Free vibration of curved sandwich beams by the method of finite elements

Free Vibration Analysis of Curved Sandwich Beams: A Dynamic Finite Element

“…In the late 1960s, pioneering works in the field of vibration analysis of viscously damped sandwich beams (Di Taranto, 1965, andMead andMarcus, 1968) used classical methods to solve the governing differential equations of motion, leading to the natural frequencies and mode shapes of the system. Ahmed (1971) applied the finite element method (FEM) to a curved sandwich beam with an elastic core and performed a comparative study of several different formulations in order to compare their performances in determining the natural frequencies and mode shapes for various different beam configurations. Interest in the vibration behaviour of sandwich beams has seen resurgence in the past decade with the availability of more powerful computing systems.…”

“…The simplest sandwich beam model utilizes Euler-Bernoulli theory for the face layers and only allows the core to deform only in shear. This assumption has been widely used in several DSM and FEM studies such as those by Banerjee (2003), Ahmed (1971Ahmed ( ,1972, Mead and Markus (1968), Fasana and Marchesiello (2001), Baber et al (1998), and in earlier papers by the authors; see e.g., Adique & Hashemi (2007), and . In more recent publications, Banerjee derived two new DSM models which exploit more complex displacement fields.…”

“…In the this Chapter, we derive a DFE formulation for the free vibration analysis of curved sandwich beams and test it against FEM and DSM to show that DFE is another viable tool for structural vibration analysis. The face layers are assumed to behave according to EulerBernoulli theory and the core deforms in shear only, as was also studied by Ahmed (1971Ahmed ( ,1972. The authors have previously developed DFE models for two straight, 3-layered, sandwich beam configurations; a symmetric sandwich beam, where the face layers are assumed to follow Euler-Bernoulli theory and core is allowed to deform in shear only Hashemi, 2007, andHashemi &, and a more general nonsymmetric model, where the core layer of the beam behaves according to Timoshenko theory while the faces adhere to Rayleigh beam theory (Adique & Hashemi, 2008).…”

“…1. Coordinate system and notation for curved symmetric three-layered sandwich beams For the beam model developed, the following assumptions made (Ahmed, 1971):…”

The Shock and Vibration Digest. Volume 9, Number 2. February 1977

“…One of the few recent successful 12 (large W/Wa, Wa = k2/I2). efforts to apply the pendulum damper involved a helicopter rotor [3]. Vibration of such rotors inTorsional isolators for rotating machinery take the cludes both translational and torsional modes.…”