Vibration of Timoshenko beams using non-classical elasticity theories

Article type: Research Article

Authors: Santos, J.V. Araújo dos | Reddy, J.N.

Affiliations: IDMEC/IST--Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, Portugal | Mechanical Engineering Department, Texas A&M University, TAMU, College Station, TX, USA

Note: [] Corresponding author. E-mail: viriato@ist.utl.pt

Abstract: This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theory results depend on the beam cross-sectional size while those of the nonlocal theory do not. Convergence of both non-classical theories to the classical theory is observed as the beam global dimension increases.

Keywords: Nonlocal elasticity theory, couple stress theory, Timoshenko beam, rotary inertia, free vibration

DOI: 10.3233/SAV-2011-0627

Journal: Shock and Vibration, vol. 19, no. 3, pp. 251-256, 2012