# Modeling and Analysis of Debonding in a Smart Beam in Sensing Mode, Using Variational Formulation

TL;DR: In this paper, a higher order finite element model has been developed for the analysis of debonding in a smart cantilever beam, where the debonding has been incorporated at the interfaces between piezo patches and the core.

Abstract: Using basic electro-elastic formulation and variational formulation, a higher order finite element model has been developed for the analysis of debonding in a smart cantilever beam. Full length piezo patch embedded at the top and bottom of the aluminium core has been assumed to be de-bonded. The debonding has been incorporated at the interfaces between piezo patches and the core, at the mid span of the beam for one third length of the beam. The effect of debonding in sensing mode has been analysed by presenting the induced potential, axial displacement, axial/transverse electric field and stresses for fully bonded and de-bonded smart cantilever beam. The variation in electric potential, electric field, axial displacement/strain/stress and shear strain/stress observed in case of debonding demonstrates that the mechanics of debonding is complex coupled electro-mechanical behaviour. In the de-bonded beam, the induced potential at the free piezo surface and at the interfaces shows a sinusoidal variation from root to the tip as compared to the linear variation in bonded beam. This is attributed to the non-linear bending moment variation from root to the tip in case of de-bonded beam. The maximum stress in debonding increases nearly 1.5 times to that of bonded beam sensing at various locations.

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09 Feb 20203 citations

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TL;DR: In this paper, the generalised system of coupled (2 + 1)-dimensional hyperbolic equations with Noether symmetries has been studied, namely u tt - u xx - u yy + P ( v ) = 0, v tt − v xx - v yy+ Q ( u ) = 1.

Abstract: We perform Noether classification of the generalised system of coupled (2 + 1)-dimensional hyperbolic equations, namely u tt - u xx - u yy + P ( v ) = 0 , v tt - v xx - v yy + Q ( u ) = 0 . Besides this we compute conservation laws corresponding to cases that have Noether symmetries for the underlying coupled hyperbolic system.

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TL;DR: In this paper, a scaling analysis is performed to demonstrate that the effectiveness of actuators is independent of the size of the structure and evaluate various piezoelectric materials based on their effectiveness in transmitting strain to the substructure.

Abstract: This work presents the analytic and experimental development of piezoelectric actuators as elements of intelligent structures, i.e., structures with highly distributed actuators, sensors, and processing networks. Static and dynamic analytic models are derived for segmented piezoelectric actuators that are either bonded to an elastic substructure or embedded in a laminated composite. These models lead to the ability to predict, a priori, the response of the structural member to a command voltage applied to the piezoelectric and give guidance as to the optimal location for actuator placement. A scaling analysis is performed to demonstrate that the effectiveness of piezoelectric actuators is independent of the size of the structure and to evaluate various piezoelectric materials based on their effectiveness in transmitting strain to the substructure. Three test specimens of cantilevered beams were constructed: an aluminum beam with surface-bonded actuators, a glass/epoxy beam with embedded actuators, and a graphite/epoxy beam with embedded actuators. The actuators were used to excite steady-state resonant vibrations in the cantilevered beams. The response of the specimens compared well with those predicted by the analytic models. Static tensile tests performed on glass/epoxy laminates indicated that the embedded actuator reduced the ultimate strength of the laminate by 20%, while not significantly affecting the global elastic modulus of the specimen.

2,719 citations

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TL;DR: In this paper, the formulation of the basic field equations, boundary conditions and constitutive equations of simple micro-elastic solids is discussed. And explicit expressions of constitutive expressions of several simple micro elastic solids are given and applied to some special problems.

Abstract: The present work is concerned with the formulation of the basic field equations, boundary conditions and constitutive equations of what we call ‘simple micro-elastic’ solids. Such solids are affected by the ‘micro’ deformations and rotations not encountered in the theory of finite elasticity. The theory, in a natural fashion, gives rise to the concept of stress moments, inertial spin and other types of second order effects and their laws of motion. The mechanism of the surface tension is contained in the theory. In a forthcoming paper (Part II) explicit expressions of constitutive equations of several simple micro-elastic solids will be given and applied to some special problems.

1,309 citations

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TL;DR: In this article, a finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings.

Abstract: A finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings. The formulation was derived from the variational principle with consideration for both the total potential energy of the structures and the electrical potential energy of the piezoceramics. An eight-node three-dimensional composite brick element was implemented for the analysis, and three-dimensional incompatible modes were introduced to take into account the global bending behavior resulting from the local deformations of the piezoceramics. Experiments were also conducted to verify the analysis and the computer simulations. Overall, the comparisons between the predictions and the data agreed fairly well. Numerical examples were also generated by coupling the analysis with simple control algorithms to control actively the response of the integrated structures in a closed loop.

472 citations

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TL;DR: In this paper, the authors present an overview and assessment of the technology leading to the development of intelligent structures, which are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning and power amplification electronics.

Abstract: HIS article presents an overview and assessment of the technology leading to the development of intelligent structures. Intelligent structures are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning, and power amplification electronics. Such actuating, sensing, and signal processing elements are incorporated into a structure for the purpose of influencing its states or characteristics, be they mechanical, thermal, optical, chemical, electrical, or magnetic. For example, a mechanically intelligent structure is capable of altering both its mechanical states (its position or velocity) or its mechanical characteristics (its stiffness or damping). An optically intelligent structure could, for example, change color to match its background.17 Definition of Intelligent Structures Intelligent structures are a subset of a much larger field of research, as shown in Fig. I.123 Those structures which have actuators distributed throughout are defined as adaptive or, alternatively, actuated. Classical examples of such mechanically adaptive structures are conventional aircraft wings with articulated leading- and trailing-edge control surfaces and robotic systems with articulated manipulators and end effectors. More advanced examples currently in research include highly articulated adaptive space cranes. Structures which have sensors distributed throughout are a subset referred to as sensory. These structures have sensors which might detect displacements, strains or other mechanical states or properties, electromagnetic states or properties, temperature or heat flow, or the presence or accumulation of damage. Applications of this technology might include damage detection in long life structures, or embedded or conformal RF antennas within a structure. The overlap structures which contain both actuators and sensors (implicitly linked by closed-loop control) are referred to as controlled structures. Any structure whose properties or states can be influenced by the presence of a closed-loop control system is included in this category. A subset of controlled structures are active structures, distinguished from controlled structures by highly distributed actuators which have structural functionality and are part of the load bearing system.

470 citations