Measurement of relevant elastic and damping material properties in sandwich thick plates

Abstract

An easy-to-implement method to measure relevant elastic and damping properties of the constituents of a sandwich structure, possibly with a heterogeneous core, is proposed. The method makes use of a one-point dynamical measurement on a thick plate. The hysteretic model for each (possibly orthotropic) constituent is written generically as "E(1 + jη)" for all mechanical parameters. The estimation method of the parameters relies on a mixed experimental / numerical procedure. The frequencies and dampings of the natural modes of the plate are obtained from experimental impulse responses by means of a high-resolution modal analysis technique. This allows for considerably more experimental data to be used. Numerical modes (frequencies, dampings, and modal shapes) are computed by means of an extended Rayleigh-Ritz procedure under the "light damping" hypothesis, for given values of the mechanical parameters. Minimising the differences between the modal characteristics yields an estimation of the values of the mechanical parameters describing the hysteretic behaviour. A sensitivity analysis assess the reliability of the method for each parameter. Validations of the method are proposed by (a) applying it to virtual plates on which a finite-element model replaces the experimental modal analysis, (b) some comparisons with results obtained by static mechanical measurements, and (c) by comparing the results on different plates made of the same sandwich material.

Identification of material properties of composite materials using nondestructive vibrational evaluation approaches: A review

“…In practice, the Rayleigh-Ritz method is said to be applicable to all plate problems, linear or nonlinear, since the principle of virtual displacements applies to all plate problems [100]. The application of Rayleigh-Ritz technique for forward computation of natural frequencies in the study of elastic properties determination can be seen in [57,63,65,67,68,[101][102][103][104][105]. Most of the investigations are done on thin rectangular orthotropic plates [57, 63, 101-103, 105, 106], followed by thin rectangular laminated plates [65,67] and thick rectangular Sandwich plates [68,104] with combinations of free-clamped edges [57,63], free edges [101][102][103][104][105][106], and elastically-restrained edges [65,67,68].…”

“…For problems with boundary conditions other than simple support or for problems involving generally orthotropic laminates, the application of trigonometric series is complicated. Thus, polynomial series came into existence and have been extensively used in computing the natural frequencies of plates due to its straightforward algebraic manipulation [65,67,68,104,107]. The use of this series is limited in the mid-1980s due to complication in setting up series compromising the geometric boundary conditions.…”

“…and Boutillon [104] used basic orthogonal polynomials similar to reference [107] to estimate the resonant frequencies of thick Sandwich plate with free-free boundary condition. In [107], the characteristic orthogonal polynomials was proven providing good results for lower modes in free-edged plates.…”

Optimization of the Effective Shear Properties of a Bidirectionally Corrugated Sandwich Core Structure

“…addition to the shear lap test, we performed eigenfrequency measurements and used the identification method of Rébillat and Boutillon [22] to determine the shear modulus. However, as for the shear lap test, no satisfactory results could be obtained since the shear deformation of the core structure contributed only little to the overall deflection of the vibrating sandwich plate.…”

Nonparametric Identification of Nonlinear Systems in Series

“…Most of identification methods of Hammerstein or Wiener systems are based on parametric models [4], which means that each unknown linear filter G n (f ) is modeled by a parametric frequency response function (FRF) model such as ARMA structure. However, a non-parametric method based on exponential swept-sine input signal x(t) and nonlinear convolution has been proposed in [5] and [6] for the estimation of the modulus |G n (f )|, and recently extended to the estimation of both the modulus and the phase of G n (f ) through the synchronization of the excitation swept sine signal [7], [8]. This method, called Synchronized Swept-Sine Method in this paper, has been successfully applied to the study of various nonlinear systems [9], [10], [8].…”