Mode Localization in a Nearly Cyclic Symmetric System

Thesis (Ph.D.)--University of Washington, 2016-06

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Cycloadditions of isobenzofuran to a constrained template bearing neighboring dienophiles

A high yielding synthesis of the pentacyclic diene-dione 1 has enabled investigation of its reactivity as a double dienophile in Diels-Alder [4+2] cycloadditions with isobenzofuran, leading to novel and highly symmetrical three-sided cavitands 3 and 4.

Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Type 1 nitrergic (ND1) cells of the rabbit retina: Comparison with other axon-bearing amacrine cells

NADPH diaphorase (NADPHd) histochemistry labels two types of nitrergic amacrine cells in the rabbit retina. Both the large ND1 cells and the small ND2 cells stratify in the middle of the inner plexiform layer, and their overlapping processes produce a dense plexus, which makes it difficult to trace the morphology of single cells. The complete morphology of the ND1 amacrine cells has been revealed by injecting Neurobiotin into large round somata in the inner nuclear layer, which resulted in the labelling of amacrine cells whose proximal morphology and stratification matched those of the ND1 cells stained by NADPHd histochemistry. The Neurobiotin-injected ND1 cells showed strong homologous tracer coupling to surrounding ND1 cells, and double-labelling experiments confirmed that these coupled cells showed NADPHd reactivity. The ND1 amacrine cells branch in stratum 3 of the inner plexiform layer, where they produce a sparsely branched dendritic tree of 400-600 mum diameter in ventral peripheral retina. In addition, each cell gives rise to several fine beaded processes, which arise either from a side branch of the dendritic tree or from the tapering of a distal dendrite. These axon-like processes branch successively within the vicinity of the dendritic field before extending, with little or no further branching, for 3-5 mm from the soma in ventral peripheral retina. Consequently, these cells may span one-third of the visual field of each eye, and their spatial extent appears to be greater than that of most other types of axon-bearing amacrine cells injected with Neurobiotin in this study. The morphology and tracer-coupling pattern of the ND1 cells are compared with those of confirmed type 1 catecholaminergic cells, a presumptive type 2 catecholaminergic cell, the type 1 polyaxonal. cells, the long-range amacrine cells, a novel type of axon-bearing cell that also branches in stratum 3, and a type of displaced amacrine cell that may correspond to the type 2 polyaxonal cell. (C) 2004 Wiley-Liss, Inc.

The status of hollow-bearing trees required for the conservation of arboreal marsupials in the dry sclerophyll forests of south-east Queensland, Australia

At 38 sites in the dry sclerophyll forests of south-east Queensland, Australia, hollow-bearing trees were studied to determine the effects of past forestry practices on their density, size and spatial distribution. The density of hollow-bearing trees was reduced at sites that had been altered by poisoning and ringbarking of unmerchantable trees. This was especially the case for living hollow-bearing trees that were now at densities too low to support the full range of arboreal marsupials. Although there are presently enough hollow-bearing stags (i.e., dead hollow-bearing trees) to provide additional denning and nesting opportunities, the standing life of these hollow-bearing stags is lower than the living counterparts which means denning and nesting sites may be limited in the near future. The mean diameter at breast height (DBH) of hollow-bearing stags was significantly less than that of living hollow-bearing trees. This indicated that many large hollow-bearing stags may have a shorter standing life than smaller hollow-bearing stags. Hollow-bearing trees appear to be randomly distributed throughout the forest in both silviculturally treated and untreated areas. This finding is at odds with the suggestion by some forest managers that hollow-bearing trees should have a clumped distribution in dry sclerophyll forests of south-east Queensland.

Somatosensation, circulation and stance balance in elderly dysvascular transtibial amputees

Objective: To establish the relationship between poor lower limb somatosensory and circulatory status with standing balance, falls history, age and mobility level in dysvascular transtibial amputees (TTAs). Design: Within-subjects evaluation of somatosensation, circulation and stance balance measures in dysvascular transtibial amputees. Setting: Physiotherapy department of a tertiary metropolitan hospital in Australia. Participants: Twenty-two community-dwelling unilateral dysvascular transtibial amputee volunteers, aged between 54 and 86 recruited from a metropolitan hospital outpatient amputee clinic. Main outcome measures: Lower limb vibration sense, light touch sensation and circulatory status were related to centre of pressure excursion during quiet stance, dynamic balance measures of forward and lateral reach distance, and demographic information such as falls history and mobility level. Results: Overall, poor somatosensory status was associated with poor stance balance. There was an association between poor vibration and circulation and increased centre of pressure excursion in quiet stance and reduced reach distance, whereas poor light touch was linked with even weight-bearing in quiet stance. Poor vibration sense was associated with a history of frequent falls. Conclusions: Compromised lower limb somatosensation and circulation was linked with poor balance and a history of frequent falls in the elderly dysvascular amputee population.

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.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.

Self-condensation of a thiazole-peptide bearing a 21-membered loop into a library of giant macrocycles with multiple orthogonal loops

Tetrapeptide analogue H-[Glu-Ser-Lys(Thz)]-OH, containing a turn-inducing thiazole constraint, was used as a template to produce a 21-membered structurally characterized loop by linking Glu and Lys side chains with a Val-Ile dipeptide. This template was oligomerized in one pot to a library (cyclo-[1](n), n = 2-10) of giant symmetrical macrocycles (up to 120-membered rings), fused to 2-10 appended loops that were carried intact through multiple oligomerization (chain extension) and cyclization (chain terminating) reactions of the template. A three-dimensional solution structure for cyclo-[1](3) shows all three appended loops projecting from the same face of the macrocycle. This is a promising approach to separating pepticle motifs over large distances.

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.