• Smart Structures and Systems
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• v.30 no.3
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• pp.221-237
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• 2022

This paper is concerned with nonlinear modeling and efficient numerical simulation of electrostrictive materials and structures. Two types of such materials are considered: relaxor ferroelectric ceramics and electrostrictive polymers. For ceramics, a geometrically linear formulation is developed, whereas polymers are studied in a geometrically nonlinear regime. In the paper, we focus on constitutive modeling first. For the reversible constitutive response under consideration, we introduce the augmented Helmholtz free energy, which is composed of a purely elastic part, a dielectric part and an augmentation term. For the elastic part, we involve an additive decomposition of the strain tensor into an elastic strain and an electrostrictive eigenstrain, which depends on the polarization of the material. In the geometrically nonlinear case, a corresponding multiplicative decomposition of the deformation gradient tensor replaces the additive strain decomposition used in the geometrically linear formulation. For the dielectric part, we first introduce the internal energy, to which a Legendre transformation is applied to compute the free energy. The augmentation term accounts for the contribution from vacuum to the energy. In our formulation, the augmented free energy depends not only on the strain and the electric field, but also on the polarization and an internal polarization; the latter two are internal variables. With the constitutive framework established, a Finite Element implementation is briefly discussed. We use high-order elements for the discretization of the independent variables, which include also the internal variables and, in case the material is assumed incompressible, the hydrostatic pressure, which is introduced as a Lagrange multiplier. The elements are implemented in the open source code Netgen/NGSolve. Finally, example problems are solved for both, relaxor ferroelectric ceramics and electrostrictive polymers. We focus on thin plate-type structures to show the efficiency of the numerical scheme and its applicability to thin electrostrictive structures.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.19-38
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• 2008

This study aims to investigate the evolution of calculating the volume of a sphere in eastern and western mathematical history. In western case, Archimedes', Cavalieri's and Kepler's approaches, and in eastern case, Nine Chapters';, Liu Hui's and Zus' approaches are worthy of noting. The common idea of most of these approaches is the infinitesimal concept corresponding to Cavalieri's or Liu-Zu's principle which would developed to the basic idea of Calculus. So this study proposes an alternative to organization of math-textbooks or instructional procedures for teaching the volume of a sphere based on the principle.

• Smart Structures and Systems
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• v.3 no.2
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• pp.147-172
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• 2007

The present paper is concerned with the design of distributed sensors and actuators. Strain type sensors and actuators are considered with their intensity continuously distributed throughout a continuous structure. The sensors measure a weighted average of the strain tensor. As a starting point for their design we introduce the concept of collocated sensors and actuators as well as the so-called natural output. Then we utilize the principle of virtual work for an auxiliary quasi-static problem to assign a mechanical interpretation to the natural output of the sensors to be designed. Therefore, we take the virtual displacements in the principle of virtual work as that part of the displacement in the original problem, which characterizes the deviation from a desired one. We introduce different kinds of distributed sensors, each of them with a mechanical interpretation other than a weighted average of the strain tensor. Additionally, we assign a mechanical interpretation to the collocated actuators as well; for that purpose we use an extended body force analogy. The sensors and actuators are applied to solve the displacement tracking problem for continuous structures; i.e., the problem of enforcing a desired displacement field. We discuss feed forward and feed back control. In the case of feed back control we show that a PD controller can stabilize the continuous system. Finally, a numerical example is presented. A desired deflection of a clamped-clamped beam is tracked by means of feed forward control, feed back control and a combination of the two.

• Smart Structures and Systems
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• v.13 no.4
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• pp.567-585
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• 2014

The piezoelectric transverse $d_{15}$ shear sensing mechanism is firstly assessed experimentally for a cantilever smart sandwich plate made of a piezoceramic axially poled patched core and glass fiber reinforced polymer composite faces. Different electrical connections are tested for the assessment of the sensor performance under a varying amplitude harmonic (at 24 Hz) force. Also, the dynamic response of the smart sandwich composite structure is monitored using different acquisition devices. The obtained experimentally sensed voltages are compared to those resulting from the benchmark three-dimensional piezoelectric coupled finite element simulations using a commercial code where realistic features, like equipotential conditions on the patches' electrodes and mechanical updating of the clamp, are considered. Numerically, it is found that the stiffness of the clamp, which is much softer than the ideal one, has an enormous influence on the sensed voltage of its adjacent patch; therefore, sensing with the patch on the free side would be more advantageous for a cantilever configuration. Apart from confirming the latter result, the plate benchmark experimental assessment showed that the parallel connection of its two oppositely poled patches has a moderate performance but better than the clamp side patch acting as an individual sensor.

• Smart Structures and Systems
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• v.12 no.5
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• pp.483-499
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• 2013

A new piezoceramic $d_{15}$ shear-induced torsion actuation mechanism representative benchmark is proposed and its experimentations and corresponding 3D finite element (FE) simulations are conducted. For this purpose, a long and thin smart sandwich cantilever beam is dimensioned and built so that it can be used later for either validating analytical Saint Venant-type solutions or for analyzing arm or blade-based smart structures and systems applications. The sandwich beam core is formed by two adjacent rows of 8 oppositely axially polarized d15 shear piezoceramic patches, and its faces are dimensionally identical and made of the same glass fiber reinforced polymer composite material. Quasi-static and static experimentations were made using a point laser sensor and a scanning laser vibrometer, while the 3D FE simulations were conducted using the commercial software $ABAQUS^{(R)}$. The measured transverse deflection by both sensors showed strong nonlinear and hysteretic (static only) variation with the actuation voltage, which cannot be caught by the linear 3D FE simulations.

• Smart Structures and Systems
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• v.18 no.2
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• pp.335-354
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• 2016

This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

• Journal of The Geomorphological Association of Korea
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• v.24 no.4
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• pp.103-115
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• 2017

This paper shows the types of deteriorated hiking trails and degrading factors at three Great Walks such as Tongariro Alpine Crossing, Routeburn Track and Kepler Track in New Zealand. The deteriorated trails could be classified into gullying, widening, narrowing, branching and sidewall erosion. Department of Conservation carefully manages overland flows on trails for preventing surface erosion, thus the Great Walks show only a minor problem of gully on trails which is usually active in a mountainous area. Widening and branching of trails caused by tread erosion are not also developed due to the restriction of visitors as well as the management of rainwash. However, despite the detailed maintenance and prevention of an overuse of trails, some trails traversing steep slopes in a alpine zone under a periglacial environment are severely degraded along their sidewalls. It suggests that a unvegetated sidewall of trails has to be strictly managed in an early stage of occurrence and a slope-traversing section should be selected with more consideration when establishing a route of hiking trails.

• Smart Structures and Systems
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• v.7 no.5
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• pp.417-432
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• 2011

The present paper is devoted to vibration canceling and shape control of piezoelastic slender beams. Taking into account the presence of electric networks, an extended electromechanically coupled Bernoulli-Euler beam theory for passive piezoelectric composite structures is shortly introduced in the first part of our contribution. The second part of the paper deals with the concept of passive shape control of beams using shaped piezoelectric layers and tuned inductive networks. It is shown that an impedance matching and a shaping condition must be fulfilled in order to perfectly cancel vibrations due to an arbitrary harmonic load for a specific frequency. As a main result of the present paper, the correctness of the theory of passive shape control is demonstrated for a harmonically excited piezoelelastic cantilever by a finite element calculation based on one-dimensional Bernoulli-Euler beam elements, as well as by the commercial finite element code of ANSYS using three-dimensional solid elements. Finally, an outlook for the practical importance of the passive shape control concept is given: It is shown that harmonic vibrations of a beam with properly shaped layers according to the presented passive shape control theory, which are attached to an resistor-inductive circuit (RL-circuit), can be significantly reduced over a large frequency range compared to a beam with uniformly distributed piezoelectric layers.

• Smart Structures and Systems
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• v.5 no.6
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• pp.613-632
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• 2009

The present paper is concerned with the design of a proper patch actuator network in order to track a desired displacement of the sidewalls of a one-storey frame structure; both, for the static and the dynamic case. Weights for each patch of the actuator network found in our previous work were based on beam theory; in the present paper a refinement of these weights by modeling the sidewalls of the frame structure as thin plates is presented. For the sake of calculating the refined weights approximate solutions of the plate equations are calculated by an extended Galerkin method. The solutions based on the analytical plate model are compared with three-dimensional Finite Element results computed in the commercially available code ANSYS. The patch actuator network is put into practice by means of four piezoelectric patches attached to each of the two sidewalls of the frame structures, to which electric voltages proportional to the analytically refined patch weights are applied. Analytical and numerical results coincide very well over a broad frequency range.

• ETRI Journal
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• v.31 no.5
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• pp.593-597
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• 2009

In this paper, we present a spatial perturbation method to control the optical patterns in semiconductor microresonators in the far-field configuration. We propose a fast all-optical switch which operates at a low light level. The switching beam controls the behavior of output beams with strong intensities. The method has been applied successfully to different optical patterns such as rolls, squares, and hexagons.