{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZOPH3O33B5SF44DAEPLYJNWVF4","short_pith_number":"pith:ZOPH3O33","schema_version":"1.0","canonical_sha256":"cb9e7dbb7b0f645e706023d784b6d52f1ba7d31dae108867b1b9f0ca5aa38e82","source":{"kind":"arxiv","id":"1210.6607","version":2},"attestation_state":"computed","paper":{"title":"Wave dispersion under finite deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP"],"primary_cat":"math-ph","authors_text":"Mahmoud I. Hussein, Mohammad H. Abedinnasab","submitted_at":"2012-10-24T17:04:27Z","abstract_excerpt":"We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green-Lagrange strain. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed methodology, however, is applicable to problems th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.6607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-24T17:04:27Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP"],"title_canon_sha256":"dc71884a2a3b0712302fc9f90bd36170366ca77952a32f018a3a9bfb0f7087a3","abstract_canon_sha256":"0d20eb2966f2f86ef0d056321d71527478dad4e9552a1e41e4a16a4293457d40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:32.534186Z","signature_b64":"OMEsGYRKMePELPkHEiRtksWAuWgLCTHP9hJmflF8mtli5UqyNBR72jmV+MGJVaXOP88xurTZ6id3l6Dik8h1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb9e7dbb7b0f645e706023d784b6d52f1ba7d31dae108867b1b9f0ca5aa38e82","last_reissued_at":"2026-05-18T03:27:32.533657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:32.533657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wave dispersion under finite deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP"],"primary_cat":"math-ph","authors_text":"Mahmoud I. Hussein, Mohammad H. Abedinnasab","submitted_at":"2012-10-24T17:04:27Z","abstract_excerpt":"We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green-Lagrange strain. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed methodology, however, is applicable to problems th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6607","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.6607","created_at":"2026-05-18T03:27:32.533751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6607v2","created_at":"2026-05-18T03:27:32.533751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6607","created_at":"2026-05-18T03:27:32.533751+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOPH3O33B5SF","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOPH3O33B5SF44DA","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOPH3O33","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4","json":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4.json","graph_json":"https://pith.science/api/pith-number/ZOPH3O33B5SF44DAEPLYJNWVF4/graph.json","events_json":"https://pith.science/api/pith-number/ZOPH3O33B5SF44DAEPLYJNWVF4/events.json","paper":"https://pith.science/paper/ZOPH3O33"},"agent_actions":{"view_html":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4","download_json":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4.json","view_paper":"https://pith.science/paper/ZOPH3O33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6607&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOPH3O33B5SF44DAEPLYJNWVF4/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOPH3O33B5SF44DAEPLYJNWVF4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4/action/storage_attestation","attest_author":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4/action/author_attestation","sign_citation":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4/action/citation_signature","submit_replication":"https://pith.science/pith/ZOPH3O33B5SF44DAEPLYJNWVF4/action/replication_record"}},"created_at":"2026-05-18T03:27:32.533751+00:00","updated_at":"2026-05-18T03:27:32.533751+00:00"}