{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T06:03:23Z","timestamp":1774505003917,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T00:00:00Z","timestamp":1587427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The sloshing behavior of systems is influenced by different factors related to the liquid level and tank specifications. Different approaches are applicable for the assessment of sloshing behavior in a tank. In this paper, a new numerical model based on the differential quadrature method and boundary element approaches is adopted to investigate the sloshing behavior of a tank with an elastic thin-walled beam. The model is developed based on small slope considerations of the free surface. The main assumption of fluid modeling is homogeneity, isotropy, inviscid, and only limited compressibility of the liquid. Indeed, the formulation is represented based on the reduced-order method and then is employed for simulating the coupling between structure and fluid in symmetric test cases. The results are verified with the ANSYS and literature for symmetric rigid structural walls and then the code is employed to study the behavior of fluid-structure interaction in a symmetric tank with new and efficient immersed structure.<\/jats:p>","DOI":"10.3390\/sym12040655","type":"journal-article","created":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T04:15:13Z","timestamp":1587528913000},"page":"655","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Numerical Modeling of Sloshing Frequencies in Tanks with Structure Using New Presented DQM-BEM Technique"],"prefix":"10.3390","volume":"12","author":[{"given":"Zhenda","family":"Wei","sequence":"first","affiliation":[{"name":"School of Economics and Management NJUST, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junwen","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Economics and Management NJUST, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8815-0852","authenticated-orcid":false,"given":"Mohammad","family":"Ghalandari","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Sharif University of Technology, P.O. Box 11155-8639, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5830-4934","authenticated-orcid":false,"given":"Akbar","family":"Maleki","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zahra","family":"Abdelmalek","sequence":"additional","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"Faculty of Medicine, Duy Tan University, Da Nang 550000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,21]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Numerical simulation of long wave runup for breaking and nonbreaking waves","volume":"25","author":"Shadloo","year":"2015","journal-title":"Int. J. Offshore Polar Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compfluid.2018.09.010","article-title":"A smoothed particle hydrodynamics approach for thermo-capillary flows","volume":"176","author":"Shadloo","year":"2018","journal-title":"Comput. Fluids"},{"key":"ref_3","unstructured":"Almasi, F., Shadloo, M.S., Hadjadj, A., Ozbulut, M., Tofighi, N., and Yildiz, M. (2019). Numerical simulations of multi-phase electro-hydrodynamics flows using a simple incompressible smoothed particle hydrodynamics method. Comput. Math. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"073101","DOI":"10.1115\/1.4039327","article-title":"Modified extended finite element methods for gas flow in fractured reservoirs: A pseudo-pressure approach","volume":"140","author":"Jiang","year":"2018","journal-title":"J. Energy Resour. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"051204","DOI":"10.1115\/1.4042414","article-title":"Design and optimization of composite offshore wind turbine blades","volume":"141","author":"Tarfaoui","year":"2019","journal-title":"J. Energy Resour. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, N., Maleki, A., Alhuyi Nazari, M., Tlili, I., and Safdari Shadloo, M. (2020). Thermal conductivity modeling of nanofluids contain MgO particles by employing different approaches. Symmetry, 12.","DOI":"10.3390\/sym12020206"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Abdelmalek, Z., Alamian, R., Shadloo, M.S., Maleki, A., and Karimipour, A. (2020). Numerical study on the performance of a homogeneous charge compression ignition engine fueled with different blends of biodiesel. J. Therm. Anal. Calorim., 1\u201311.","DOI":"10.1007\/s10973-020-09513-1"},{"key":"ref_8","first-page":"1","article-title":"The dynamic behavior of liquids in moving containers. NASA SP-106","volume":"106","author":"Abramson","year":"1966","journal-title":"NASA Spec. Publ."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ibrahim, R.A. (2005). Liquid Sloshing Dynamics: Theory and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511536656"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Jamalabadi, M.Y.A., Ho-Huu, V., and Nguyen, T.K. (2018). Optimal design of circular baffles on sloshing in a rectangular tank horizontally coupled by structure. Water, 10.","DOI":"10.3390\/w10111504"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1016\/S0955-7997(03)00046-8","article-title":"Evaluation of sloshing problem by variational boundary element method","volume":"27","author":"Gedikli","year":"2003","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1016\/j.finel.2010.07.001","article-title":"Dynamic response of structure coupled with liquid sloshing in a laminated composite cylindrical tank with baffle","volume":"46","author":"Biswal","year":"2010","journal-title":"Finite Elem. Anal. Des."},{"key":"ref_13","unstructured":"Scholl, H.F., and Stephens, D.G. (1967). Effectiveness of Flexible and Rigid Ring Baffles for Damping Liquid Oscillations in Large-Scale Cylindrical Tanks."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF00042849","article-title":"Resonant frequencies of a fluid in containers with internal bodies","volume":"25","author":"Watson","year":"1991","journal-title":"J. Eng. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/0045-7949(96)00084-3","article-title":"Sloshing characteristics in rectangular tanks with a submerged block","volume":"61","author":"Choun","year":"1996","journal-title":"Comput. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1002\/(SICI)1096-9845(199907)28:7<763::AID-EQE841>3.0.CO;2-W","article-title":"Sloshing analysis of rectangular tanks with a submerged structure by using small-amplitude water wave theory","volume":"28","author":"Choun","year":"1999","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.jsv.2007.03.014","article-title":"Slosh dynamics of liquid-filled containers with submerged components using pressure-based finite element method","volume":"304","author":"Mitra","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0022-247X(71)90110-7","article-title":"Differential quadrature and long-term integration","volume":"34","author":"Bellman","year":"1971","journal-title":"J. Math. Anal. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, Z., Hu, T., Tao, Y., Zhang, T., and Li, Z. (2019). Fast calculation method for transient response of transmission line based on chebyshev pseudospectral\u2013two-step three-order boundary value coupled method. Symmetry, 11.","DOI":"10.3390\/sym11050721"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0020-7683(97)00073-5","article-title":"Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method","volume":"35","author":"Malik","year":"1998","journal-title":"Int. J. Solids Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0263-8231(88)90025-0","article-title":"Nonlinear bending analysis of thin circular plates by differential quadrature","volume":"6","author":"Striz","year":"1988","journal-title":"Thin-Walled Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1002\/nme.1620280306","article-title":"Application of differential quadrature to static analysis of structural components","volume":"28","author":"Jang","year":"1989","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_23","first-page":"99","article-title":"In-Plane Extensional Vibration Analysis of Curved Beams Using DQM","volume":"17","author":"Kang","year":"2002","journal-title":"J. Korean Soc. Saf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s12205-014-0278-8","article-title":"Analysis of stressed Timoshenko beams on two parameter foundations","volume":"19","author":"Hassan","year":"2015","journal-title":"Ksce J. Civ. Eng."},{"key":"ref_25","first-page":"804","article-title":"Flutter speed estimation using presented differential quadrature method formulation","volume":"13","author":"Ghalandari","year":"2019","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_26","first-page":"254","article-title":"Numerical simulation of nanofluid flow inside a root canal","volume":"13","author":"Ghalandari","year":"2019","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_27","first-page":"892","article-title":"Mechanics Aeromechanical optimization of first row compressor test stand blades using a hybrid machine learning model of genetic algorithm, artificial neural networks and design of experiments","volume":"13","author":"Ghalandari","year":"2019","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.ijheatmasstransfer.2018.06.108","article-title":"Numerical simulation of PV cooling by using single turn pulsating heat pipe","volume":"127","author":"Alizadeh","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zarandi, S., Lai, H.-W., Wang, Y.-C., and Aizikovich, S. (2019). Residual stress analysis of an orthotropic composite cylinder under thermal loading and unloading. Symmetry, 11.","DOI":"10.3390\/sym11030320"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"052907","DOI":"10.1115\/1.4038845","article-title":"A general boundary integral solution for fluid flow analysis in reservoirs with complex fracture geometries","volume":"140","author":"Zhang","year":"2018","journal-title":"J. Energy Resour. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Christensen, E., Brunty, J., Christensen, E., and Brunty, J. (1997, January 7\u201310). Launch vehicle slosh and hydroelastic loads analysis using the boundary element method. Proceedings of the 38th Structures, Structural Dynamics, and Materials Conference, Kissimmee, FL, USA.","DOI":"10.2514\/6.1997-1036"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1002\/(SICI)1097-0207(20000330)47:9<1633::AID-NME851>3.0.CO;2-1","article-title":"Analysis of the small amplitude sloshing of a liquid in a rigid container of arbitrary shape using a low-order boundary element method","volume":"47","author":"Dutta","year":"2000","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1002\/nme.1620171105","article-title":"The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems","volume":"17","author":"Nakayama","year":"1981","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"135","DOI":"10.2534\/jjasnaoe1968.2000.188_135","article-title":"Multiple domain boundary element method applied to fluid motions in a tank with internal structure","volume":"2000","author":"Zhu","year":"2000","journal-title":"J. Soc. Nav. Archit. Jpn."},{"key":"ref_35","first-page":"519","article-title":"Investigation frequencies of elastic submerged structure on sloshing","volume":"13","author":"Ghalandari","year":"2019","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_36","first-page":"1","article-title":"Effects of nanoparticle enhanced lubricant films in thermal design of plain journal bearings at high reynolds numbers","volume":"11","author":"Jamalabadi","year":"2019","journal-title":"Symmetry"},{"key":"ref_37","first-page":"519","article-title":"Investigation of submerged structures flexibility on sloshing frequency using a boundary element method and finite element analysis","volume":"13","author":"Ghalandari","year":"2019","journal-title":"Eng. Appl. Comput. Fluid Mech."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/655\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:45:07Z","timestamp":1760363107000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,21]]},"references-count":37,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["sym12040655"],"URL":"https:\/\/doi.org\/10.3390\/sym12040655","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,21]]}}}