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This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin’s method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger’s method. An approximate solution technique—the method of multiple scales—is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

This paper deals with the problem of vibration health monitoring (VHM) in structures with nonlinear dynamic behaviour. It aims to introduce two viable VHM methods that use large amplitude vibrations and are based on nonlinear time series analysis. The methods suggested explore some changes in the state space geometry/distribution of the structural dynamic response with damage and their use for damage detection purposes. One of the methods uses the statistical distribution of state space points on the attractor of a vibrating structure, while the other one is based on the Poincare map of the state space projected dynamic response. In this paper both methods are developed and demonstrated for a thin vibrating plate. The investigation is based on finite element modelling of the plate vibration response. The results obtained demonstrate the influence of damage on the local dynamic attractor of the plate state space and the applicability of the proposed strategies for damage assessment. The approach taken in this study and the suggested VHM methods are rather generic and permit development and applications for other more complex nonlinear structures.

PURPOSE Evidence is emerging that the abrupt compliance mismatch that exists at the junction between the stent ends and the host arterial wall disturbs both the vascular hemodynamics and the natural wall stress distribution. These stent-induced alterations are greatly reduced by smoothing the compliance mismatch between the stent and host vessel. A stent that provides this smooth transition in compliance, the compliance matching stent (CMS), has been developed. This study attempts to evaluate the hemodynamics and wall mechanical consequences of the CMS both in vitro and in vivo. MATERIALS AND METHODS Finite element analysis was used to assess the solid mechanical behavior (compliance and stress) of the CMS in a stent/artery hybrid structure. A similar analysis was performed with a Palmaz stent. In vivo hemodynamics and wall mechanical changes induced by the CMS were investigated in a swine model from direct measurements of flow, pressure, diameter, and histology in the stented segment of superficial femoral arteries after 7 days. RESULTS Finite element analysis showed that the abrupt compliance mismatch was substantially smoothed between the vessel portions with and without the stent with CMS segments. Circumferential stress was also markedly reduced with the CMS compared to other stent. The in vivo results showed that the CMS was efficient in compliance matching and did not dampen flow or pressure waves downstream the stent. Concurrent histology showed limited thrombus and inflammatory cell accumulation around the stent struts. CONCLUSION These results indicate that the stent/artery hybrid structure can be compliance matched with proper stent design and that this structure limits solid mechanical stress and hemodynamic disturbances. It remains to be seen whether compliance-matched vascular stents reduce in-stent restenosis.

The mismatch between the elastic properties and initial geometry of a host artery and an implanted stent or graft cause significant stress concentration at the zones close to junctions. This may contribute to the often observed intimal hyperplasia, resulting in late lumen loss and eventual restenosis. This study proposes a mathematical model for stress-induced thickening of the arterial wall at the zones close to an implanted stent or graft. The host artery was considered initially as a cylindrical shell with constant thickness that was clamped to the stent or graft, which was assumed to be non-deformable in the circumferential direction. It was assumed that the abnormal circumferential and axial stresses due to the bending of the arterial wall cause wall thickening that tends to restore the stress state close to that existing far from the junction. The linear equations of a cylindrical shell with variable thickness were coupled to an evolution equation for the wall thickness. These equations were solved numerically and a parametric study was performed using finite difference method and explicit time step. The results show that the remodeling process is self-limiting and leads to local thickening that gradually decreases with distance from the edge of the stent/graft. Model predictions were tested against morphological findings existing in the literature. Recommendations on stent designs that reduce stress concentrations are discussed.

Vascular stents are being used in increasing numbers to correct arterial flow limiting disorders. Although data exist on the in vivo performance of these devices, comparatively little is known about how these devices affect the arterial mechanical environment. The long-term success of stenting is very likely affected by the blood flow patterns and artery wall stresses that follow stent placement. This study was undertaken to identify the mechanical environment in stented arteries and to propose a stent design that minimizes the “mechanical trauma” of stent implantation. A series of pulsatile flow visualization experiments were performed with a Johnson & Johnson Palmaz/Schatz stent inserted in a straight compliant tube. A flow loop was constructed that was capable of applying a physiologic pulsatile flow indicative of conditions in the femoral or coronary arteries. The results showed that this stent design creates complex flow patterns including large-scale vortices, and that these patterns are caused by the compliance mismatch between the stented vessel and adjacent unstented vessel. The compliance mismatch also would be expected to create abnormal stress concentrations in the artery wall near the ends of the stent. A simplified model of an artery was constructed to estimate the stress in the artery wall. The stent/artery structure was assumed to be an axisymmetric thin shell made of a linear elastic, orthotropic material that undergoes small deformations. The stent diameter was assumed to be equal to the artery systolic diameter. The stresses were estimated under diastolic pressure, when the deflection of the artery due to the presence of the stent is greatest. It was found that the circumferential and axial stresses at the ends of the stent were 2 to 3 times higher than the stress far from the stent. Based on these mechanical studies, a new stent design was proposed that provides a smooth transition in compliance at the proximal and distal ends of the tube. Flow visualization studies with this new stent indicate that the flow disturbances are greatly reduced with this new design. The transition zone was incorporated into the shell model to estimate the artery wall stresses induced by this new model. It was found that the stress concentration was reduced by as much as 36% from the rigid stent value. These studies demonstrate the potential complexity of flow in stented arteries and provide some recommendations for optimizing stent design from a biomechanical point of view. This work was supported in part by a Linkage Grant from NATO.

The present work describes a method for the determination of the position of a point with respect to a simple-connected domain. It is intended for application in the finite element mesh generation. The proposed method for identification of a point with respect to a domain appears as an extension of Sloan's method, which is an improved version of Nordbeck's and Rydsteadt's one, for identification of a point with respect to a polygon. FORTRAN 77 computer programs are added implementing the proposed method.

An electro-mechanical system of vibrational energy harvesting is studied. The beam is excited by external and kinematic periodic forces and damped by an electrical resistor through the coupled piezoelectric transducer. Nonlinearities are introduced by stoppers limiting the transverse displacements of the beam. The interaction between the beam and the stoppers is modeled as Winkler elastic foundation. The mechanical properties of the piezoelectric layer are taken into account and the beam is modeled as a composite structure. For the examined composite beam, the geometrically nonlinear version of the Timoshenko’s beam theory is assumed. The equations of motion are derived by the principle of virtual work considering large deflections. An isogeometric approach is applied for space discretization and B-Splines are used as shape functions. Finally, the power output and the efficiency of the system due to harmonic excitations are discussed. The influence of the position of the stoppers and their length on the dynamics of the beam and consequently on the power output are analyzed and presented.

Dynamics of a composite beam subjected to thermal and mechanical loadings is presented in the paper. The extended Timoshenko beam model takes into account shear and inertia of the cross-section and nonlinear longitudinal displacement caused by mechanical and thermal loadings. It has been shown that thermal and mechanical fields are fully coupled and the heat pulse may change the transient dynamics of the system. For the case of elevated temperature and a steady state problem the model is reduced to nonlinear ordinary differential equations of motion. It has been shown that the elevated ambient temperature may drastically change its response.