHC) are employed to assess the stability of the fixed points corresponding to the steady-state solutions. They are also used to demonstrate the frequency response curves. The nonlinear stability analysis is performed by examining the stability and instability ranges. Resonance curves and time history plots are presented to analyze the behavior of the system for specific parameter values. The investigation delves into a comprehensive analysis of bifurcation diagrams (BDs) and Lyapunov exponent spectra (LEs), aiming to uncover the various types of motion present within the system. Systematic examination of these charts reveals critical insights into transitions between stable, quasi-stable, and chaotic dynamical behaviors. This work has practical applications in various fields, such as robotics, pump compressors, rotor dynamics, and transportation devices. It can be used to study the vibrational motion of these systems.

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An analytical investigation of nonlinear response and stability characteristics of beam with three-dimensional tip mass

Cited by 2 publications

References 38 publications

A generalized Bouc–Wen model for simulating the quasi-static and dynamic shear responses of helical wire rope isolators

A generalized Bouc–Wen model for simulating the quasi-static and dynamic shear responses of helical wire rope isolators

Vibrational and stability analysis of planar double pendulum dynamics near resonance

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