{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T01:14:30Z","timestamp":1780535670736,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T00:00:00Z","timestamp":1761264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Lattice structures find broad application in aerospace, automotive, biomedical, and energy systems owing to their exceptional structural stability. These systems typically exhibit complex internal couplings that facilitate vibration propagation across the entire network. The primary objective of this study is to achieve total decoupling of 2D lattice vibration system, which involves eliminating all inter-subsystem interactions while preserving spectrum. Building upon prior research, we develop structure-preserving isospectral transformation flow (SPITF) framework to address this challenge. Two principle results are established: first, the equations of motion are systematically derived for lattice vibration systems; second, total decoupling is successfully realized for such systems. Numerical experiments validate the decoupling capability of lattice vibration systems.<\/jats:p>","DOI":"10.3390\/axioms14110781","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T03:44:39Z","timestamp":1761795879000},"page":"781","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Total Decoupling of 2D Lattice Vibration"],"prefix":"10.3390","volume":"14","author":[{"given":"Nan","family":"Jiang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"},{"name":"College of Forestry, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qizhi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianwei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1137\/S0036144500381988","article-title":"The quadratic eigenvalue problem","volume":"43","author":"Tisseur","year":"2001","journal-title":"SIAM Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jsv.2007.05.052","article-title":"Total decoupling of general quadratic pencils, partII: Structure preserving isospectral flows","volume":"309","author":"Chu","year":"2008","journal-title":"J. Sound Vib."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1115\/1.3643949","article-title":"Classical normal modes in damped linear dynamic system","volume":"27","author":"Caughey","year":"1960","journal-title":"J. Appl. Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1016\/j.ymssp.2008.11.007","article-title":"Diagonalizable quadratic eigenvalue problems","volume":"23","author":"Lancaster","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0888-3270(03)00048-7","article-title":"Optimal complex modes and an index of damping non-proportionality","volume":"18","author":"Adhikari","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1115\/1.2930112","article-title":"Frequency response of non-proportionally damped, lumped parameter, linear dynamic systems","volume":"112","author":"Bellos","year":"1990","journal-title":"J. Vib. Acoust."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0022-460X(86)80134-1","article-title":"Quantification of the extent of non-proportional viscous damping in discrete vibratory systems","volume":"104","author":"Prater","year":"1986","journal-title":"J. Sound Vib."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/S0045-7949(99)00230-8","article-title":"Identification of non-proportionality of damping in discrete vibratory systems","volume":"77","author":"Liu","year":"2000","journal-title":"Comput. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1006\/mssp.2000.1326","article-title":"Evaluation of damping non-proportionality using identified modal information","volume":"15","author":"Liu","year":"2001","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1006\/jsvi.1994.1554","article-title":"An index of damping non-proportionality for discrete vibrating systems","volume":"174","author":"Tong","year":"1994","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lancaster, P., Sneddon, I.N., Stark, M., and Kahane, J.P. (1966). Lambda-Matrices and Vibrating System, Pergamon Press.","DOI":"10.1016\/B978-0-08-011664-8.50008-0"},{"key":"ref_12","unstructured":"Gohberg, I., Lancaster, P., and Rodman, L. (1982). Matrix Polynomials, Academic Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1145\/2450153.2450156","article-title":"An algorithm for the complete solution of quadratic eigenvalue problems","volume":"39","author":"Hammarling","year":"2013","journal-title":"ACM Trans. Math. Softw."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.jsv.2009.02.005","article-title":"The decoupling of damped linear systems in oscillatory free vibration","volume":"324","author":"Ma","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3182","DOI":"10.1016\/j.jsv.2010.02.017","article-title":"The decoupling of damped linear systems in free or forced vibration","volume":"329","author":"Ma","year":"2010","journal-title":"J. Sound Vib."},{"key":"ref_16","first-page":"583","article-title":"Classical normal modes in damped linear dynamic system","volume":"32","author":"Caughey","year":"1965","journal-title":"ASCE J. Appl. Mehcanics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jsv.2019.01.009","article-title":"Structure-Preserving Isospectral Transformation for Total or Partial Decoupling of Self-Adjoint Quadratic Pencils","volume":"449","author":"Jiang","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"109283","DOI":"10.1016\/j.ijmecsci.2024.109283","article-title":"Full-band vibration isolation and energy absorption via cuttlebone-inspired lattice structures","volume":"274","author":"Wang","year":"2024","journal-title":"Int. J. Mech. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1103\/RevModPhys.73.515","article-title":"Phonons and related crystal properties from density-functional perturbation theory","volume":"73","author":"Baroni","year":"2001","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.1016\/j.cpc.2014.02.015","article-title":"ShengBTE: A solver of the Boltzmann transport equation for phonons","volume":"185","author":"Li","year":"2014","journal-title":"Comput. Phys. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1002\/nme.6866","article-title":"Infill topology and shape optimization of lattice-skin structures","volume":"123","author":"Xiao","year":"2022","journal-title":"Int. J. Methods Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117642","DOI":"10.1016\/j.compstruct.2023.117642","article-title":"Vibration characteristics of additive manufactured IWP-type TPMS lattice structures","volume":"327","author":"Zhang","year":"2024","journal-title":"Compos. Struct."},{"key":"ref_23","first-page":"2495","article-title":"Micro-architectured materials: Past, present and future","volume":"466","author":"Fleck","year":"2010","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gibson, I., Rosen, D.W., and Stucker, B. (2014). Additive Manufacturing Technologies, Springer.","DOI":"10.1007\/978-1-4939-2113-3"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1038\/s41563-023-01500-9","article-title":"Single-atom vibrational spectroscopy with chemical-bonding sensitivity","volume":"22","author":"Zhou","year":"2023","journal-title":"Nat. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1038\/s41563-020-0798-1","article-title":"Mechanically robust lattices inspired by deep-sea glass sponges","volume":"20","author":"Fernandes","year":"2020","journal-title":"Nat. Mater."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1038\/nature04586","article-title":"Folding DNA to create nanoscale shapes and patterns","volume":"440","author":"Rothemund","year":"2006","journal-title":"Nature"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"8239","DOI":"10.1038\/s41467-023-43947-z","article-title":"A microscopic Kondo lattice model for the heavy fermion antiferromagnet CeIn3","volume":"14","author":"Simeth","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_29","unstructured":"Timoshenko, S.P., and Goodier, J.N. (1951). Theory of Elasticity, McGraw-Hill. [3rd ed.]."},{"key":"ref_30","unstructured":"Spanos, P.T.D. (1976). Linearization Techniques for Non-Linear Dynamical Systems. [Ph.D. Thesis, California Institute of Technology]."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"21","DOI":"10.13001\/1081-3810.1246","article-title":"Linearization of regular matrix polynomials","volume":"17","author":"Lancaster","year":"2008","journal-title":"Electron. J. Linear Algebra"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1006\/jsvi.2002.5165","article-title":"Co-ordinate tranfromations for second order systems, I: General transformations","volume":"258","author":"Garvey","year":"2002","journal-title":"J. Sound Vib."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S1064827594276424","article-title":"The MATLAB ODE suite","volume":"18","author":"Shampine","year":"1997","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/11\/781\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T03:59:58Z","timestamp":1761796798000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/11\/781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,24]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["axioms14110781"],"URL":"https:\/\/doi.org\/10.3390\/axioms14110781","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,24]]}}}