?url_ver=Z39.88-2004&rft_id=arXiv%3A1608.01077&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3665%2F&rft.title=Optimal+design+of+low-frequency+band+gaps+in+anti-tetrachiral+lattice+meta-materials&rft.creator=Bacigalupo%2C+Andrea&rft.creator=Gnecco%2C+Giorgio&rft.creator=Lepidi%2C+Marco&rft.creator=Gambarotta%2C+Luigi&rft.subject=QA75+Electronic+computers.+Computer+science&rft.subject=T+Technology+(General)&rft.description=The+elastic+wave+propagation+is+investigated+in+the+beam+lattice+material+characterized+by+a+square+periodic+cell+with+anti-tetrachiral+microstructure.+With+reference+to+the+Floquet-Bloch+spectrum%2C+focus+is+made+on+the+band+structure+enrichments+and+modifications+which+can+be+achieved+by+equipping+the+cellular+microstructure+with+tunable+local+resonators.+By+virtue+of+its+composite+mechanical+nature%2C+the+so-built+inertial+meta-material+gains+enhanced+capacities+of+passive+frequency-band+filtering.+Indeed+the+number%2C+placement+and+properties+of+the+inertial+resonators+can+be+designed+to+open%2C+shift+and+enlarge+the+band+gaps+between+one+or+more+pairs+of+consecutive+branches+in+the+frequency+spectrum.+In+order+to+improve+the+meta-material+performance%2C+a+nonlinear+optimization+problem+is+formulated.+The+maximum+of+the+largest+band+gap+amplitudes+in+the+low-frequency+range+is+selected+as+suited+objective+function.+Proper+inequality+constraints+are+introduced+to+restrict+the+optimal+solutions+within+a+compact+set+of+mechanical+and+geometric+parameters%2C+including+only+physically+realistic+properties+of+both+the+lattice+and+resonators.+The+optimization+problems+related+to+full+and+partial+band+gaps+are+solved+independently%2C+by+means+of+a+globally+convergent+version+of+the+numerical+method+of+moving+asymptotes%2C+combined+with+a+quasi-Monte+Carlo+multi-start+technique.+The+optimal+solutions+are+discussed+and+compared+from+the+qualitative+and+quantitative+viewpoints%2C+bringing+to+light+the+limits+and+potential+of+the+meta-material+performance.+The+clearest+trends+emerging+from+the+numerical+analyses+are+pointed+out+and+interpreted+from+the+physical+viewpoint.+Finally%2C+some+specific+recommendations+about+the+microstructural+design+of+the+meta-material+are+synthesized.&rft.publisher=arXiv&rft.date=2016&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F3665%2F1%2F1608.01077.pdf&rft.identifier=++Bacigalupo%2C+Andrea+and+Gnecco%2C+Giorgio+and+Lepidi%2C+Marco+and+Gambarotta%2C+Luigi++Optimal+design+of+low-frequency+band+gaps+in+anti-tetrachiral+lattice+meta-materials.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fabs%2F1608.01077&rft.relation=arXiv%3A1608.01077