Nonlinear Dynamics Modeling and Subharmonic Resonances Analysis of a Laminated Composite Plate by Ting Ma, Xiao Juan Song, Shu Feng Lu

“…The two-degree-of-freedom ordinary differential equations that describe the vibration of the rectangular plate are obtained by the Galerkin method. The multiscale method is used to obtain an approximate solution to the resonance problem. …”
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Study on Galloping Oscillation of Iced Catenary System under Cross Winds by Guo Chen, Yiren Yang, Yang Yang, Peng Li

“…The partial differential vibration equation of the system is converted into the ordinary differential equation by the Galerkin method and then numerically solved. The condition of the unstable catenary motion in simulation is in agreement with that from theoretical stability analysis. …”
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Spectral framework using modified shifted Chebyshev polynomials of the third-kind for numerical solutions of one- and two-dimensional hyperbolic telegraph equations by S. M. Sayed, A. S. Mohamed, E. M. Abo-Eldahab, Y. H. Youssri

“…Abstract This investigation discusses a numerical approach to solving the hyperbolic telegraph equation in both one and two dimensions. Applying the Galerkin method is the basis of this approach. We use appropriate combinations of third-kind modified shifted Chebyshev polynomials (3KMSCPs) as basis functions to transform the governing partial differential equations into a collection of algebraic equations. …”
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Nonlinear Vibration of a Continuum Rotor with Transverse Electromagnetic and Bearing Excitations by Haiyang Luo, Yuefang Wang

“…The governing equation of motion is derived and discretized as a group of ordinary differential equations using the Galerkin's method. The stability of the equilibrium of the rotor is analyzed with the Routh-Hurwitz criterion and the occurrence of the Andronov-Hopf bifurcation is pointed out. …”
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Thermal simulation of hybrid nanomaterial-assisted freezing in porous media by Ali Al Khabyah

“…This work presents a simulation of the transient cold energy storage process in a porous container, accounting for both radiation and conduction mechanisms. The Galerkin method is applied to model the intricate system interactions, while adaptive mesh refinement increases the accuracy of the numerical simulations. …”
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Flap/Lag Stall Flutter Control of Large-Scale Wind Turbine Blade Based on Robust H2 Controller by Tingrui Liu, Wei Xu

“…The aeroelastic partial differential equations are reduced by Galerkin method, with the aerodynamic forces decomposed by strip theory. …”
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Nonlinear Vibration Analysis of Submerged Floating Tunnel Tether by Sheng-nan Sun, Zhi-bin Su, Yun-fen Feng

“…According to the linear vibration mode of tether, the partial differential equation is converted into ordinary differential equations by Galerkin method and the nonlinear vibration equation of tether for the in-plane first four modes and the out-of-plane first four modes are obtained. …”
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Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations by Meilan Qiu, Liquan Mei, Dewang Li

“…Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1) or second-order central difference method for (1<α<2), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. …”
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Pull-In and Snap-Through Analysis of Electrically Actuated Viscoelastic Curved Microbeam by Ehsan Akrami-Nia, Hamid Ekhteraei-Toussi

“…Integrodifferential governing equation of the curved viscoelastic microbeam is obtained by assuming modified couple stress theory and using Hamilton’s principle. By applying the Galerkin method, the obtained governing equation is discretized, converted to a nonlinear differential equation, and solved by MATLAB software. …”
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Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane by Mingyue Shao, Jimei Wu, Yan Wang, Qiumin Wu

“…The velocity is presumed as harmonic change that takes place over uniform average speed, and the nonlinear vibration equation of the axially moving membrane is inferred according to the D’Alembert principle and the von Kármán nonlinear thin plate theory. The Galerkin method is employed for discretizing the vibration partial differential equations. …”
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Numerical simulation and dynamical system for solving biomathematical model with optimal control by A.M.S. Mahdy, D.S. Mohamed

“…The SEIASqEqHR form is based on the Legendre-Galerkin method. The proposed number-based ways of doing things are fantastic. …”
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Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation by Yan-Lei Zhang, Hui-Rong Feng, Li-Qun Chen

“…The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. …”
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Modeling and Dynamical Behavior of Rotating Composite Shafts with SMA Wires by Yongsheng Ren, Qiyi Dai, Ruijun An, Youfeng Zhu

“…The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin method. The model incorporates the transverse shear, rotary inertia, and anisotropy of composite material. …”
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Nonlinear Dynamic Analysis of Macrofiber Composites Laminated Shells by Xiangying Guo, Dameng Liu, Wei Zhang, Lin Sun, Shuping Chen

“…The vibration mode-shape functions are obtained according to the boundary conditions, and then the Galerkin method is employed to transform partial differential equations into two nonlinear ordinary differential equations. …”
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Dynamic Characteristics of Blade with Viscoelastic Damping Block Based on Complex Eigenvalue Method by Jiao Wang, Yue-hao Zhang, Tao Yu, Qing-kai Han

“…The dynamical equation of the system is established and the Galerkin method is used to discretize the partial differential equations to a 3-DOF system so as to compute the dynamic natural frequencies and responses of the VE-blade. …”
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Size-Dependent Dynamic Behavior of Axially Moving Graphene Nanosheets Using Nonlocal First-Order Shear Deformation Theory by Huafeng Tian

“…Using Hamilton's principle, nonlinear equations governing motion are extracted and then discretized using the Galerkin method. Based on the numerical method, the dynamic response and vibration characteristics of these systems are determined. …”
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A numerical framework for simulating fluid-structure interaction phenomena by A. De Rosis, S. de Miranda, C. Burrafato, F. Ubertini

“…The lattice Boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the Time Discontinuous Galerkin method are adopted to predict structure dynamics. …”
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Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation by Luis Fernando Paullo Muñoz, Paulo B. Gonçalves, Ricardo A. M. Silveira, Andréa Silva

“…The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. …”
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Numerical Analysis Method considering Coupled Effects of THMC Multifields on Unsaturated Expansive Soil Subgrade Treated with Lime by Jie Liu, Pan Chen, Zheng Lu, Hailin Yao

“…The finite element discretization of the response model was implemented based on the Galerkin method. The processes of salt leaching and accumulating were analyzed in the numerical results. …”
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