Finite amplitude vibrations of a Mooney-Rivlin oscillator

The solution for the finite amplitude, uniaxial motion of a Mooney-Rivlin oscillator on suspension, compression, or horizontal supports, and for arbitrary initial data is presented. The problem is unusual. Depending upon the initial data, the type of support, the amount of static stretch, and the value of a Mooney-Rivlin parameter, the solution may have one of three distinct possible periodic forms. The three cases are solved exactly, and simple bounds on the period of the finite motion are given. Some special situations are illustrated, both analytically and graphically. The effect of the amount of static stretch on the period of superimposed small amplitude oscillations also is described. The appropriate results are compared with those obtained previously for the neo-Hookean model.Dedicated to Clifford Truesdell, in admiration and gratitude, on the occasion of the twenty-fifth anniversary of the Society for Natural Philosophy.     

On the transverse vibration of a rubber string

The nearly constant pitch of the sound radiated by a sufficiently stretched rubber cord, a phenomenon observed independently by two experimenters at the turn of the century, is explained analytically for three ideal rubberlike material models. Transverse vibrational frequency data for three kinds of rubber strings, obtained with the aid of a novel laser apparatus, are compared with the analytical results. A numerical scheme is introduced to compute from the experimental data the apparent average number of links in a molecular chain of a rubberlike material from both simple tension and transverse frequency measurements. It is shown that the nearly flat frequency response is a molecular network finite extensibility effect that is controlled by the apparent number of links in a chain of the molecular network structure.     

Assessing the exchange coupling in binuclear lanthanide(iii) complexes and the slow relaxation of the magnetization in the antiferromagnetically coupled Dy2 derivative

We report here the synthesis and the investigation of the magnetic properties of a series of binuclear lanthanide complexes belonging to the metallacrown family. The isostructural complexes have a core structure with the general formula [Ga₄Ln₂(shi^3–)₄(Hshi^2–)₂(H₂shi^–)₂(C₅H₅N)₄(CH₃OH)_x(H₂O)_x]·xC₅H₅N·xCH₃OH·xH₂O (where H₃shi = salicylhydroxamic acid and Ln = Gd^III1; Tb^III2; Dy^III3; Er^III4; Y^III5; Y^III_0.9Dy^III_0.16). Apart from the Er-containing complex, all complexes exhibit an antiferromagnetic exchange coupling leading to a diamagnetic ground state. Magnetic studies, below 2 K, on a single crystal of 3 using a micro-squid array reveal an opening of the magnetic hysteresis cycle at zero field. The dynamic susceptibility studies of 3 and of the diluted DyY 6 complexes reveal the presence of two relaxation processes for 3 that are due to the excited ferromagnetic state and to the uncoupled Dy^III ions. The antiferromagnetic coupling in 3 was shown to be mainly due to an exchange mechanism, which accounts for about 2/3 of the energy gap between the antiferro- and the ferromagnetic states. The overlap integrals between the Natural Spin Orbitals (NSOs) of the mononuclear fragments, which are related to the magnitude of the antiferromagnetic exchange, are one order of magnitude larger for the Dy₂ than for the Er₂ complex.     

Effects of Ultraviolet Radiation (UVA+UVB) and Copper on the Morphology,Ultrastructural Organization and Physiological Responses of the Red Alga Pterocladiella capillacea

The effect of ultraviolet (UV) radiation and copper (Cu) on apical segments of Pterocladiella capillacea was examined under two different conditions of radiation, PAR (control) and PAR+UVA+UVB (PAR+UVAB), and three copper concentrations, ranging from 0 (control) to 0.62, 1.25 and 2.50 μm . Algae were exposed in vitro to photosynthetically active radiation (PAR) at 70 μmol photons m^?2 s^?1, PAR + UVB at 0.35 W m^?2 and PAR +UVA at 0.70 W m^?2 during a 12‐h photocycle for 3 h each day for 7 days. The effects of radiation and copper on growth rates, content of photosynthetic pigments and photosynthetic performance were analyzed. In addition, samples were processed for light and transmission electron microscopy. The content of photosynthetic pigments decreased after exposure to radiation and Cu. Compared with PAR radiation and copper treatments modified the kinetics patterns of the photosynthesis/irradiance curve. The treatments also caused changes in the ultrastructure of cortical and subcortical cells, including increased cell wall thickness and accumulation of plastoglobuli, as well as changes in the organization of chloroplasts. The results indicate that the synergistic interaction between UV radiation and Cu in P. capillacea, led to the failure of protective mechanisms and causing more drastic changes and cellular imbalances.     

A comparative study of crack propagation models for PMMA and PVC

An analysis of examining the validity of a unified approach proposed earlier by the authors for the fatigue crack propagation (FCP) of engineering materials to include PMMA and PVC is described. The proposed formulation has been shown capable of characterizing a diversified range of materials with a master FCP diagram and expressed as da/dN = A(ΔG)^m/(G_c − G_max).An experimental program is undertaken to measure fatigue growth rate with the standard compact tension specimen. The FCP results are for the first instance analysed for each material using the unified formulation. The validity of the formulation for producing a master FCP diagram is verified when the fatigue crack growth rates of the materials are successfully characterized in one master diagram, yielding an excellent coefficient of correlation of 0.993. No such success is attained using a number of conventional FCP laws considered most acceptable to characterize polymeric materials.     

A rotating field mhd hydrostatic thrust bearing

It is found that the load capacity of a magnetohydrodynamic thrust bearing with a rotating disk can be increased by rotating the axial magnetic field at a suitable speed in a direction opposite to that of the disk rotation. This method of improving the bearing performance is considered to be efficient if the Hartmann number is not too large. Thus for a given load, the size and weight of the magnet to be used in a thrust bearing with rotating field can be reduced considerably.Nomenclature a radius of plenum recess - b outside disk radius - B ₀ magnetic induction of applied axial magnetic field - hE ₀ ^1/2/a ^1/2, nondimensionalized electric field - E ₀ radial electric field at r=a - E _r radial electric field - h half of lubricant film thickness - M (B ₀ ² h ²/)^1/2, Hartmann number - P pressure - P _e pressure at r=b - P ₀ pressure at r=a - Q volume flow rate of lubricant - Q ₀ volume flow rate of a nonrotating bearing in the absence of applied magnetic field - r radial coordinate - u, v fluid velocity components in radial and circumferential directions, respectively - W load capacity of bearing - W ₀ load capacity of a nonrotating bearing in the absence of a magnetic field having a flow rate which the same bearing would have at Hartmann number M - z axial coordinate - azimuthal coordinate - coefficient of viscosity of lubricant - _e magnetic permeability - fluid density - electrical conductivity - angular velocity of rotating disk - _C critical disk velocity at which W=0 - _M angular velocity of axial magnetic field - optimum angular velocity of magnetic field On leave of absence from Department of Aero-Space Engineering, University of Notre Dame, Notre Dame (Ind.), U.S.A.     

A numerical method for reconstructing the coefficient in a wave equation

We present a numerical method for reconstructing the coefficient in a wave equation from a single measurement of partial Dirichlet boundary data. The original inverse problem is converted to a nonlinear integral differential equation, which is solved by an iterative method. At each iteration, one linear second‐order elliptic problem is solved to update the reconstruction of the coefficient, then the reconstructed coefficient is used to solve the forward problem to obtain the new data for the next iteration. The initial guess of the iterative method is provided by an approximate model. This model extends the approximate globally convergent method proposed by Beilina and Klibanov, which has been well developed for the determination of the coefficient in a special wave equation. Numerical experiments are presented to demonstrate the stability and robustness of the proposed method with noisy data.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 289–307, 2015     

The hydrolytic effect of moisture and hygrothermal aging on poly(butylene succinate)/organo-montmorillonite nanocomposites

The study of hydrolysis on biodegradable poly(butylene succinate) (PBS) is essential to predict the materials properties in a humid environment. In this study, PBS nanocomposites were exposed to different conditions of relative humidity (RH) and temperature. The moisture uptake increased with organo-montmorillonite (OMMT) loading and the RH of the testing environment. The exposure of PBS and the nanocomposites to a humid environment caused changes in the mechanical properties. The hydrolytic degradation becomes more pronounced upon hygrothermal aging at high temperature, whereby premature failure occurred. PBS nanocomposites were found to exhibit a better hydrolytic stability than neat PBS. The degradation was evaluated through Fourier transform infrared (FTIR) spectroscopy and gel permeation chromatography (GPC). A drastic reduction in the molecular weight of PBS has revealed the occurrence of degradation after exposure to moisture and heat. This has led to an alteration of the thermal behavior as investigated using differential scanning calorimetry (DSC).     

Effect of CO2 laser treatment on cotton surface

In this study, CO₂ laser was used for treating cotton fabric to create surface effects which were found to vary with laser process parameters, i.e. resolution and pixel time. The resolutions used were 40, 50 and 60 dpi while the pixel time used were 100, 110 and 120 μs. Both physical and chemical properties at the surface of fabrics treated with different combinations of resolution and pixel time were analysed by the Scanning Electron Microscopy (SEM), Fourier Transform Infrared Spectroscopy with Attenuated Total Reflection mode (FTIR-ATR), and X-ray Photoelectron Spectroscopy (XPS). SEM investigation revealed the appearance of various numbers of pores, cracks and fragments present on the fibre surface after laser treatment. FTIR-ATR spectra showed that the laser-treated cotton fabric suffered changes in chemical structure with the hydroxyl (–OH) stretching group being oxidised to carbonyl/carboxyl groups. The XPS analysis revealed a change in surface elemental composition after laser treatment. Furthermore, the wicking property of the laser-treated cotton fabrics was evaluated.