Analysis of vibrating circular plates of nonuniform thickness by the method of differential quadrature

The case of vibrating circular plates of linearly varying thickness is tackled using a method proposed by Bellman in the early 1970s.     

Analysis of vibrating, thin, rectangular plates with point supports by the method of differential quadrature

The title problem is solved by an approach first suggested by Bellman early in the 1970s and which has recently been used in the solution of solid mechanics problems. It is shown that the methodology offers several important advantages from the point of view of naval analysts and designers.     

Optimization of variational methods

Lord Rayleigh proposed his now classical method (based on a one-term deflection function) in 1870. On the other hand, he suggested in 1894 the possibility of optimizing the eigenvalues (natural frequencies or buckling loads) by minimizing them with respect to an exponential parameter contained in the coordinate function. This optimization approach has become increasingly popular in the last decade and it has been extended to other variational methods and bounding techniques. The present paper reviews recent developments in this area which consists, essentially, in a nonlinear optimization process of the coordinate functions in a global sense. The technique is applicable in a large variety of applied mechanics problems of considerable interest to ocean engineers dealing with the analysis of mechanical systems.     

Free vibrations of a cantilever beam with a spring–mass system attached to the free end

An exact solution for the title problem is obtained using the Bernoulli–Euler theory of beam vibrations. Natural frequencies are obtained for a wide range of the intervening physical parameters. The problem is of interest in naval and ocean engineering systems since in order to avoid dangerous resonance conditions the designer must be able to predict natural frequencies of the overall mechanical system: structure–motor and its elastic mounting.     

Interaction between Climate Changes, Eustacy and Land Subsidence in the North Adriatic Region, Italy

Abstract. The North Adriatic coastal area has experienced a serious relative sea level rise whose main component is land subsidence. Geological regional subsidence is ascribable to compaction and to deformation of substratum. Anthropogenic subsidence, which is due to ground fluid removal, has been severe in the second half of the 19th century, reaching values in meters. It is without doubt the main factor responsible for the instability of the entire coastal ecosystem. Widespread retreat of shoreline, seawater invasion, decay of vegetation, changes in the habitat of the flora and fauna have occurred. Sea level rise alone is linked to climate changes, which exhibit fluctuations of the order of a few hundred years; here, cold-wet periods alternated with warm-dry periods and, within them, shorter cold-wet and hot-dry cycles lasting for decades also alternated.     

The East Pacific Rise and its flanks 8–18° N: History of segmentation,propagation and spreading direction based on SeaMARC II and Sea Beam studies

SeaMARC II and Sea Beam bathymetric data are combined to create a chart of the East Pacific Rise (EPR) from 8°N to 18°N reaching at least 1 Ma onto the rise flanks in most places. Based on these data as well as SeaMARC II side scan sonar mosaics we offer the following observations and conclusions. The EPR is segmented by ridge axis discontinuities such that the average segment lengths in the area are 360 km for first-order segments, 140 km for second-order segments, 52 km for third-order segments, and 13 km for fourth-order segments. All three first-order discontinuities are transform faults. Where the rise axis is a bathymetric high, second-order discontinuities are overlapping spreading centers (OSCs), usually with a distinctive 3:1 overlap to offset ratio. The off-axis discordant zones created by the OSCs are V-shaped in plan view indicating along axis migration at rates of 40–100 mm yr^–1. The discordant zones consist of discrete abandoned ridge tips and overlap basins within a broad wake of anomalously deep bathymetry and high crustal magnetization. The discordant zones indicate that OSCs have commenced at different times and have migrated in different directions. This rules out any linkage between OSCs and a hot spot reference frame. The spacing of abandoned ridges indicates a recurrence interval for ridge abandonment of 20,000–200,000 yrs for OSCs with an average interval of approximately 100,000 yrs. Where the rise axis is a bathymetric low, the only second-order discontinuity mapped is a right-stepping jog in the axial rift valley. The discordant zone consists of a V-shaped wake of elongated deeps and interlocking ridges, similar to the wakes of second-order discontinuities on slow-spreading ridges. At the second-order segment level, long segments tend to lengthen at the expense of neighboring shorter segments. This can be understood if segments can be approximated by cracks, because the propagation force at a crack tip is directly proportional to crack length.There has been a counter-clockwise change in the direction of spreading on the EPR between 8 and 18° N during the last 1 Ma. The cumulative change has been 3°–6°, producing opening across the Orozco and Siqueiros transform faults and closing across the Clipperton transform. The instantaneous present-day Cocos-Pacific pole is located at approximately 38.4° N, 109.5° W with an angular rotation rate of 2.10° m.y.^–1 This change in spreading direction explains the predominance of right-stepping discontinuities of orders 2–4 along the Siqueiros-Clipperton and Orozco-Rivera segments, but does not explain other aspects of segmentation which are thought to be linked to patterns of melt supply to the ridge axis.There are 23 significant seamount chains in the mapped area and most are created very near the spreading axis. Nearly all of the seamount chains have trends which fall between the absolute and relative plate motion vectors.     

Oxidative stress in Laeonereis acuta (Polychaeta, Nereididae): environmental and seasonal effects

Laeonereis acuta was seasonally collected in an industrially polluted site (P) and in an unpolluted site (UP) at the Patos Lagoon estuary (southern Brazil). Glutathione S-transferase (GST), superoxide dismutase (SOD) and catalase (CAT) activity (U/mg protein) was determined in five groups of worms from each site. Metallothionein (MT – μmol GSH/g ww) and lipid peroxides content (LPO – nmoles of cumene hydroperoxide/g ww) were also measured. Annual mean values for CAT (UP=3.7±0.3; P=5.7±0.6), GST (UP=0.034±0.003; P=0.045±0.004) and MT (UP=0.15±0.02; P=0.23±0.03) were higher (p<0.05) in worms from the P site. In autumn, CAT activity was higher (p<0.05) in worms from the P site (7.6 ± 1.3) than in those from the UP site (3.6 ± 0.4). In summer, MT concentration was higher in worms from the P site (0.37 ± 0.03) than in those from the UP site (0.19 ± 0.01). No significant difference (p>0.05) in the LPO content was observed in worms from the different sites or collected in different seasons. These results indicate that worms from the polluted site showed higher antioxidant responses than those from the unpolluted site, sufficient to prevent oxidative damage in terms of LPO.     

Transverse vibrations of rectangular orthotropic plates with one or two free edges while the remaining are elastically restrained against rotation

A survey of the literature reveals that the title problem has not been previously solved. The fundamentals frequency of transverse vibration of the orthotropic structural element is determined by expanding the displacement amplitude function in terms of simple polynomial coordinate functions which satisfy identically the essential boundary conditions and approximately some of the natural edge requirements.The Ritz method is then used to generate the frequency equations.