A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures

Fiber reinforced composite laminates are increasingly replacing traditional metallic materials The manufacturing process and service of the composite laminates frequently lead to delamination Vibration analysis is an integral part of most engineering structures In the present article we provide a relevant survey on the various analytical models and numerical analyses for the free vibration of delaminated composites A basic understanding of the influence of the delamination on the natural frequencies and the mode shapes of composite laminates is presented In addition, other factors affecting the vibration of the delaminated composites are discussed Particular attention is given to composite laminates having piezoelectric sensors and actuators, and ones subjected to axial loadings

Vibration of Delaminated Composite Laminates: A Review

This paper proposes a Convolutional Neural Network (CNN) based approach for the classification and prediction of various types of in-plane and through-the-thickness delamination in smart composite laminates using low-frequency structural vibration outputs. An electromechanically coupled mathematical model is developed for the healthy and delaminated smart composite laminates, and their structural vibration responses are obtained in the time domain. Short Time Fourier Transform (STFT) is employed to transform the transient responses into two-dimensional spectral frame representation. A convolutional neural network is incorporated to distinguish between the damaged and undamaged states, as well as various types of damage of the laminated composites, by automatically extracting discriminative features from the vibration-based spectrograms. The CNN showed a classification accuracy of 90.1% on one healthy and 12 delaminated cases. The study of the confusion matrix of CNN provided further insights into the physics of the problem. The predictive performance of a pre-trained CNN classifier was also evaluated on unseen cases of delamination, and physically consistent results were obtained.

Structural vibration-based classification and prediction of delamination in smart composite laminates using deep learning neural network

This paper deals with non-linear dynamic stability of initially imperfect piezoelectric functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates under a combined thermal and electrical loadings and interaction of parametric and external resonance. The excitation, which derives from harmonically varying actuators voltage, results in both external and parametric excitation. The governing equations of the piezoelectric CNTRC plates are derived based on first order shear deformation plate theory (FSDT) and von Karman geometric non-linearity. The material properties of FG-CNTRC plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed aligned, straight and a uniform layout. The linear buckling and vibration behavior of perfect and imperfect plates are obtained in the first step. Then, Galerkin's method is employed to derive the non-linear governing equations of the problem with quadratic and cubic non-linearities associated with mid-plane stretching. Periodic solutions and their stability are determined by using the harmonic balance method with simply supported boundary conditions. The effect of the applied voltage, temperature change, plate geometry, imperfection, the volume fraction and distribution pattern of the SWCNTs on the parametric resonance, in particular the positions and sizes of the instability regions of the smart CNTRC plates as well as amplitude of steady state vibration are investigated through a detailed parametric study.

Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection

This paper reviews most of the recent research done in the field of dynamic stability/ dynamic instability/ parametric excitation /parametric resonance characteristics of structures with special attention to parametric excitation of plate and shell structures. The solution of dynamic stability problems involves derivation of the equation of motion, discretization and determination of dynamic instability regions of the structures. The purpose of this study is to review most of the recent research on dynamic stability in terms of the geometry (plates, cylindrical, spherical and conical shells), type of loading (uniaxial uniform, patch, point loading ….), boundary conditions (SSSS, SCSC, CCCC ….), method of analysis (exact, finite strip, finite difference, finite element, differential quadrature and experimental ….), the method of determination of dynamic instability regions (Lyapunovian, perturbation and Floquet’s methods ), order of theory being applied (thin, thick, 3D, nonlinear….), shell theory used (Sanders’, Love’s and Donnell’s), materials of structures (homogeneous, bimodulus, composite, FGM….) and the various complicating effects such as geometrical discontinuity, elastic support, added mass, fluid structure interactions, non-conservative loading and twisting etc. The important effects on dynamic stability of structures under periodic loading have been identified and influences of various important parameters are discussed. Review on the subject for non-conservative systems in detail will be presented in Part-2.

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Research Advances in the Dynamic Stability Behavior of Plates and Shells: 1987–2005—Part I: Conservative Systems

Dynamic instability of composite laminates using a higher order theory

The focus of this investigation is on the development and validation of non-linear structural dynamic reduced order models of structures undergoing large deformations, with particular emphasis on aircraft panels. Significant efforts are devoted to the formulation and assessment of “dual modes” which when combined with the linear transverse modes form an excellent basis for the representation of the displacement and stress fields in the reduced order model. This task is first successfully achieved for isotropic/symmetric composite structures and then extended to asymmetric and functionally graded ones. Examples of application are presented that demonstrate the high accuracy of the proposed reduced order models as compared to full finite element preditions, even with a small number of modes.

Nonlinear reduced order modeling of isotropic and functionally graded plates

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

A higher order shear deformation theory is used to investigate the instability associated with delaminated composite plates subject to dynamic loads. Both transverse shear and rotary inertia effects are taken into account. The procedure is implemented using the finite element method. Delamination is modeled using the penalty parameter approach. The natural frequencies are computed and compared with NASTRAN 3D results and available experimental data. The effect of delamination on the critical buckling load and the first two instability regions is investigated for various loading conditions, plate thickness and boundary conditions. As expected the natural frequencies and the critical buckling load of the delaminated plate are lower than those of the nondelaminated plate. They decrease with increase in delamination length. Increase in delamination length causes instability regions to be shifted to lower parametric resonance frequencies and the normalized width of the instability regions to increase.

Adrian G. Radu

Papers

Dynamic instability of composite laminates using a higher order theory

Nonlinear reduced order modeling of isotropic and functionally graded plates

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

A higher order plate theory for dynamic stability analysis of delaminated composite plates

Stability of delaminated composite plates using a higher order theory