Damping analysis of partially covered sandwich beams

Rayleigh-Ritz Analysis of Sandwich Beams

“…For a correct evaluation of integrals (6), and the following calculation of modes, some care has to be taken in the choice of the admissible functions G and G . Polynomials, as proposed in reference [14], have been used in this work, as summarized in Table 1.…”

“…Of course, the powers , , and depend on the coe$cients k, i, r and s in equation (6). The implementation of the second formula is much slower than the "rst, but shown to be necessary when numerical simulations were carried out, for various boundary conditions, for admissible functions in the form [14] G " K>G(1!…”

“…Some of the results collected in reference [6], namely, Problem II, and regarding simply supported conditions, are shown in Table 3.…”

“…&&Markus method'' indicates the values obtained by implementing the method proposed in reference [15], &&Rayleigh}Ritz method'' indicates the values obtained by implementing the method proposed in reference [6] (transverse displacement is modelled with a sum of sinusoidal functions), &&Cum-search method'' indicates the values obtained by solving a sixth order di!erential equation [7], &&Conventional method'' indicates the values obtained by implementing the method proposed in reference [16]. The correspondence is excellent for loss factor estimations, whilst some percent di!erences exist for frequencies.…”

Explicit solution for the natural frequency of structures with partial viscoelastic treatment

“…Thus, the design of viscoelastic treatment for damping of flexible structures requires an accurate estimation of the damping level, which again requires the solution of the full eigenvalue problem in state-space with relaxation properties governed by additional state variables or by an iterative procedure with a frequency dependent dynamic stiffness matrix [1,2].…”