Robust identification of material model by means of forced sinusoidal excitation measurements

Robust identification of material model by means of forced sinusoidal excitation measurements Dynamic Mechanical Analysis (DMA) test instruments are commonly employed to identify the mechanical behaviour of materials at different temperatures and frequencies. In a typical dynamic measurement, a sinusoidal excitation is applied to a beam specimen of known geometry and the displacement response is obtained. The DMA output can be processed to obtain the D(ω) material stress (σ) versus strain (ε) relationship, i.e. σ (ω)=D(ω)× ε (ω), by means of the Timoshenko or Euler Bernoulli beam model assumption. Nevertheless, the approach shows some limitations since these model assumptions do not take into account of the many other factors influencing the measurement output: the effective boundary conditions, the structural instrument frame model coupling, the inertial and dissipative contribution of the excitation moving substructure, so that a multi-DOF (MDOF) system results. Many techniques are known for identifying a MDOF system model typically requiring measurements being done in some experimental DOFs, and requiring data not directly available from within the typical DMA set-up, so that an additional test measurement system is needed, being not synchronized with the DMA measurements. Some calibration procedures are commonly proposed by the many commercial instrument firms, but the related accuracy is generally poor, as it is shown in this work in some identification examples related to a harmonic steel specimen. This work deals with specimens in the form of slender, uniform, homogeneous beams with clamped double pendulum boundary conditions excited by means of a sinusoidal flexural force at different frequencies at the mobile free beam end, where both excitation and displacement response are measured at the same time, i.e. in the single cantilever experimental set-up. A single experimental DOF is measured with respect to both input and output, frequency range [0.01-200] Hz. In this work a calibration technique for dynamic mechanical analysis (DMA) experimental systems, using only data obtained from tests made within the commercially available instrument itself, is adopted and it is shown as a part of the identification procedure. The calibration technique is based on an optimisation algorithm and deals with the identification of a 2 DOFs frame model coupled to the specimen beam model by using as input the single beam DOF force and displacement measurements made on some reference uniform specimens. The aim is to obtain measurement estimates being filtered from the contribution of the experimental system. The robustness of the proposed technique is tested on some numerical model cases with added noise. A sensitivity based numerical technique is also proposed to evaluate the contribution of each identification unknown during the optimisation process. The technique is applied to some dynamical measurements made on material specimens whose model is known in advance and then to some non standard material configurations. The technique is also applied on two DMA systems made by two different manufacturers. The results are shown and critically discussed.