Rayleigh-Ritz Analysis of Sandwich Beams

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

“…This has allowed for more complex finite element models to be developed. Sainsbury and Zhang (1999), Baber et al (1998), and Fasana and Marchesiello (2001) are just some among many researchers who investigated FEM application in the analysis of visco-elastically damped sandwich beams. The Dynamic Stiffness Method (DSM), which employs symbolic computation to combine all the governing differential equations of motion into a single ordinary differential equation, has also been well established.…”

“…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.…”

A Quasi-Exact Dynamic Finite Element for Free Vibration Analysis of Sandwich Beams

“…This model has been used by many other researchers [1,3] and has provided an important basis for further development of the subject. It has also been extended to viscoelastic core, by simply assigning a complex value to the shear modulus of the core in the formulation (see, for example, [4,8,9] for further literature reviews).…”

“…They used the analytical solution methods to determine the natural frequencies and modes of the system. The solutions based on conventional Finite Element Methods (FEM) have also been proposed [5][6][7][8]. Banerjee [9] developed an 'exact' dynamic stiffness matrix (DSM) to solve the free vibration problem of sandwich beams, where the beam was allowed to deflect laterally only.…”

“…The modelling the dynamics of layered beams has been implemented using different methods and the research interest in this area has led to various publications [2][3][4][5][6][7][8][9][10][11][12]. Di Taranto [1], Plantema [2] and Mead and Marcus [3] are among the first investigators who studied the free vibration problems of sandwich beams, with proper attention to the shear between layers.…”