Arcangelo Messina

On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damaged beams

This paper deals with the detection of open cracks in beam structures that undergo transverse vibrations. The investigation is aimed at detecting the location of open cracks in damaged beams by minimizing measurement data and baseline information of the structure. The study is carried out by using the continuous wavelet transform (CWT). The application of this recent, but advanced, mathematical tool is initially presented through a theoretical background, which is believed to be valuable for bridging the gap between the CWT and previous existing techniques. It is shown how the possibility to efficiently identify localized damages by CWT comes up from the intrinsic capability of the wavelets to collect several mathematical tools in only one mathematical aspect: derivatives, convolution and appropriate smoothing of data are translated into the CWT. Simulations show how the redundancy of the CWT in the functional space is able to efficiently identify locations of open cracks in the presence of noisy or clean data. Indeed, the possibility to approach the problem by using different families of wavelets, for several available scales, allows a successful application of the characteristic microscopy of the wavelets. The technique may be promisingly applied to discrete vibrational data.

Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory

This paper deals with the free vibration of open, laminated composite, circular cylindrical panels having a rectangular plan-form and all their edges free of external tractions. The material arrangement of the shell panels considered may vary from this of the single isotropic (or special orthotropic) layer to that of a general angle-ply lay-up. The analysis is based on the application of the Ritz approach on the energy functional of the Love-type version of a unified shear deformable shell theory. A through-thickness parabolic distribution of the transverse shear deformation is mainly assumed but, for comparison purposes, numerical results that are based on the assumptions of the classical Love-type shell theory are also presented. The Ritz method is a powerful analytical technique since, provided that a complete set of trial functions is employed, it can provide the exact solution of the problem considered in infinite series forms. The mathematical formulation is therefore presented in a general form, appropriate for any set of basis functions. The variational approach is, however, finally applied in conjunction with a complete functional basis made of the appropriate admissible orthonormal polynomials.

The influence of boundary conditions and transverse shear on the vibration of angle-ply laminated plates, circular cylinders and cylindrical panels

Abstract This paper investigates the influence of the edge boundary conditions on the vibration characteristics of transverse shear deformable composite plates, closed cylindrical shells and open cylindrical panels having an arbitrary angle-ply lay-up. The shell model employed for this purpose is equivalent to the unified shear deformable Love-type theory introduced in Refs. [6,7], whereas the analysis is based on the Ritz method. Following some recent relevant developments [1–5], in which the method was applied successfully in connection with vibration problems of shear deformable cross-ply laminates, the Ritz method is employed in conjunction with complete functional bases formed by appropriate orthonormal polynomials. The present vibration study is based on angle-ply laminates having different combinations of simply supported, clamped and free edge boundaries. Apart from the convergence tests performed and the new results presented, the success of the present analysis is verified through comparisons with the corresponding results based on classical plate and shell theories as well as through comparisons with corresponding numerical and experimental results that are available in the literature.

A general vibration model of angle-ply laminated plates that accounts for the continuity of interlaminar stresses

Abstract This paper presents the generalisation of a well documented two-dimensional shear deformable laminated shell theory [Compos. Struct. 25 (1993) 165] that, based on a fixed number of unknown variables, was initially proposed for laminates made of specially orthotropic layers only. The theory is here specialised for laminated plates but is able to encompass monoclinic layers in a general multilayered configuration. Moreover, it is able to account for the interlaminar continuity of both displacements and transverse shear stresses. Higher-order effects, as shear deformation and rotary inertia, are naturally included into the formulation. In order to obtain the relevant governing differential equations, both Hamiltons variational principle and a recently proposed vectorial approach [Compos. Engng. 3 (1993) 3] have been independently used. The effectiveness of the present model is tested numerically by comparing its results with exact three-dimensional elasticity results obtained under the particular condition that the plates vibrate in cylindrical bending.

Influence of edge boundary conditions on the free vibrations of cross-ply laminated circular cylindrical panels

This paper deals with the influence of different sets of edge boundary conditions on the dynamic characteristics of shear deformable, cross-ply laminated circular cylindrical panels. The analysis is based on the conjunction of the Ritz method with an appropriate, complete functional basis and its subsequent application on the energy functional of the Love-type version of a unified shear-deformable shell theory [T. Timarci and K. P. Soldatos, J. Sound Vib. 187, 609–624 (1995); J. Eng. Math (to appear January 2000)]. As a result, two different kinds of shear deformable Love-type shell theories are employed and tested, including versions that either fulfill or violate the continuity of the interlaminar stresses along the shell thickness. Although the main theoretical model employed makes use of a certain type of continuous interlaminar stress, the results of the present analysis are initially tested and validated through appropriate comparisons with corresponding numerical results obtained in the relevant li...

Free vibrations of multilayered doubly curved shells based on a mixed variational approach and global piecewise-smooth functions

Abstract This paper presents the extension of a two-dimensional model that, recently appeared in literature, deals with freely vibrating laminated plates. The extension takes into account the corresponding theory describing the dynamic of freely vibrating multilayered doubly curved shells. The relevant governing differential equations, associated boundary conditions and constitutive equations are derived from one of Reissner’s mixed variational theorems. Both the governing differential equations and the related boundary conditions are presented in terms of resultant stresses and displacements. In spite of the multi-layer nature of the shell, the theory is developed as if the shell were virtually made of a single layer. This choice does not limit the performances of the model, which are comparable to the corresponding three-dimensional theory. This ability is accomplished by an appropriate global expansion of the relevant kinetic and stress quantities, through the thickness of the multilayered shell. The mentioned expansion is realized by a novel selection of global piecewise-smooth functions. Numerical tests illustrate the performance of the model with respect to several elements subjected to a class of simply supported boundary conditions: plates, circular cylindrical shells, spherical and saddle-shape laminates. The model is first tested by comparing its resulting eigen-parameters , with those few existing of exact or approximate three-dimensional models and, finally, new results are provided for several geometrical and material characteristics for plates and shells.

A Multiple-Damage Location Assurance Criterion Based on Natural Frequency Changes

A new method for locating multiple damage sites in elastic structures is introduced. It uses only the natural frequencies for diagnosis and obviates the need to have complete experimental mode shapes. Results from three damaged structures are presented. A 2-bar truss illustrates the basis for the method, a 15-bar truss shows its use with symmetrical structures, and a redundant-bar truss is used to compare the new method with that of Pandey and Biswas. Correct predictions of the location and relative amounts of damage at multiple sites are obtained, even when low damage levels are present in the structure.

Exact modeling for control of flexible manipulators

This work presents the dynamic modeling and active vibration control of planar multilink manipulators having flexible links. Since the eigenvalue problem of such continuous structures is strongly dependent on the posture configuration, at first an efficient matrix formulation is provided in order to derive exact natural frequencies and mode shapes of a robot in its general posture. The analytical modal data are used to develop the forced vibration model; this is accomplished through the analytical decoupling of the modal coordinates of the manipulator; to this latter end, orthogonality conditions of modal shapes sets of planar multilink manipulators are demonstrated. The suppression of vibrations is challenged through a full-state linear quadratic regulator controller by optimally placing collocated sensor/actuator pairs. An optimal stochastic observer is designed in line with the noise-corrupted truncated model, i.e. the continuous Kalman-Bucy filter. The simulation results demonstrate that the presented matrix formulation for deriving exact modal data is effective, and the designed control method, along with the forcedvibration solving strategy, is feasible and efficient.

Three-dimensional free vibration of multi-layered piezoelectric plates through approximate and exact analyses

This article presents two models that have the aim of analysing three-dimensional freely vibrating plates made of an arbitrary combination of structural and/or piezoelectric layers. The first model is derived from a displacement-based variational statement, and it investigates the possibility of approaching exact three-dimensional results at any degree of accuracy. This model has been developed as if the plates were virtually made of a single layer, and it is herein referred to as the approximate analysis model. The second model is based on solving the set of three-dimensional linear equations coupling the relevant mechanical and electric quantities, and it therefore provides exact results. The latter model is derived from the transfer-matrix technique which, having shown numerical instability in the multiphysics problem being dealt with, was then successfully modified to provide exact and reliable results. Excellent agreement has been obtained between the models, and this shows how the exact approach here designed is stably able to overcome ill conditioning problems, while the first model, having been validated by the exact results, could be applied to effectively investigate multiphysics problems for general boundary conditions, and for cross- and/or angle-ply laminates, at any level of required accuracy.

Three-Dimensional Free Vibration Analysis of Cross-Ply Laminated Rectangular Plates through 2D and Exact Models

In this article, an analytical 2D model describing freely vibrating multilayered plates is presented and subsequently validated through the comparison with exact results. The model completely takes the relevant equations of the three-dimensional theory into account and is based on a “single-layer” formulation. Although any combination of classical edge boundary conditions can be taken into account, the validation is carried out within the frame of simply supported plates for which an exact analysis is possible. The comparisons regard eigenvalues displacement and stress fields. The comparisons show the capability of the 2D model to approach exact results; results are provided for future comparisons.