Vibration Analysis of a Damped Arch Using an Iterative Laminate Model

A harmonic balance method for the non-linear vibration of viscoelastic shells

“…The aim of this section is to get approximate solutions of the non-linear problem (1). As a first approximation, the solution is assumed to be harmonic in time and almost parallel to a single mode in space with an arbitrary complex amplitude.…”

“…In the linear range, the damping properties are characterized by two modal parameters which are the frequency and the loss factor. Several analytical and numerical works have been developed to determine these quantities in the linear vibration analysis of viscoelastic shells [1]. In the case of non-linear viscoelastic structures, only a few investigations have been devoted to take into account the non-linear geometrical effects.…”

Uncertainty propagation and experimental verification of nonlinear viscoelastic sandwich beams

“…However, the resolution of the equations of motion for structures with viscoelastic materials are relevant aspects to be considered, since their mechanical properties depends on frequency and operation temperature [4]. This is a reason for which linear vibrations analyses of viscoelastically-damped systems have been performed [5][6][7] for the purposes of vibration attenuation. However, due to the frequent occurrence of large displacements in most of the practical applications of CVLs, the vibrations induced by the geometric nonlinearities differ significantly from those of linear approaches [8], and a nonlinear modeling is found to be necessary.…”

Non-linear vibrations of sandwich viscoelastic shells

“…Several procedures have been developed to determine these quantities. Analytical methods were devoted to simple structures [1][2][3][4][5][6][7][8][9][10], and numerical ones using finite element simulations were introduced to design structures with complex geometries and generic boundary conditions [11][12][13][14][15][16][17][18][19][20][21][22]. The simplest technique is the modal strain energy method used by Ma and He [12], which defines a rather good estimate of the loss factor from a sort of one-mode Galerkin approximation.…”