Unsteady Aerodynamic Modeling Based on POD-ARX by Xiaopeng Wang, Chen’an Zhang, Wen Liu, Famin Wang, Zhengyin Ye

“…The lack of stability is a problem encountered when applying the classical POD-Galerkin method to problems of unsteady compressible flows around a moving structure. …”
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Circular thin plates buckling analysis with HRPIM method by Baid Sokayna, Hilali Youssef, Mesmoudi Saïd, Bourihane Oussama

“…The governing partial differential equations are discretized using the Galerkin method and solved by combining a Taylor series expansion with a continuation procedure. …”
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A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid by Le Thi Phuong Ngoc, Truong Thi Nhan, Nguyen Thanh Long

“…In Part 1, we use the Galerkin method and compactness method to prove the existence of a unique weak solution of the problem above on (0,T), for every T>0. …”
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Nonlinear Dynamic Behavior of Winding Hoisting Rope under Head Sheave Axial Wobbles by Guoying Wang, Xingming Xiao, Chi Ma, Gang Cheng, Xiao Di

“…The governing equations are nonlinear infinite-dimensional partial differential equations, which are discretized into the finite-dimensional ordinary differential equations through the Galerkin method. The dynamic responses of the hoisting rope under the head sheave axial wobbles are given by MATLAB simulation when the winding hoist is lifting or lowering. …”
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Modeling and 1 : 1 Internal Resonance Analysis of Cable-Stayed Shallow Arches by Jiangen Lv, Zhicheng Yang, Xuebin Chen, Quanke Wu, Xiaoxia Zeng

“…Nonlinear dynamic responses of a cable-stayed shallow arch subjected to external excitations with simultaneous 1 : 1 internal resonances are investigated. Firstly, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equations. …”
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Theoretical Analysis and Experimental Validation on Galloping of Iced Transmission Lines in a Moderating Airflow by Bing Huo, Xuliang Li, Fujiang Cui, Shuo Yang

“…The partial differential equations of the iced transmission line are established based on the Hamilton theory. The Galerkin method is then applied on the continuous model, and a discrete model is derived along with its first two in-plane and torsional modes. …”
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A New Approach for Solving Rub-Impact Dynamic Characteristics of Shrouded Blades Based on Macroslip Friction Model by Guofang Nan, Jianyang Lou, Chuanchong Song, Min Tang

“…By means of the harmonic balance method, the friction force and the normal pressure are translated into the equivalent stiffness and the equivalent damping. The Galerkin method is adopted to reduce the dimension of the equation to obtain the 1-DOF equation of motion, and the dynamic response of the shrouded blade is solved by Runge–Kutta numerical method. …”
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Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect by Zhou Chen, Hongxin Lin, Deyuan Deng, Wanjie Xu, Hanwen Lu, Zepeng Chen

“…Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. …”
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Study on Electroosmosis Consolidation of Punctiform Electrode Unit by Xiaoyu Yang, Yongbin Xie, Jianhua Dong, Guosheng Liu, Yalin Zheng

“…The electric potential field of the electrode unit and the finite element form of the electroosmotic consolidation equation are given by the Galerkin method. The PyEcFem finite-element numerical library is developed using Python programming to calculate. …”
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Simulation of cold storage process via Galerkin approach implementing nanoparticles by Wajdi Rajhi, Ali Basem, Ziyad Jamil Talabany, Hussein A.Z. AL-bonsrulah, Moaz Al-lehaibi, Ibrahim Ali Alsayer, Awatif M.A. Elsiddieg, Lioua Kolsi

“…The simulations, performed using the Galerkin method, include a dynamically adapted mesh to accurately track the solidification front. …”
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Method of formation of numerical projection-grid algorithm on basis of «three-dimensional regular element» for calculation of 3D-models of magnetic field in cylindrical coordinate... by A. A. Tatevosyan, E. G. Andreeva

“…The use of the «three-dimensional regular element» makes it possible to automate the process of forming a global system of linear algebraic equations in the projection-grid Galerkin method in combination with the finite element method bypassing the stage of constructing elemental systems of equations. …”
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Non-local piezoelasticity to incorporate the influence of small-scale factors on the resonance behavior of the Mindlin piezoelectric polymeric nanoplates by Narinderjit Singh Sawaran Singh, Waqed H. Hassan, Zainab Mоhammed Ameen Ahmed, Younis Mohamed Atiah Al-zahy, Soheil Salahshour, Mostafa Pirmoradian

“…By employing a variational approach to derive the governing equations, this work advances the understanding of how various parameters such as the non-local parameter, dimensions of the nanoplate, excitation voltage, and mass of the nanoparticle affect resonance frequencies. The Galerkin method is utilized to solve the partial differential equations governing the dynamics of the piezoelectric polymeric nanoplate, marking a significant methodological contribution to the field. …”
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A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements by A. A. Soliman

“…Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. …”
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