Unifying lamination parameters with spectral-Tchebychev method for variable-stiffness composite plate design

This paper describes an efficient framework for the design and optimization of the variable-stiffness composite plates. Equations of motion are solved using a Tchebychev polynomials-based spectral modeling approach that is extended for the classical laminated plate theory. This approach provides highly significant analysis speed-ups with respect to the conventional finite element method. The proposed framework builds on a variable-stiffness laminate design methodology that utilizes lamination parameters for representing the stiffness properties compactly and master node variables for modeling the stiffness variation through distance-based interpolation. The current study improves the existing method by optimizing the locations of the master nodes in addition to their lamination parameter values. The optimization process is promoted by the computationally efficient spectral-Tchebychev solution method. Case studies are performed for maximizing the fundamental frequencies of the plates with different boundary conditions and aspect ratios. The results show that significant improvements can be rapidly achieved compared to optimal constant-stiffness designs by utilizing the developed framework. In addition, the optimization of master node locations resulted in additional improvements in the optimal response values highlighting the importance of including the node positions within the design variables

A spectral Tchebychev solution for electromechanical analysis of thin curved panels with multiple integrated piezo-patches

This paper presents an electromechanical model for predicting the dynamics of curved panels with multiple surface-integrated piezo-patches. The boundary value problem governing the electro-elastic dynamic behavior of a (doubly-) curved panel and piezo-patch structure is derived following the first order shear deformation (FSDT) theory. Spectral Tchebychev approach is used to numerically solve the system dynamics and obtain voltage and mechanical frequency response functions (FRFs). Mass and stiffness contributions of piezo-patch(es) as well as two-way electromechanical coupling behavior are incorporated in the model for both modal analysis and frequency response calculations. To validate the accuracy of the developed solution technique, the results for various cases including a single patch and multiple patches on a straight/curved host panel are compared to those obtained from finite-element (FE) analyses. It is shown that the maximum difference in the predicted natural frequencies between the ST and FE results is below 1%, and the harmonic analyses’ results obtained using the presented solution technique excellently match the FE results. Furthermore, the effect of multiple piezoelectric patches to achieve higher voltage values in the application of energy harvesting is investigated when the mode jumping phenomenon occurs due to the increasing curvature

Electromechanical analysis of functionally graded panels with surface-integrated piezo-patches for optimal energy harvesting

This paper presents an electromechanical modeling approach for predicting the dynamics of (straight/curved)functionally graded panels with multiple surface‐integrated piezo‐patches. Bi‐axial material variation is considered using the theory of mixture approach. The governing equations are derived following the first order shear deformation theory and the Hamilton’s principle. The derived boundary value problem is solved numerically using a meshless approach based on Chebyshev polynomials. Mass and stiffness contributions of piezo‐patch(es), as well as two‐way electromechanical coupling behavior, are incorporated both for modal and harmonic analyses. To validate the accuracy of the presented solution technique, the results for various cases are com-\pared to those obtained from finite‐element analyses. It is shown that the maximum difference in the predicted natural frequencies is below 1%, but for a fraction of the computational time. Furthermore, the harmonic analysis results excellently match FE results. Note that material variation changes the spatial stiffness of the panel and thus, the functionally graded panel can be designed according to a predefined objective function using the proposed modeling approach. As a demonstration, specific to energy harvesting application, the voltage/power output was maximized through material and geometry/shape variations. It was demonstrated that significant improvements can be achieved through the presented methodology

Prediction of Vibro-Acoustic Response of Enclosed Spaces by Using Structural Modification Techniques

Low frequency noise caused by vibrating panels can become a problem for vehicles from NVH standpoint. The vibro-acoustic analysis of a simplified vehicle model is presented in this study. Analysis of vibro-acoustic behavior includes frequency response analysis of structure by Finite Element Method (FEM) and sound pressure level (SPL) prediction of the cabin interior by Boundary Element Method (BEM). The structural design of the vibrating panels can be modified by adding stiffeners to improve the acoustic field inside the cabin. The dynamic analysis of the structural model must be repeated after every modification which will be a time consuming process in the design stage. In this study, a methodology that utilizes the frequency response functions (FRFs) of the original model for the reanalysis of the structure that is subjected to structural modification is adapted. Modal analysis of the original structure is performed only once to obtain the receptance values. Then, the structural modification method is used to calculate the receptances of the modified system. The structural modification method uses the receptances of the original system and the dynamic stiffness matrix of the modifying part of the structure. The response of the structure obtained from receptances of the modified structure is then used to supply vibration data as boundary condition for acoustic analysis of the cavity for SPL prediction at desired points

Dynamic analysis of doubly curved composite panels using lamination parameters and spectral-Tchebychev method

Efficient modeling and optimization techniques are required to overcome the high design complexity and computational costs concerning the engineering of composite structures. In this paper, a modeling framework for the dynamic analysis of doubly curved composite panels is developed. Lamination parameters are used to characterize the stiffness properties of the laminate, and the responses are calculated through the two-dimensional spectral-Tchebychev method. The proposed framework combines the computational efficiency advantages of both lamination parameters formulation and spectral-Tchebychev method which is extended for dynamic analysis of curved composite laminates. Compared to the finite element method, the developed model significantly decreases the computation duration, thereby leading to analysis speed-ups up to 40 folds. In the case studies, fundamental frequency contours for the doubly curved composite panels are obtained in lamination parameters space for the first time. The results show that, unlike flat or singly curved laminates, the maximum frequency design points for doubly curved panels can be inside the feasible region of lamination parameters requiring multiple layer angles. The fundamental mode shapes for the maximum frequency designs are also computed to investigate the influence of panel curvatures on the vibration patterns, which can exhibit mode switching phenomenon

A general electromechanical model for plates with integrated piezo-patches using spectral-Tchebychev method

This paper presents a general electromechanical model for predicting the dynamics of thin or moderately thick plates with surface-integrated piezo-patches. Using spectral Tchebychev (ST) technique, the boundary value problem governing the electroelastic dynamics of the two dimensional (2D) plate and piezo-patch structure is developed with Mindlin plate theory assumptions. Mass and stiffness contributions of piezo-patch(es) as well as two-way electromechanical coupling behavior are incorporated in the model for both modal analysis and frequency response calculations. To validate the accuracy of the developed solution technique, the modal analysis results are compared against the existing Rayleigh-Ritz solution from the literature as well as the finite-element simulation results for various piezo-patch sizes on thin and moderately thick host plates; and it is shown that the maximum difference in the predicted natural frequencies between the ST and FE results are below 1%. The electromechanical frequency response functions (FRFs) including the vibration response and electrical output of the system under a transverse point force excitation are obtained using the ST model and the results are shown to match perfectly with the finite element (FE) simulations. Additionally, comparisons of the electromechanical FRFs calculated based on Rayleigh-Ritz method from the literature versus the developed framework is presented to highlight that the exclusion of shear deformation terms in the former model leads to an inaccurate estimation of electroelastic behavior for the case of thicker plates with integrated piezo-patches. Finally, the investigated case studies demonstrate that the computational efficiency of the developed method is significantly higher than that of FE simulations

A New Design Approach for Rapid Evaluation of Structural Modifications Using Neural Networks

Design optimization of structural systems is often iterative, time consuming and is limited by the knowledge of the designer. For that reason, a rapid design optimization scheme is desirable to avoid such problems. This paper presents and integrates two design methodologies for efficient conceptual design of structural systems involving computationally intensive analysis. The first design methodology used in this paper is structural modification technique (SMT). The SMT utilizes the frequency response functions (FRFs) of the original model for the reanalysis of the structure that is subjected to structural modification. The receptances of the original structure are coupled with the dynamic stiffness of the components that are added to or removed from the original structure to perform the structural modification. Then, the coupled matrices are used to calculate the mobility matrices of the modified structure in an efficient way. The second design methodology used in this paper is neural networks (NN). Once sufficient input and output relationships are obtained through SMT, a NN model is constructed to predict the FRF curves of the system for further analysis of the system performance while experimenting different design parameters. The input-output sets used for training the network are increased by applying an interpolation scheme to improve the accuracy of the NN model. The performance of the proposed method integrated through SMT and NN technique is demonstrated on a rectangular plate to observe the effect of the location and thickness of stiffeners on the frequency response of the structure. It is observed that both methods combined with the proposed interpolation scheme work very efficiently to predict the dynamic response of the structure when modifications are required to improve the system performance. [DOI: 10.1115/1.4023156

Multi-objective optimization of composite sandwich panels using lamination parameters and spectral Chebyshev method

Composite materials are widely used in various industries because of their distinct properties. Hybridization is an efficient way of designing composite panels to decrease the cost and/or weight while maintaining stiffness properties. In this study, an accurate and efficient framework is developed to optimize laminated sandwich panels composed of high-stiffness face sheets and low-stiffness core. The stiffness properties of face sheets and core are represented using lamination parameters. The governing equations are derived following first-order shear deformation theory and solved using the spectral Chebyshev approach. In multi-objective optimization problems, genetic algorithm is used to determine Pareto-optimal solutions for fundamental frequency, frequency gap, buckling load, and cost metrics. In these analyses, optimal lamination parameters and thickness are found for face-sheets and core of sandwich panels, and the results are presented as 2D and 3D Pareto-optimal design points. When the individual performance metrics lead to different optimum points, a scattering behavior is observed in the 3D Pareto sets whose boundaries are defined by the 2-objective Pareto fronts. The results provide insights into the design requirements for improving the dynamic and load-carrying behavior of sandwich laminates while minimizing the cost that presents the usability of the presented approach in the multi-objective optimization