Segmented Actuators Research Articles

Bone transport of the tibia with a motorized intramedullary lengthening nail — a case report

Bone resection and subsequent bone transport and bone lengthening is a well-established treatment for a tibial non-union with shortening (Rozbruch et al. 2008). To our knowledge, this is the first description in the literature of bone transport and subsequent bone lengthening of the tibia only by use of a motorized intramedullary nail. A 53-year-old male twisted his leg while downhill skiing and sustained an OTA classification 43-A2.3 (4) closed fracture of the distal tibia and fibula (Marsh et al. 2007). Both fractures were treated with open reduction and locking plates in January 2009. A non-union developed with loosening of the osteosynthesis, and 7 months after the initial operation the patient was reoperated with bone allograft and exchange of the plates and screws. The non-union did not heal. The patient was referred to our institution 20 months after the first reoperation. At this time, the tibial plate was loose, with broken screws (Figure 1). The tibia had a varus deformity of 16 degrees and was 2.2 cm shortened (Figure 1). The non-union site was tested clinically and found to be loose. Figure 1. Frontal plane varus deformity without sagittal plane deformity of the tibia, with leg-length discrepancy of 2.2 cm in patient with tibial non-union. We operated the patient 24 months after the first reoperation. After removal of all previously inserted implants and screws, except a distal AP screw, the non-union site was found at surgery to be atrophic. The non-union site (3.1 cm bone segment) was resected to vital bone. The fibula was osteotomized at the level of the tibial resection. A proximal percutaneous tibial osteotomy was performed 9 cm from the knee joint line. A custom-made motorized tibial lengthening nail (Fitbone TSA (Tibial Segment Actuator) was inserted. The nail had a length of 35 cm and was capable of 4 cm of bone transport initially and 2 cm of bone lengthening subsequently. The nail had 8 degrees of anterior bending, starting 40 mm from the proximal tip of the nail. The nail was locked with 2 proximal and 2 distal locking screws to the tibia. In addition, a screw was inserted into a sliding hole in the middle part of the tibia, allowing bone transport of the middle tibial segment (Figure 2). A tibio-fibular screw was inserted distally to protect the distal tibio-fibular joint. Acute shortening of the bone defect was not performed. A radiograph taken immediately after surgery showed that 3.1 cm of bone had been resected. Bone transport was initiated 10 days postoperatively at a rate of 1 mm daily (Figure 3). There were no clinical signs of infection and the white blood cell and C-reactive protein levels were normal before surgery. However, biopsies of the resected bone were cultured and showed growth of coagulase-negative staphylococci, which were sensitive to dicloxacillin. Dicloxacillin was therefore administered orally for 3 months. Figure 2. Immediately postoperatively, showing tibial bone gap after bone resection. The bone transport and lengthening nail is inserted in the tibia after proximal tibial osteotomy and distal fibula osteotomy. Figure 3. A. 1 month after surgery. 4 weeks postoperatively, 3.3 mg of recombinant BMP-7 (eptotermin alfa, Osigraft; Stryker) was administered percutaneously to the docking site. A loose proximal locking screw was exchanged at the same surgery and intraoperative fluoroscopy showed that the fibula osteotomy was still loose, allowing lengthening of the fibula. Partial weight bearing was allowed from 2 months postoperatively when the proximal tibia had been lengthened 5 cm (3 cm of bone transport plus 2 cm of leg lengthening). The docking site was united 5 months postoperatively, and full weight bearing was allowed at this time. Healing time for the regenerate was 45 days/cm of bone lengthening. The distal tibio-fibular screw bothered the patient and was removed at 6 months postoperatively. The nail was removed 15 months postoperatively. At the latest follow-up, 18 months after nail insertion and 3 months after nail removal, the patient had no pain or restrictions in daily activities. Motion of the knee and the ankle on the operated side was equal to that on the healthy side. Motion of the knee was from full extension to 140 degrees of flexion and motion of the ankle was from 15 degrees of dorsal flexion to 30 degrees of plantar flexion. An AP radiograph showed no mechanical axis deviation in the operated leg compared to the healthy leg. There was equal leg length. There was a 3-degree varus deformity in the frontal plane. There was no deformity in the sagittal plane on the lateral radiograph. The posterior proximal tibial angle (PPTA) and the anterior distal tibial angle (ADTA) equalled the preoperative values of 78 degrees (PPTA) and 83 degrees (ADTA). There have not been any clinical signs of infection.

Bone transport of the tibia with a motorized intramedullary lengthening nail — a case report

Bone resection and subsequent bone transport and bone lengthening is a well-established treatment for a tibial non-union with shortening (Rozbruch et al. 2008). To our knowledge, this is the first description in the literature of bone transport and subsequent bone lengthening of the tibia only by use of a motorized intramedullary nail. A 53-year-old male twisted his leg while downhill skiing and sustained an OTA classification 43-A2.3 (4) closed fracture of the distal tibia and fibula (Marsh et al. 2007). Both fractures were treated with open reduction and locking plates in January 2009. A non-union developed with loosening of the osteosynthesis, and 7 months after the initial operation the patient was reoperated with bone allograft and exchange of the plates and screws. The non-union did not heal. The patient was referred to our institution 20 months after the first reoperation. At this time, the tibial plate was loose, with broken screws (Figure 1). The tibia had a varus deformity of 16 degrees and was 2.2 cm shortened (Figure 1). The non-union site was tested clinically and found to be loose. Figure 1. Frontal plane varus deformity without sagittal plane deformity of the tibia, with leg-length discrepancy of 2.2 cm in patient with tibial non-union. We operated the patient 24 months after the first reoperation. After removal of all previously inserted implants and screws, except a distal AP screw, the non-union site was found at surgery to be atrophic. The non-union site (3.1 cm bone segment) was resected to vital bone. The fibula was osteotomized at the level of the tibial resection. A proximal percutaneous tibial osteotomy was performed 9 cm from the knee joint line. A custom-made motorized tibial lengthening nail (Fitbone TSA (Tibial Segment Actuator) was inserted. The nail had a length of 35 cm and was capable of 4 cm of bone transport initially and 2 cm of bone lengthening subsequently. The nail had 8 degrees of anterior bending, starting 40 mm from the proximal tip of the nail. The nail was locked with 2 proximal and 2 distal locking screws to the tibia. In addition, a screw was inserted into a sliding hole in the middle part of the tibia, allowing bone transport of the middle tibial segment (Figure 2). A tibio-fibular screw was inserted distally to protect the distal tibio-fibular joint. Acute shortening of the bone defect was not performed. A radiograph taken immediately after surgery showed that 3.1 cm of bone had been resected. Bone transport was initiated 10 days postoperatively at a rate of 1 mm daily (Figure 3). There were no clinical signs of infection and the white blood cell and C-reactive protein levels were normal before surgery. However, biopsies of the resected bone were cultured and showed growth of coagulase-negative staphylococci, which were sensitive to dicloxacillin. Dicloxacillin was therefore administered orally for 3 months. Figure 2. Immediately postoperatively, showing tibial bone gap after bone resection. The bone transport and lengthening nail is inserted in the tibia after proximal tibial osteotomy and distal fibula osteotomy. Figure 3. A. 1 month after surgery. 4 weeks postoperatively, 3.3 mg of recombinant BMP-7 (eptotermin alfa, Osigraft; Stryker) was administered percutaneously to the docking site. A loose proximal locking screw was exchanged at the same surgery and intraoperative fluoroscopy showed that the fibula osteotomy was still loose, allowing lengthening of the fibula. Partial weight bearing was allowed from 2 months postoperatively when the proximal tibia had been lengthened 5 cm (3 cm of bone transport plus 2 cm of leg lengthening). The docking site was united 5 months postoperatively, and full weight bearing was allowed at this time. Healing time for the regenerate was 45 days/cm of bone lengthening. The distal tibio-fibular screw bothered the patient and was removed at 6 months postoperatively. The nail was removed 15 months postoperatively. At the latest follow-up, 18 months after nail insertion and 3 months after nail removal, the patient had no pain or restrictions in daily activities. Motion of the knee and the ankle on the operated side was equal to that on the healthy side. Motion of the knee was from full extension to 140 degrees of flexion and motion of the ankle was from 15 degrees of dorsal flexion to 30 degrees of plantar flexion. An AP radiograph showed no mechanical axis deviation in the operated leg compared to the healthy leg. There was equal leg length. There was a 3-degree varus deformity in the frontal plane. There was no deformity in the sagittal plane on the lateral radiograph. The posterior proximal tibial angle (PPTA) and the anterior distal tibial angle (ADTA) equalled the preoperative values of 78 degrees (PPTA) and 83 degrees (ADTA). There have not been any clinical signs of infection.

Dynamic Modeling and Effect of Dehydration on Segmented IPMC Actuators Following Variable Parameter Pseudo-Rigid Body Modeling Technique

An ionic polymer-metal composite actuator has been analyzed following the variable parameters pseudo-rigid body modeling (VPPRBM) technique in order to assess the effect of dehydration on bending resistance and bending response. An experiment is conducted with a single patch IPMC actuator and the dehydration factor is obtained following the Cobb-Douglas production method. An energy-based dynamic model of the patches has been derived after developing the forward kinematics incorporating loss due to dehydration. Simulation has been performed for two segmented IPMC patches to demonstrate the change in bending resistance, bending response, and end-tip positioning for various input voltages.

Laminar flow control with distributed surface actuation: damping Tollmien-Schlichting waves with active surface displacement

Control strategies for laminar flow control above an unswept wing are investigated. An actuation method based on a flexible membrane displaced by multiple piezo-polymer composite elements is developed for wind tunnel experiments. A model predictive control algorithm is applied to control the multi-bar actuator. The direct negative superposition method of damping Tollmien–Schlichting waves is compared to a biomimetic approach imitating the damping mechanisms of a compliant skin. In both cases, a model predictive control algorithm is applied to control the multi-bar actuator segments. For the biomimetic approach, reduced, real-time solvable models of compliant surfaces are developed and parametrized by direct optimization and according to numerically generated optimal wall properties. Damping results of up to 85 % RMS value are achieved, shifting the onset of transition about 100 mm downstream with a single actuation membrane. Additional experiments with cascaded multiple membranes show the potential for a further shift.

Mechanics of undulatory swimming in a frictional fluid.

The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a “granular frictional fluid” and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.

Minimizing the wavefront error degradation for primary mirror segments with failed hexapod actuators

The performance of a segmented space telescope depends in part upon the ability to maintain the alignment and phasing of its primary mirror segments. Failures of segment control actuators pose a threat to mission success, but their effects can be mitigated by using the remaining segment actuators to optimize the pose of each affected segment. This paper considers the effect of actuator failures on the final wavefront error of a segmented space telescope whose primary mirror consists of 18 hexagonal segments, each controlled by a 3-6 hexapod. Optimization algorithms that minimize the wavefront error for single- and multiple-failure cases are developed, and simulation results are presented. When one actuator fails, the affected segment can still attain a pose with zero wavefront error by exploiting the rotational symmetry of the primary. When two actuators fail, the resulting wavefront error depends upon which hexapod legs fail and at what lengths; cases where both legs of a bipod fail are an order of magnitude worse than other cases. Finally, Monte Carlo simulations of many failures randomly distributed across an initially well-phased segmented primary show that more than 10% of the actuators must fail before the root-mean-square wavefront error degrades significantly.

Spatial Electrostrictive Actuations of Flexible Circular Tubes

This paper is aimed to study dynamic actuation of circular tubular shell structures coupled with distributed electrostrictive actuator segments. A mathematical model of the hybrid elastic/electrostrictive circular tubular shell, including the electrostrictive/elastic/control couplings, is derived. The generalized electrostrictive control actuation induced by an arbitrary electrostrictive actuator segment consists of three contributing components: the circumferential membrane control action, the longitudinal bending control action, and the circumferential bending control action. In particular, spatial modal actuation characteristics of the total actuation and the three contributing components corresponding to various design parameters (e.g., actuator thickness, shell radius, and thickness) are evaluated and compared with respect to actuator patch sizes. Analysis data suggest that the electrostrictive membrane control actuation dominates the overall control action in lower shell modes; however, the control moment becomes important in higher shell modes. Optimal placements of electrostrictive actuator segments on the circular tubular shell are identified. Modal filtering behaviors, due to cancellation of internal attenuation/amplification effects, occur when large-size actuators are used, rendering the actuation less effective.

Design of a Flexible Imaging Probe for Robotics Surgery

Minimally invasive surgery assisted by robots has shown higher efficiency and precision. In spite of the good performance of the state of the art surgery robotics systems, the size and number of external incisions required by instruments should be reduced to lower the scarring and incisional pain experienced by the patient. Other important improvement derived from the use of smaller incisions is the diminishment of time required for recovery. This research develops a flexible scope of small diameter driven by segmented multiple actuators to produce a deflection of the imaging probe at its distal end providing better visualization than the current rigid cameras. The research is conducted in cooperation with the Biorobotics Laboratory at the University of Washington USA, where our scope will be incorporated to Raven, a 7-DOF cable-actuated surgical robot. The flexible scope is composed of three segments as illustrated in Figure 1, where it is possible to see that the device contains a ring of cables enclosed externally and internally by two different springs and a semi rigid covering. The main mechanism of bending is the compression and extension of the external spring at the distal end. The change of length in this spring is controlled by an active system that combines pulling and releasing actions through the ring of cables. The device has advantages in its simplicity of actuation and the high elasticity and flexibility at the distal end. In the current state of the project, a testing system is under construction.

Stability of Homogeneous Smart Beams based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation

1 Abstract—This paper studies stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter and foundation coefficient on the stability of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. Keywords—Stability, Homogeneous beam- Piezoelectric layer. I. INTRODUCTION HE applications of the smart materials have drawn attention in aerospace engineering, civil engineering, mechanical and even bio-engineering. The analysis of a coupled piezoelectric structure has recently been keenly researched because piezoelectric materials are more extensively used either as actuators or sensors. Examples include the analytical modelling and behaviour of a beam with surface-bonded or embedded piezoelectric sensors and actuators (1-3), and the use of piezoelectric materials in composite laminates and for vibration control (4). The use of finite element method in the analysis of piezoelectric coupled structures has been studied (5-8). Crawley and de Luis (9) developed the analytical model for the static and dynamic response of a beam structure with segmented piezoelectric actuators either bonded or embedded in a laminated composite. LaPeter and Cudney (10) proposed an analytic model for the segmented piezoelectric actuators bonded on a beam or a plate, and found the equivalent forcing functions of the actuators. The piezoelectric bimorph column structures were used as sensing elements. Dobrucki and Pruchnicki (11) presented an analysis theory of an axisymmetric piezoelectric bimorph. They also described a sensing theory for using the axisymmetric piezoelectric bimorph. Chandrashekhara and Bhatia (12) developed a finite element model for the active buckling control of laminated composite plates with surface bonded or embedded piezoelectric sensors that are either continuous or segmented. The dynamic buckling behavior of the laminated plate subjected to a linearly increasing compression load is investigated in their work. Chase and Bhashyam (13) derived optimal design equations to actively stabilize laminated plates loaded in excess of the critical buckling load using a large number of sensors and actuators. To the author's knowledge, there is no analytical solution available in the open literatures for stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. In the present work, stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation studied. Appling the Hamilton's principle, the equilibrium equations of beam are derived and solved. The effects of applied voltage, dimensionless geometrical parameter and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators

This study is concerned with the detailed analysis of fiber-reinforced composite plates with integrated piezoceramic fiber composite actuators. A multiscale framework based on the asymptotic expansion homogenization method is used to couple the microscale and macroscale field variables. The microscale fluctuations in the mechanical displacement and electric potential are related to the macroscale deformation and electric fields through 36 distinct characteristic functions. The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method. The homogenized electroelastic properties of a representative material element are computed using the characteristic functions and the material properties of the fiber and matrix. The three-dimensional macroscopic equilibrium equations for a laminated piezoelectric plate are solved analytically using the Eshelby–Stroh formalism. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. The microscale stresses and electric displacement in the fibers and matrix are computed from the macroscale fields through interscale transfer operators. The multiscale analysis procedure is illustrated using two model problems. In the first model problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/polymer layers is studied. The second model problem concerns a cantilever graphite/polymer substrate with segmented piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.

Distributed actuation characteristics of clamped-free conical shells using diagonalpiezoelectric actuators

In spacecraft, severe vibrations induced by the launch vehicle may cause damage to theprecision payload. Therefore active adapters with vibration suspending characteristics areneeded. This paper presents theoretical studies of the active vibration controlcharacteristics of conical shells with laminated piezoelectric actuators. A diagonalpiezoelectric actuator is proposed to control the axial, lateral and transverse vibrations ofthe conical shell. Modal functions are designed to represent the free vibrations of theconical shell with clamped-free boundary conditions. General formulae of the modal controlforce and corresponding components are derived based on the converse piezoelectriceffects and then specified for the diagonal actuators. By using an open-loop controlmethod, the modal control characteristics of diagonal actuator segments at differentlocations are investigated and compared, and the axial, lateral and transversevibrations of two conical shell models are evaluated. The optimal locations ofactuator segments for the control of different natural modes are also investigated.

Evaluation of dehydration loss and investigation of its effect on bending response of segmented IPMC actuators

Efforts were made to estimate and analyze the effect of dehydration on the bending response of segmented ionic polymer–metal composite (IPMC) actuators. An experiment was conducted with an IPMC actuator to study the variation of bending characteristics with input voltage. Based on the experimental data, the Cobb–Douglas production method was used to obtain the dehydration factor in terms of input voltage and time. The motion of the patches was restricted to planar in two dimensions. A single-patch IPMC actuator was then modeled following the Euler–Bernoulli approach incorporating loss due to dehydration. A forward kinematics model for the segmented actuators was formulated after constituting the homogeneous coordinate transformation matrix, assuming it is a serial link multi-degree of freedom manipulator. An energy-based dynamic model of the patches was derived using the Lagrange principle. Simulations were performed for single and two segmented IPMC patches to demonstrate the bending response for various input voltages. The results demonstrate the gradual reduction of bending response of an actuator owing to moisture loss.

Active buckling control of beams using piezoelectric actuators and strain gaugesensors

In this paper, a finite element model incorporating active control techniques has beendeveloped to stabilize the first two buckling modes of both a simply supported and acantilevered beam. The goal is to increase the corresponding beam buckling loads by usingpiezoelectric actuators along with optimal feedback control.The uniform beams are bonded with two pairs of segmented piezoelectric actuators at thetop and bottom. Resistive strain gauges are attached to the centres of the actuators assensors. Measurements are taken using these, to estimate the system states. The beamsare simply supported or cantilevered and subjected to a slowly increasing axialcompressive load. Finite element formulations based on the classical Euler–Bernoullibeam theory and linear piezoelectric constitutive equations for the actuators arepresented. The associated reduced-order modal equations and the state-spaceequations are derived for the design of a standard linear quadratic regulator (LQR).The finite element analysis and the active control simulation results are consistent withboth theoretical analysis results and experimental data. The designed full state feedbackLQR controller is shown to be successful in stabilizing the first two buckling modes ofthe beams. Also the control simulation shows that the present optimally locatedsegmented actuator pairs along the beam are more effective for buckling control.

Design of an Adaptive Gust Response Alleviation Control System: Simulations and Experiments

An adaptive gust response alleviation control system based on fuzzy logic was designed for a large-aspect-ratio and two-control-surface wing model. A state-space model consisting of an elastic wing model, an actuator segment, and a gust segment was established. Time-domain and frequency-domain simulations and analyses were conducted for continuous random gust response alleviation. Experiments and simulations of continuous sinusoidal gust response alleviation were spread out over time and frequency domains. The simulated results agree well with the experimental results. The control system effectively acts on random gusts in simulations. The control system has similar effects on sinusoidal gusts of different frequencies at different flow velocities in the experiments. The alleviation efficiency of sinusoidal gusts is higher than the alleviation efficiency of random gusts, while the range of the wing-tip gust response is the same.

Development of an Automated Steering Mechanism for Bladder Urothelium Surveillance

Given the advantages of cystoscopic exams compared with other procedures available for bladder surveillance, it would be beneficial to develop an improved automated cystoscope. We develop and propose an active programmable remote steering mechanism and an efficient motion sequence for bladder cancer detection and postoperative surveillance. The continuous and optimal path of the imaging probe can enable a medical practitioner to readily ensure that images are produced for the entire surface of the bladder in a controlled and uniform manner. Shape memory alloy (SMA) based segmented actuators disposed adjacent to the distal end of the imaging probe are selectively activated to bend the shaft to assist in positioning and orienting the imaging probe at a plurality of points selected to image all the interior of the distended bladder volume. The bending arc, insertion depth, and rotational position of the imaging probe are automatically controlled based on patient-specific data. The initial prototype is tested on a 3D plastic phantom bladder, which is used as a proof-of-concept in vitro model and an electromagnetic motion tracker. The 3D tracked tip trajectory results ensure that the motion sequencing program and the steering mechanism efficiently move the image probe to scan the entire inner tissue layer of the bladder. The compared experimental results shows 5.1% tip positioning error to the designed trajectory given by the simulation tool. The authors believe that further development of this concept will help guarantee that a tumor or other characteristic of the bladder surface is not overlooked during the automated cystoscopic procedure due to a failure to image it.

Optimal electrode shaping for precise modal electromechanical filtering

This paper addresses the optimal shape design of segmented spatial sensors and actuators that isolate selected mode shapes and perform modal filtering. Electromechanical filters have reappeared with the new manufacturing capabilities of micro-electro-mechanical structures (MEMS). In such small dimensions it proves essential to treat their elastic behaviour as continuous rather than discrete systems that require suitable design methods, some of which are developed here. In MEMS filters, the input signal is converted to external electrostatic forces and in order to perform the desired filtering, the electrodes need to be shaped such that they excite only a desired part of the dynamics. An optimization scheme that shapes these electrodes to achieve optimal filtering is developed. In order to enhance the filter’s performance and minimize energy lost to the supporting structure, a special support tuning method is proposed. Several simulated examples examine the effectiveness of the proposed optimization methods.

Forced response of cylindrical shells coupled with nonlinear shape-memory-alloy (SMA) actuators regulated by sinusoidal and saw-tooth temperature profiles

Dynamic responses of cylindrical shells coupled with shape-memory alloy (SMA) ring segments placed at critical locations are investigated. Since the SMA actuators are highly nonlinear and governed by the temperate-dependent stiffness and martensite/austenite fraction, input shaping and phase shift of temperature profiles are incorporated to control the shell vibrations. Open-loop equations of an elastic cylindrical shell panel are defined first and then used with assumed mode-shape functions satisfying specified boundary conditions in the free-vibration analysis. Modal-analysis data are used to determine spatial strain distributions of natural modes. Distributed modal-signal characteristics suggest optimal placements of SMA actuator segment(s) for each given mnth mode. Based on the modal-expansion method, the open-loop control force induced by the SMA ring segments applied to a simply supported cylindrical shell panel is formulated. This formulation indicates that only the odd modes in the circumferential direction can be controlled. Longitudinal modes are controlled via placing specific number, depending on the mode, of actuator segments along the panel length. To predict control effects of the nonlinear SMA ring segments, the modal participation factor response is determined for an external harmonic excitation applied to the shell along with induced SMA control forces, via sinusoidal and saw-tooth temperature profiles to generate desirable control forces and to eliminate the unwanted effects. Analysis results suggest that with proper choice of temperature waveform function to the SMA ring segments and minor modifications to frequency and phase, the SMA ring segments can attenuate unwanted external vibrations of cylindrical shells.

An efficient quadrilateral element based on improved zigzag theory for dynamic analysis of hybrid plates with electroded piezoelectric actuators and sensors

An efficient four-node quadrilateral element is developed using a coupled improved zigzag theory for the dynamic analysis of hybrid plates with segmented piezoelectric sensors and actuators. The theory considers a third-order zigzag approximation for inplane displacements, a layerwise quadratic approximation for the electric potential and a layerwise variation of the deflection to account for the piezoelectric transverse normal strain. The conditions on transverse shear stresses at the interfaces and at the top and bottom are satisfied exactly in the presence of electric loading. In a novel concept, the degrees of freedom (dof) corresponding to the quadratic component of the electric potential distribution are associated with the physical nodes and the electric potentials of the electroded piezoelectric surfaces are attached to separate electric nodes. The requirement of C1 continuity of interpolation functions of the deflection is circumvented by employing an improved discrete Kirchhoff constraint technique. Comparison of the present results for natural frequencies and mode shapes for a variety of bimorph, hybrid composite and sandwich plates, with three-dimensional (3D) analytical and FE solutions, and those of other available elements establishes the superiority of the present element with respect to accuracy, robustness and computational efficiency. The comparison also establishes the superiority of the zigzag theory over the smeared third-order theory having the same number of dof.

Magnetostrictive Microactuations and Modal Sensitivities of Thin Magnetoelastic Shells

This study is to evaluate distributed microscopic actuation characteristics and control actions of segmented magnetostrictive actuator patches laminated on a flexible cylindrical shell panel. A mathematical model and its modal domain governing equations of the cylindrical shell panel laminated with distributed magnetostrictive actuator patches are presented first, followed by the formulation of distributed magnetostrictive control forces and microcontrol actions including circumferential membrane∕bending and longitudinal bending control components. Transverse mode shape functions with simply supported boundary conditions are used in the modal control force expressions and the microcontrol action analyses. Control effectives and spatial characteristics of distributed actuators depend on applied magnetic fields and on geometrical (e.g., spatial segmentation, location, and shape) and material (i.e., various actuator materials) properties. Spatially distributed magnetoelectromechanical actuation characteristics contributed by circumferential membrane∕bending and longitudinal bending control actions are investigated. Distributed control forces and microactuations of a magnetostrictive actuator patch at various locations are analyzed, and modal-dependent spatial control effectiveness is evaluated.

Optimal actuator locations and precision micro-control actions on free paraboloidal membrane shells

Flexible paraboloidal shells, as key components, are increasingly utilized in antennas, reflectors, optical systems, aerospace structures, etc. To explore precise shape and vibration control of the paraboloidal membrane shells, this study focuses on analysis of microscopic control actions of segmented actuator patches laminated on the surface of a free paraboloidal membrane shell. Governing equations of the membrane shell system and modal control forces of distributed actuator patches are presented first, and followed by the analysis of dominating micro-control actions based on various natural modes, actuator locations and geometrical parameters. Finally, according to the parametric analysis, simulation data reveal main factors significantly influencing active control behavior on smart free-floating paraboloidal membrane shell systems, thus providing design guidelines to achieve optimal control of paraboloidal shell systems.