{"doi":"10.1115/1.4052286","title":"Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Beams","abstract":"Abstract Fractional models and their parameters are sensitive to intrinsic microstructural changes in anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we study the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelasticity is described by a distributed-order fractional model. We employ Hamilton's principle to obtain the equation of motion with the choice of specific material distribution functions that recover a fractional Kelvin–Voigt viscoelastic model of order α. Through spectral decomposition in space, the resulting time-fractional partial differential equation reduces to a nonlinear time-fractional ordinary differential equation, where the linear counterpart is numerically integrated through a direct L1-difference scheme. We further develop a semi-analytical scheme to solve the nonlinear system through a method of multiple scales, yielding a cubic algebraic equation in terms of the frequency. Our numerical results suggest a set of α-dependent anomalous dynamic qualities, such as far-from-equilibrium power-law decay rates, amplitude super-sensitivity at free vibration, and bifurcation in steady-state amplitude at primary resonance.","journal":"Journal of Computational and Nonlinear Dynamics","year":2021,"id":186222,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":24,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9528,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":743551,"name":"Ehsan Kharazmi","orcid":"0000-0002-3680-5500","position":1,"is_corresponding":false},{"id":744206,"name":"Pegah Varghaei","orcid":null,"position":2,"is_corresponding":false},{"id":361108,"name":"Maryam Naghibolhosseini","orcid":"0000-0002-7310-8456","position":3,"is_corresponding":false},{"id":743552,"name":"Mohsen Zayernouri","orcid":"0000-0002-0831-2610","position":4,"is_corresponding":false},{"id":743550,"name":"Jorge L. Suzuki","orcid":"0000-0002-3003-3685","position":0,"is_corresponding":true}],"reference_count":70,"raw_metadata":null,"created_at":"2026-07-18T23:48:42.632147Z","pmid":"35832656","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}