This work explores the use, in structural health monitoring, of the so-called modal effective electromechanical coupling coefficient (EMCC) as a damage indicator for structures with failures such as cracks. For this purpose, a discrete layered finite element (FE) model for smart beams is proposed and applied to short-circuit (SC) and open-circuit (OC) modal analyses of healthy and damaged (cracked) cantilever beams with symmetrically surface-bonded piezoelectric patches. Focus is made here on enhancing the electrical behavior modeling by introducing a quadratic bubble function in the electric potential through-the-thickness approximation. Therefore, the corresponding higher-order potential (HOP) degree of freedom is condensed at the ply level, leading to a passive stiffening effect (SE) similar to the so-called higher-order induced potential (HIP); then the physical equipotential (EP) electrode effect, often neglected in the piezoelectric FE literature, is here implemented after the electrodes' FE assembly. After its validation against available analytical and experimental results, the proposed piezoelectric FE is used for parametric analyses of SC-based and OC-based EMCC change factors (ECFs) and frequency change factors (FCFs) in terms of the crack depth and position ratios. It was found that the EP effect was more influential on the ECF than the SE. However, for the FCFs, the EP effect was influential only when it is defined from the OC frequencies. Finally, the ECFs were found to be higher than the FCFs, in particular for higher modes.
SUMMARY A distributed transfer function (DTF) approach is proposed for the free‐vibration analysis of moderately thick cantilever beams with symmetrically bonded piezoelectric patches. The piezoelectric adaptive structure is decomposed into three sections; the first and third sections contain only the bare parts of the beam before and after the patches, whereas the second section contains the beam part equipped with the piezoelectric patches bonded to its upper and lower surfaces. The analytical formulation assumes first‐order shear deformation kinematics and linear electric potential through each patch thickness and uses the extended Hamilton's principle to derive the equations of motion and electromechanical boundary conditions. The latter are then transformed into a first‐order state space equation using the DTF approach in order to get the short‐circuit and open‐circuit free‐vibration problems that consider the equipotential physical conditions on the electroded upper and lower surfaces of the piezoelectric patches. The implemented DTF approach is validated by running three benchmarks from open literature. The comparison of the obtained results with those provided by three‐dimensional finite elements using a commercial software shows reasonable correlation. Copyright © 2011 John Wiley & Sons, Ltd.
The cubic-plus-chain (CPC) equation of state (Sisco & Abutaqiya et al., Ind. Eng. Chem. Res., 2019) is a recent development in the literature in which the classical cubic equation of state is hybridized with the chain term from the statistical associating fluid theory (SAFT) to produce an equation of state capable of describing the shape and interaction energy of nonpolar chainlike molecules. In this work, the CPC framework is used to model vapor–liquid and liquid–liquid phase equilibria for various polymer–solvent systems. Polypropylene, high-density polyethylene, low-density polyethylene, and polystyrene polymers are modeled with various nonpolar solvents, and various factorsincluding temperature, solvent character, polymer molecular weight, and concentrationare investigated to study their effects on the saturation points predicted by the CPC equation of state. The modeling results from CPC are compared to those generated using the perturbed-chain SAFT (PC-SAFT) equation of state and also the experimental data reported in the literature. Though the predictive capability of CPC is not yet on par with PC-SAFT, it is impressive that this conceptually simple framework can qualitatively describe polymer phase behavior while retaining the numerical stability and fast execution times that make the cubic equations of state appealing.
The cubic-plus-chain (CPC) equation of state hybridizes the classical cubic equation of state with the chain term from the statistical associating fluid theory. The addition of the chain term allows the model to account for the physics of both short-chain and long-chain compounds within the same framework. The CPC framework is not restricted to a specific monomer formulation and radial distribution function, instead numerous modifications can be applied to the model. In this work, the three pure-component parameters are correlated with vapor pressures and liquid densities for 53 nonassociating components from different chemical families, including n-alkanes, alkenes, benzene derivatives, branched alkanes, cycloalkanes, ethers, and gases. The CPC-SRK-b(T) model proposed in this work uses a temperature-dependent segment covolume parameter (b) based on perturbation theory to describe short-range soft repulsion between molecules, whereas the previous version of CPC uses a temperature-invariant b. This CPC formulation is compared with two CPC versions for selected n-alkanes. The addition of the temperature-dependent function in b allows the CPC-SRK-b(T) model to outperform the other two forms in modeling the vapor pressure and liquid density. Furthermore, the vapor−liquid and liquid−liquid equilibria of various binary mixtures are simulated with the CPC-SRK-b(T) model showing excellent agreement with experimental data obtained from the literature.
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