Degrees Of Freedom In Distribution Research Articles

Model updating of uncertain parameters of carbon/epoxy composite plates using digital image correlation for full-field vibration measurement

Model updating is usually based on the contrast between the modal characteristics predicted by the models and those experimentally identified. Traditional experimental methods are based on the use of contacting sensors, but more recently other techniques as 3D Digital Image Correlation (DIC) have also been used successfully. In this paper the results obtained by applying these alternative techniques are compared, to obtain physically-sound models of carbon/epoxy composite plates. Primarily a roving hammer exciting the plates at evenly distributed degrees of freedom (DoF), and a mono-axial accelerometer attached to a single DoF reference point, have been used for modal identification. Alternatively, high speed cameras were applied to measure full-field vibrations of the plates. 3D DIC allowed obtaining a lower number of natural frequencies but much smoother mode shapes and similar results for model updating. The experimental setup has been benchmarked using two different sets of plates varying thickness and ply stacking.

Model updating of uncertain parameters of carbon/epoxy composite plates from experimental modal data

This work presents a methodology to obtain physically-sound models of composite structure laminates using a combination of modal analysis, numerical modelling and parameter updating, avoiding the common uncertainties on the constructions of similar numerical models. Moreover this model establishes the baseline (pristine situation) of the dynamic behaviour of the set of composite plates. Therefore it could be applied for condition assessment or quality manufacturing control of existing structures through a non-destructive Structural Health Monitoring (SHM), and hence it could help to detect degradation or defects of the composite components. The driven data of the methodology were the modal frequencies and shapes of composite plates. To obtain these values an extensive experimental campaign of modal analysis has been performed on a set of carbon/epoxy laminates. A multiple input single output technique has been applied, using a roving hammer exciting the plates at evenly distributed Degrees of Freedom (DoF), and a mono-axial accelerometer attached to a single DoF reference point. The use of a high dense grid of points has allowed to identify a number of natural frequencies greater than usual in similar works, as well as improving the smoothness of the mode shape. Modal characteristics numerically obtained from a Finite Element Method (FEM) model based on manufacturer reference data were compared with experimental results. This baseline model was updated through a gradient based optimization algorithm. Before the process of model updating, a sensitivity analysis has been performed to identify the driven uncertain parameters using a Montecarlo approach. This technique reduces the number of parameters to be optimized to a small set increasing the efficiency of the methodology. As a result of the whole process, a physically more accurate model is obtained on which discrepancies with the corresponding experimentally measured modal parameters are drastically reduced. Analysis of the consistency of the adjusted numerical parameters has been done with alternative experimental tests (Quasi Static Loading (QSL) and Ultrasonic inspection).

Modeling and prototyping of a soft closed-chain modular gripper

PurposeThis paper aims to present a soft closed-chain modular gripper for robotic pick-and-place applications. The proposed biomimetic gripper design is inspired by the Fin Ray effect, derived from fish fins physiology. It is composed of three axisymmetric fingers, actuated with a single actuator. Each finger has a modular under-actuated closed-chain structure. The finger structure is compliant in contact normal direction, with stiff crossbeams reorienting to help the finger structure conform around objects.Design/methodology/approachStarting with the design and development of the proposed gripper, a consequent mathematical representation consisting of closed-chain forward and inverse kinematics is detailed. The proposed mathematical framework is validated through the finite element modeling simulations. Additionally, a set of experiments was conducted to compare the simulated and prototype finger trajectories, as well as to assess qualitative grasping ability.FindingsKey Findings are the presented mathematical model for closed-loop chain mechanisms, as well as design and optimization guidelines to develop controlled closed-chain grippers.Research limitations/implicationsThe proposed methodology and mathematical model could be taken as a fundamental modular base block to explore similar distributed degrees of freedom (DOF) closed-chain manipulators and grippers. The enhanced kinematic model contributes to optimized dynamics and control of soft closed-chain grasping mechanisms.Practical implicationsThe approach is aimed to improve the development of soft grippers that are required to grasp complex objects found in human–robot cooperation and collaborative robot (cobot) applications.Originality/valueThe proposed closed-chain mathematical framework is based on distributed DOFs instead of the conventional lumped joint approach. This is to better optimize and understand the kinematics of soft robotic mechanisms.

Systematic Approach for Portmanteau Tests in View of the Whittle Likelihood Ratio

Box and Pierce (1970) proposed a test statistic TBP which is the squared sum of m sample autocorrelations of the estimated residual process of an autoregressive-moving average model of order (p,q). TBP is called the classical portmanteau test. Under the null hypothesis that the autoregressive-moving average model of order (p,q) is adequate, they suggested that the distribution of TBP is approximated by a chi-square distribution with (m-p-q) degrees of freedom, ``if m is moderately large". This paper shows that TBP is understood to be a special form of the Whittle likelihood ratio test TPW for autoregressive-moving average spectral density with m-dependent residual processes. Then, it is shown that, for any finite m, TPW does not converge to a chi-square distribution with (m-p-q) degrees of freedom in distribution, and that if we assume Bloomfield's exponential spectral density, TPW is asymptotically chi-square distributed for any finite m. From this observation we propose a modified T†PW which is asymptotically chi-square distributed. In view of the likelihood ratio, we also mention the asymptotics of a natural Whittle likelihood ratio test TWLR which is always asymptotically chi-square distributed. Its local power is also evaluated. Numerical studies illuminate interesting features of TPW, T†PW, and TWLR. Because many versions of the portmanteau test have been proposed and been used in a variety of fields, our systematic approach for portmanteau tests and proposal of tests will give another view and useful applications.