• Steel and Composite Structures
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• v.45 no.3
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• pp.409-423
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• 2022

Nowadays, there is a high demand for great structural implementation and multifunctionality with excellent mechanical properties. The porous structures reinforced by graphene platelets (GPLs) having valuable properties, such as heat resistance, lightweight, and excellent energy absorption, have been considerably used in different engineering implementations. However, stiffness of porous structures reduces significantly, due to the internal cavities, by adding GPLs into porous medium, effective mechanical properties of the porous structure considerably enhance. This paper is relating to vibration analysis of fluidconveying cantilever porous graphene platelet reinforced (GPLR) pipe with fractional viscoelastic model resting on foundations. A dynamical model of cantilever porous GPLR pipes conveying fluid and resting on a foundation is proposed, and the vibration, natural frequencies and primary resonant of such a system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with the fractional viscoelastic model is used to govern the construction relation of nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied to the pipe and the excitation frequency is close to the first natural frequency. The governing equation for transverse motions of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.389-403
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• 2023

In order to explore the influence of tooth root cracks on the dynamic characteristics of multi-stage planetary gear transmission systems, a concentrated parameter method was used to construct a nonlinear dynamic model of the system with 30-DOF in bending and torsion, taking into account factors such as crack depth, length, angle, error, time-varying meshing stiffness (TVMS), and damping. In the model, the energy method was used to establish a TVMS model with cracks, and the influence of cracks on the TVMS of the system was studied. By using the Runge- Kutta method to calculate the differential equations of system dynamics, a series of system vibration diagrams containing cracks were obtained, and the influence of different crack parameters on the vibration of the system was analyzed. And vibration testing experiments were conducted on the system with planetary gear cracks. The results show that when the gear contains cracks, the TVMS of the system will decrease, and as the cracks intensify, the TVMS will decrease. When cracks appear on the II-stage planetary gear, the system will experience impact effects with intervals of rotation cycles of the II-stage planetary gear. There will be obvious sidebands near the meshing frequency doubling, and the vibration trajectory of the gear will also become disordered. These situations will become more and more obvious as the degree of cracks intensifies. Through experiments, the theoretical results are in good agreement with experimental results, verifying the correctness of the theoretical model. This provides a theoretical basis for fault diagnosis and reliability research of the system.

• Steel and Composite Structures
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• v.50 no.2
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• pp.201-216
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• 2024

This paper is motivated by the lack of studies relating to vibration and nonlinear resonance of fluid-conveying cantilever porous GPLR pipes with fractional viscoelastic model resting on nonlinear foundations. A dynamical model of cantilever porous Graphene Platelet Reinforced (GPLR) pipes conveying fluid and resting on nonlinear foundation is proposed, and the vibration, natural frequencies and primary resonant of such system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with fractional viscoelastic model is used to govern the construction relation of the nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied on pipe and excitation frequency is close to the first natural frequency. The governing equation for transverse motion of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.