A Numerical Approach for Modeling the Shunt Damping of Thin Panels with Arrays of Separately Piezoelectric Patches

Two-dimensional thin plates are widely used in many aerospace and automotive applications. Among many methods for the attenuation of vibration of these mechanical structures, piezoelectric shunt damping is a promising way. It enables a compact vibration damping method without adding significant mass and volumetric occupancy. Analyzing the dynamics of these electromechanical systems requires precise modeling tools that properly consider the coupling between the piezoelectric elements and the host structure. This paper presents a methodology for separately shunted piezoelectric patches for achieving higher performance on vibration attenuation. The Rayleigh-Ritz method is used for performing the modal analysis and obtaining the frequency response functions of the electro-mechanical system. The effectiveness of the method is investigated for a broader range of frequencies, and it was shown that separately shunted piezoelectric patches are more effective.Comment: arXiv admin note: substantial text overlap with arXiv:2103.1317

Comparative study of peridynamics and finite element method for practical modeling of cracks in topology optimization

Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization

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

Peridynamics-informed effect of micro-cracks on topology optimization of lightweight structures

Most structures are preferred to be light-weighted when they are used in industrial applications such as automotive, aerospace, and naval structures. Classical continuum mechanics (CCM) formulations are commonly adopted to solve the topology optimization problems. However, CCM brings about some restrictions to the modeling, analysis, and solution of complex structures with structural discontinuities, defects, and micro/macro damages. Unlike CCM, peridynamic theory provides a wider range of analysis options because of its nonlocal integration nature, which can eliminate the need for partial derivatives in the equation of motion, thereby being suitable for effective modeling of cracks, damages, etc. This paper presents an application of peridynamics based topology optimization (PD-TO) to study the effect of micro-damages for designing lightweight engineering structures. The PD-TO algorithm used herein is based on the coupling of bond-based method and Optimality Criteria (OC) topology optimization method. The structure is designed by locating various microcracks for investigating the microdamage effect on the optimal topologies. To this end, the PD-TO model is implemented using an in-house MATLAB code, and strain energy density distributions are compared between different topologies. As a result, the importance of including damage regions within the lightweight design optimization stage is revealed

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

Analysis of smart laminated composites integrated with piezoelectric patches using spectral element method and lamination parameters

This paper investigates the effect of stacking sequence on the power output of a smart composite panel integrated with piezoelectric patches, using lamination parameter formulation and spectral element method (SEM). The deformation of the panel is expressed using the first-order shear deformation theory. The strain energy of the host plate is formulated using lamination parameters and the governing equations are derived following Hamilton's principle. To solve the governing equations accurately and efficiently, a spectral element method is applied where the structure is divided into regions that are continuous in terms of geometry, and element matrices of each region are calculated using the spectral Chebyshev approach. This method benefits both from the (geometry) flexibility of the finite element method and the accuracy of the meshless methods. The developed electromechanical model is used to study the effect of the number of piezo patches and their sizes. To demonstrate the accuracy and performance of the presented SEM, six case studies were investigated by comparing natural frequencies, structural/voltage frequency response functions (FRFs), and computational duration to those obtained from a finite element analysis (FEA). The maximum difference in the predicted natural frequencies between the SEM and FEA results is below 1% and the FRFs obtained using the presented solution technique excellently match the FEA results. Yet, the simulation duration is significantly reduced compared to FEA. To exploit the computational efficiency of the presented analysis approach, optimization case studies were also performed implementing a genetic algorithm to maximize the power output by optimizing the stacking sequence and patch distribution

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

Combination of peridynamics and genetic algorithm based topology optimization methods for additive manufacturing-friendly designs

Topology optimization (TO) is a practical tool to generate light-weighted engineering structures for various manufacturing industries. However, manufacturing constraints and surface smoothing are still considerable challenges for TO algorithms. Existing TOframeworks utilize mechanical analysis approaches that discretize the whole domain with elements or particles. Therefore, obtained geometries from TO have been criticized for their complex shapes. In this study, we propose a coupled framework to generate additive manufacturing (AM)-friendly designs which result in less support structure and higher surface quality. For this purpose, the generative topology optimization method (GTO), which uses genetic algorithm to search for the best alternative set of geometry within all the possible topology results, is coupled with the peridynamics topology optimization (PD-TO) method to evolve the PD-TO results into AM-friendly shapes. The PD-TO discretizes the problem domain using equally spaced particles during the TO process. Hence, PD-TO generates a point cloud file with relevant artificial material density values in the final state. Then, the GTO method utilizes the point cloud and material densities as an input file to achieve better final geometry. AM-friendly designs achieved from GTO are compared with the initial results obtained from PD-TO to demonstrate the efficiency and capability of the proposed method