Applicatin of Krein's method for determination of natural frequencies of periodically supported beam based on simplified Bresse-Timoshenko equations

DOI10.1007/BF01184284zbMath0606.73070OpenAlexW1983741417MaRDI QIDQ1084938

B. George

Publication date: 1987

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01184284

zbMATH Keywords

natural frequenciesrotary inertiaFree vibrationshear deformationsApproximate differential equationscontinuity requirementsdifferent boundary conditions at their endsequations in finite differencesKrein's methodmultispanperiodically spaced bandsperiodically supportedsimplified Bresse- Timoshenko theorythree-, five- and ten-span beams

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45)

Related Items (13)

Issues related to the second spectrum, Ostrogradsky's energy and the stabilization of Timoshenko-Ehrenfest-type systems ⋮ A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory ⋮ Impact of the damaging consequences of the second spectrum on the stabilization of nonlinear Timoshenko systems ⋮ Buckling mode localization in a multi-span periodic structure with a disorder in a single span ⋮ An investigation on the nonlinear free vibration analysis of beams with simply supported boundary conditions using four engineering theories ⋮ A new scenario for stability of nonlinear Bresse‐Timoshenko type systems with time dependent delay ⋮ Vibration analysis of a new type of compliant mechanism with flexible-link, using perturbation theory ⋮ Existence of attractors for a nonlinear Timoshenko system with delay ⋮ Application of the homotopy method for the analytic approach of the nonlinear free vibration analysis of the simple end beams using four engineering theories ⋮ Unnamed Item ⋮ Transfer matrix method for the determination of the natural vibration characteristics of realistic thrusting launch vehicle -- part I ⋮ A nonlinear Timoshenko beam formulation based on the modified couple stress theory ⋮ On the nature of dissipative Timoshenko systems at light of the second spectrum of frequency

Cites Work

• Some closed-form solutions in random vibration of Bernoulli-Euler beams
• A brief survey of transfer matrix techniques with special reference to the analysis of aircraft panels
• Natural frequencies of continuous Timoshenko beams
• Unnamed Item

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