This paper proposes a two-stage approach for damage assessment in beam-like structures using two-dimensional Isogeometric Analysis (IGA) and Finite Element Method (FEM) combined with optimization ...techniques. In the first stage, the Local Frequencies Change Ratio (LFCR) indicator and a newly developed damage indicator based on normalized Modal Strain Energy Indicator (nMSEDI) are introduced to locate effectively the potential damaged elements. In order to verify nMSEDI, different scenarios based on single and multiple damages are studied using numerical experiments. In the second stage, the Teaching-Learning-Based Optimization Algorithm (TLBO) is utilized and its performance is compared with that of Particle Swarm Optimization (PSO) and Bat Algorithm (BA). The three optimizations techniques are combined with IGA using nMSEDI as objective function. In addition, experimental vibration tests using laboratory steel been are conducted to validate the proposed technique. The obtained results clearly indicate that the proposed approach can be used to determine accurately and efficiently both damage location and severity in beam-like structures.
Experimental modal analysis is commonly used to identify models for the vibratory behavior of structures. This is done by conducting a set of experiments to obtain the structure’s governing equations ...and information in the form of eigenfrequencies, mode shapes, and damping. However, linearity of the test structure is assumed within this identification procedure. Hence, as it stands, experimental modal analysis is not readily applicable to build models when nonlinearities are present through, for example, friction, (electro-) magnetic fields, or large deformations. To identify governing equations for such systems, a robust and systematic identification procedure is proposed in this article. The identification routine is formulated in the frequency domain, and a noise reduction scheme and a simplification routine are employed to obtain sparse and robust models. The identification procedure is implemented in an automated script (FrID), which is applied to forced response measurements stemming from structures with magnets, clamps, and bolted joints as well as systems with multiple active modes and internal resonances. The identified governing equations accurately fit the experimentally obtained frequency response measurements and can also be utilized to extrapolate the response for different forcing amplitudes. Moreover, nonlinear modes of the underlying conservative system can be computed from the identified governing equations.
•Identification procedure yielding governing equations of nonlinear oscillators.•Identified models are physically interpretable and robust.•System identification routine assembled in an automated script (FrID).•AModeling of structures with magnets, clamps, and joints from experimental data.•Experimental validation for SDOF, MDOF, and internally resonant systems.
The article introduces a method for selecting the best clamping conditions to obtain vibration reduction during the milling of large-size workpieces. It is based on experimental modal analysis ...performed for a set of assumed, fixing conditions of a considered workpiece to identify frequency response functions (FRFs) for each tightening torque of the mounting screws. Simulated plots of periodically changing nominal cutting forces are then calculated. Subsequently, by multiplying FRF and spectra of cutting forces, a clamping selection function (CSF) is determined, and, thanks to this function, vibration root mean square (RMS) is calculated resulting in the clamping selection indicator (CSI) that indicates the best clamping of the workpiece. The effectiveness of the method was evidenced by assessing the RMS value of the vibration level observed in the time domain during the real-time face milling process of a large-sized exemplary item. The proposed approach may be useful for seeking the best conditions for fixing the workpiece on the table.
The durability and simplicity of the programming of meta-heuristic algorithms make them important in the optimization field. This paper presents a novel application for double cracks identification ...in Carbon Fiber Reinforced Polymer (CFRP) cantilever beams based on experimental and numerical analyses using enhanced optimization techniques. A new hybrid algorithm Particle Swarm Optimization and YUKI (PSO-YUKI) is proposed and combined with Radial Basis Functions (RBF) for solving fast inverse problems. The direct problem is based on the results of the dynamic experimental test of CFRP laminate, measuring the dynamics characteristics of a healthy beam, and the variation in the response corresponding to different scenarios of double cracks with different depths. The Finite Element Method (FEM) is used to simulate this vibrational behavior considering double cracks in different locations. The goal is creating an accurate damage identification method that has a high computational performance, based on the idea of building models that combines the vibrational responses issued from the experiments and simulations. The suggested method is tested based on collected data from numerical and experimental modal analyses in the case of undamaged and damaged CFRP laminates to demonstrate its accuracy and efficiency. The provided results show the robustness of PSO-YUKI compared with PSO for double cracks depth identification. The Matlab Code of PSO-YUKI can be found at https://github.com/Samir-Khatir/Hybrid-PSO-YUKI-.git.
In this paper, the free vibrational behavior of composite conical shells stiffened by bevel stiffeners is investigated using experimental, analytical and numerical techniques. The smeared method is ...employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole structure. Due to the specific geometry of the conical shell, the whole structure is converted to a conical shell with variable stiffness and thickness. The stiffeners are considered to be of beam-type which support shear load and bending moments in addition to the axial loads. The geodesic path is applied to the stiffeners. The governing equations have been derived based on the first-order shear deformation theory and using the Ritz method. In order to validate the analytical achievements, the experimental modal test is conducted on a stiffened cone. The specimen has been fabricated by a specially-designed filament winding setup. A 3-D finite element model was also built using ABAQUS software to further validate the analytical results and help with parametric study. Comparison of the results obtained from the three approaches revealed good agreements. The effects of the shell geometrical parameters and variations in the cross stiffeners angle on the natural frequencies have been discussed and investigated. The present achievements are novel and can be used as a benchmark for further studies.
•Report analytical formulae for ID of modal parameters in EMA.•Characterize the difference in ID of modal parameters between EMA and OMA.•Mode shape c.o.v. for EMA shares the same formula as that for ...OMA.•Provide the scientific basis for planning the single-input forced vibration test.
‘Uncertainty law’ aims at closed-form asymptotic formulas for the relationship between the identification uncertainties of modal properties (e.g., natural frequency, damping ratio) and test configuration (e.g., noise level, number and location of sensors, data duration). Existing developments focused on the case of unknown-input (ambient), where it has been found that identification uncertainty does not vanish even for noiseless instruments, essentially because the input is unknown. A natural question is then on how the uncertainty depends on test configuration when the input is known, not to mention how the configuration should be quantified. Motivated by these and related questions, this paper develops the uncertainty laws of modal parameters for well-separated modes with known single broadband input, e.g., vibration test with a single shaker as in experimental modal analysis. Asymptotic expressions for the posterior coefficient of variation of modal parameters are derived via the Fisher Information Matrix for long data and small damping scenarios. Assumptions and theory are validated using synthetic and field test data. Governing factors motivated by the theory are investigated, including the equivalent modal signal-to-noise ratio (for known input), the number of measured degrees of freedom, shaker location, and data duration. By virtue of the Cramér-Rao bound in classical statistics, the developed uncertainty laws represent the lower bound of identification uncertainty with known broadband input that can be achieved by any unbiased estimator. They provide a scientific basis for planning and managing identification uncertainties in vibration tests with known input.
The importance and role of a specific class of global transmissibility matrices (global TFs), here named response-based frequency response functions (R-FRFs), in the areas of the identification and ...continuous monitoring of structures, is discussed and expanded in the present paper. The R-FRFs, as specialized frequency response functions, have been recently introduced in the literature, and, as originally proved, they are able to inherently provide local poles related to the system under investigation, but, virtually, with a different set of boundary conditions; i.e. as if some of the original degrees of freedom, arbitrarily chosen by the analyst, were constrained to ground. In this paper, such a concept is extended, including mode shapes. Herein, we show that the R-FRFs are also able to provide local modes associated with the aforementioned local poles. In this regard, we provide a parametric model of the R-FRFs matrix, suitable for being tackled through frequency-domain estimators from the field of experimental and operational modal analysis, which let these additional modal parameters to be identified. Such a conceptual extension is carried out by both a theoretical and a numerical point of view. We process data sets from numerical and real-world experimental case studies and discuss the corresponding results. The estimated poles and modes are employed to detect structural modifications, in turn confirming the significance of response-based frequency response functions in the field of damage detection and structural health monitoring (SHM).
•Response-based FRFs (R-FRFs) as a tool for analyzing the system in a local sense.•R-FRF modal decomposition in terms of perturbated original system modal parameters.•Modes of the original structure when subjected to virtual boundary conditions.•Modal parameter estimation based on frequency-domain estimator from the OMA field.•Sensitivity of R-FRF modal parameters for enhanced damage localization.
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