Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters. (C) 2004 Elsevier Ltd. All rights reserved.

The effect of weightbearing exercise with low frequency, whole body vibration on lumbosacral proprioception: A pilot study on normal subjects

Patients with low back pain (LBP) often present with impaired proprioception of the lumbopelvic region. For this reason, proprioception training usually forms part of the rehabilitation protocols. New exercise equipment that produces whole body, low frequency vibration (WBV) has been developed to improve muscle function, and reportedly improves proprioception. The aim of this pilot study was to investigate whether weightbearing exercise given in conjunction with WBV would affect lumbosacral position sense in healthy individuals. For this purpose, twenty-five young individuals with no LBP were assigned randomly to an experimental or control group. The experimental group received WBV for five minutes while holding a static, semi-squat position. The control group adopted the same weightbearing position for equal time but received no vibration. A two-dimensional motion analysis system measured the repositioning accuracy of pelvic tilting in standing. The experimental (WBV) group demonstrated a significant improvement in repositioning accuracy over time (mean 0.78 degrees) representing 39% improvement. It was concluded that WBV may induce improvements in lumbosacral repositioning accuracy when combined with a weightbearing exercise. Future studies with WBV should focus on evaluating its effects with different types of exercise, the exercise time needed for optimal outcomes, and the effects on proprioception deficits in LBP patients.

Changes in joint stability with muscle contraction measured from transmission of mechanical vibration

A non-invasive in vivo technique was developed to evaluate changes in wrist joint stability properties induced by increased co-activation of the forearm muscles in a gripping task. Mechanical vibration at 45, 50 and 55 Hz was applied to the radial head in ten healthy volunteers. Vibrations of the styloid process of the radius and the distal end of the metacarpal bone of the index finger were measured with triaxial accelerometers. Joint stability properties were quantified by the transfer function gain between accelerations on either side of the wrist-joint. Gain was calculated with the muscles at rest and at five force levels ranging from 5% to 25% of maximum grip force (%MF). During contraction the gain was significantly greater than in control trial (0%MF) for all contractions levels at 45 and 50 Hz and a trend for 15%MF and higher at 55 Hz. Group means of contraction force and gain were significantly correlated at 45 (R-2 = 0.98) and 50 Hz (R-2 = 0.72), but not at 55 Hz (R-2 = 0.10). In conclusion, vibration transmission gain may provide a method to evaluate changes in joint stability properties. (c) 2005 Published by Elsevier Ltd.

Highly demanding resistive vibration exercise program is tolerated during 56 days of strict bed-rest

Several studies have tried to find countermeasures against musculoskeletal de-conditioning during bed-rest, but none of them yielded decisive results. We hypothesised that resistive vibration exercise (RVE) might be a suitable training modality. We have therefore carried out a bed-rest study to evaluate its feasibility and efficacy during 56 days of bed-rest. Twenty healthy male volunteers aged 24 to 43 years were recruited and, after medical check-ups, randomised to a non-exercising control (Ctrl) group or a group that performed RVE 11 times per week. Strict bed-rest was controlled by video surveillance. The diet was controlled. RVE was performed in supine position, with a static force component of about twice the body weight and a smaller dynamic force component. RVE comprised four different units (squats, heel raises, toe raises, kicks), each of which lasted 60 - 100 seconds. Pre and post exercise levels of lactate were measured once weekly. Body weight was measured daily on a bed scale. Pain questionnaires were obtained in regular intervals during and after the bed-rest. Vibration frequency was set to 19 Hz at the beginning and progressed to 25.9 Hz (SD 1.9) at the end of the study, suggesting that the dynamic force component increased by 90%. The maximum sustainable exercise time for squat exercise increased from 86 s (SD 21) on day 11 of the BR to 176 s (SD 73) on day 53 (p = 0.006). On the same days, post-exercise lactate levels increased from 6.9 mmol/l (SD2.3) to 9.2 mmol/l (SD 3.5, p = 0.01). On average, body weight was unchanged in both groups during bed-rest, but single individuals in both groups depicted significant weight changes ranging from -10% to + d10% (p < 0.001). Lower limb pain was more frequent during bed-rest in the RVE subjects than in Ctrl (p = 0.035). During early recovery, subjects of both groups suffered from muscle pain to a comparable extent, but foot pain was more common in Ctrl than in RVE (p = 0.013 for plantar pain, p = 0.074 for dorsal foot pain). Our results indicate that RVE is feasible twice daily during bed-rest in young healthy males, provided that one afternoon and one entire day per week are free. Exercise progression, mainly by progression of vibration frequency, yielded increases in maximum sustainable exercise time and blood lactate. In conclusion, RVE as performed in this study, appears to be safe.

Illusory changes in head position induced by neck muscle vibration can alter the perception of elbow position

Acuity for elbow joint position sense (JPS) is reduced when head position is modified. Movement of the head is associated with biomechanical changes in the neck and shoulder musculoskeletal system, which may explain changes in elbow JPS. The present study aimed to determine whether elbow JPS is also influenced by illusory changes in head position. Simultaneous vibration of sternocleidomastoid (SCM) and the contralateral splenius was applied to 14 healthy adult human subjects. Muscle vibration or passive head rotation was introduced between presentation and reproduction of a target elbow position. Ten out of 14 subjects reported illusions consistent with lengthening of the vibrated muscles. In these 10 subjects, absolute error for elbow JPS increased with left SCM/right splenius vibration but not with right SCM/left splenius vibration. Absolute error also increased with right rotation, with a trend for increased error with left rotation. These results demonstrated that both actual and illusory changes in head position are associated with diminished acuity for elbow JPS, suggesting that the influence of head position on upper limb JPS depends, at least partially, on perceived head position.

Influence of imperfect interfaces on bending and vibration of laminated composite shells

This paper is devoted to modeling elastic behavior of laminated composite shells, with special emphasis on incorporating interfacial imperfection. The conditions of imposing traction continuity and displacement jump across each interface are used to model imperfect interfaces. Vanishing transverse shear stresses on two free surfaces of a shell eliminate the need for shear correction factors. A linear theory underlying elastostatics and kinetics of laminated composite shells in a general configuration is presented from Hamilton's principle. In the special case of vanishing interfacial parameters, this theory reduces to the conventional third-order zigzag theory for perfectly bonded laminated shells. Numerical results for bending and vibration problems of laminated circular cylindrical panels are tabulated and plotted to indicate the influence of the interfacial imperfection. (C) 2000 Elsevier Science Ltd. All rights reserved.

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.

Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.

A novel nucleation apparatus for regime separated granulation

A novel nucleation apparatus is presented for the production of narrow sized nuclei from various powder and binder liquid combinations. Mono-sized binder liquid droplets are produced by a specially designed mono-disperse droplet generator. The droplet generator is positioned above a conveyor belt, transporting a powder bed through the spray zone of the droplet generator. By nucleating powder on a conveyer belt, the nucleation mechanism is completely separated from all other granulation mechanisms due to the lack of relative motion between primary particles and/or formed nuclei. Nucleation tests were performed using chalcopyrite and limestone powders with water as the binder liquid. At all operating conditions, the formed nuclei were found to originate from multiplicities of drops that merged on the powder bed surface. Investigation of the dynamics of nuclei formation showed that powder-binder liquid combinations with fast penetration dynamics result in less variation in the number of droplets from which nuclei originate. Smaller and more narrowly distributed nuclei were also achieved by increasing powder speed through the spray zone.

Coupling of a Jahn-Teller pseudorotation with a hindered internal rotation in an isolated molecule: 9-hydroxytriptycene

The irregular vibronic structure in the S-1<--S-0 resonant two-photon ionization (R2PI) spectrum of supersonically cooled triptycene is a result of a classic Exe Jahn-Teller effect [A. Furlan et al., J. Chem. Phys. 96, 7306 (1992)]. This is well characterized and can be used as an effective probe of intramolecular perturbations. Here we examine the S-1<--S-0 R2PI spectrum of 9-hydroxytriptycene and the fluorescence from various excited state vibronic levels. In this system the pseudorotation of the Jahn-Teller vibration is strongly coupled to the torsional motion of the bridgehead hydroxy group. This torsional motion results in a tunneling splitting in both the ground and excited states. The population of the upper level in the ground electronic state results in additional vibronic transitions becoming symmetry allowed in the R2PI spectrum that are forbidden in the bare triptycene molecule. The assignment of the R2PI and fluorescence spectra allows the potential energy surfaces of these vibrational modes to be accurately quantified. The full C-3v vibronic point group must be used to interpret the spectra. The time scale of the internal rotation of the-OH group and the butterfly flapping of the Jahn-Teller pseudorotation are of similar magnitude. The tunneling between the nine minima on the three dimensional potential energy surface is such that the Jahn-Teller pseudorotation occurs in concert with the-OH internal rotation. The Berry phase that is acquired during this motion is discussed. The simple physical picture emerges of the angle between two of the three benzene moieties opening in three equivalent ways in the S-1 electronic state. This geometry follows the position of the hydroxy group, which preferentially orients itself to point between these two rings. (C) 1998 American Institute of Physics. [S0021-9606(98)02348-4].