Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I: Non-linear model and stability analysis

The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in the transversal displacement and torsional angle of the beam. The linear stability of the trivial equilibrium is studied, revealing the existence of buckling, flutter and double-zero critical points. Interaction between conservative and non-conservative loads with respect to the stability problem is discussed. The critical spectral properties are derived and the corresponding critical eigenspace is evaluated.     

Dynamic Analysis of Linear and Nonlinear Oscillations of a Beam Under Axial and Transversal Random Poisson Pulses

This paper proposes an approximate explicit probability density function for the analysis of external and parametric oscillation of a simply supported beam driven by random pulses. The impulsive loading model adopted is Poisson white noise, which is a process having Dirac delta occurrences with random intensity distributed in time according to Poisson's law. The response probability density function can be obtained by solving the related Kolmogorov–Feller integro-differential equation. An approximate solution is derived by transforming this equation to a first-order partial differential equation. The method of characteristics is then applied to obtain an explicit solution. The theory has been validated through numerical simulations.     

High-Performance Thin-Layer Chromatographic Analysis of the Polar Lipid Content of Human Urine and Urine from BALB/c Mice Experimentally Infected with Echinostoma caproni

JPC – Journal of Planar Chromatography – Modern TLC - High-performance thin-layer chromatography was used to examine the phospholipid profiles in the urine of Echinostoma caproni...     

Microwave spectra of eight isotopic modifications of 1-chloro-1-fluoroethylene

The rotational spectra of eight isotopomers of 1-chloro-1-fluoroethylene in the 6-22 GHz region have been collected and analyzed. Each rotational transition is split into hyperfine components by the chlorine (either ³⁵Cl or ³⁷Cl) nuclear quadrupole coupling interaction and additionally, one or more smaller interactions such as the spin-rotation interaction due to the fluorine atom, hydrogen-hydrogen spin-spin coupling interactions, and in appropriately substituted species, the deuterium nuclear quadrupole hyperfine interaction. The rotational constants derived from these isotopomers allow the determination of average and Kraitchman substitution structures for 1-chloro-1-fluoroethylene, whereas the availability of the diagonal chlorine nuclear quadrupole coupling constants for all the isotopomers provides complete quadrupole coupling tensors for both ³⁵Cl and ³⁷Cl. In the course of this work, the rotational spectrum of an excited vibrational state of the normal isotopomer was observed, which ab initio calculations suggest should be assigned to ν₉=1, an in-plane bending motion at the CFCl end of the molecule.     

Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces II. Post-critical analysis

The post-critical behavior of a cantilever beam with rectangular cross-section, under simultaneous action of conservative and non-conservative loads, is analyzed. An internally constrained Cosserat rod model is adopted to describe the dynamics of the beam in finite displacement regime. The bifurcation equations for simple buckling (divergence), simple flutter (Hopf) and double-zero (Takens-Bogdanova-Arnold) bifurcations are derived by means of the multiple time scales method. Due to the nilpotent eigenvalue at the double-zero critical point, the evaluation of the generalized Keldysh's eigenfunctions is required. Finally, some numerical results are shown and the bifurcation scenario of the beam is discussed.     

Stable isotopes to discriminate lambs fed herbage or concentrate both obtained from C(3) plants

This study was aimed at determining whether isotopic ratio mass spectrometry (IRMS) enables us to discriminate between lambs fed herbage or concentrate, both obtained from C(3) plants, and those fed a concentrate obtained from C(4) plants. Thirty-four Comisana male lambs (age 45 days) were assigned to three feeding treatments. Fourteen lambs were fed vetch (Vicia sativa) ad libitum. Another fourteen lambs received a barley-based concentrate. The remaining six lambs were fed a maize-based concentrate. After 60 days of experimental treatment the animals were slaughtered and the wool, perirenal fat and muscle longissimus dorsi were sampled. The delta(13)C and delta(15)N values of the muscle, wool and feed were measured by continuous flow elemental analysis (CF-EA)-IRMS. The delta(13)C of the fat was determined likewise. The isotopic composition of the tissues reflected that of the three diets. For the lambs which were fed herbage the muscle delta(13)C values were higher (P < 0.0005) and delta(15)N values were lower (P < 0.0005) than those of the lambs receiving concentrates. The delta(15)N and delta(13)C values in the muscle and delta(13)C values in the adipose tissue allowed perfect discrimination between the lambs fed the three different diets. The regression between the delta(13)C values measured in muscle and in wool of lambs was linear (R(2) = 0.99; P < 0.0005). This result shows that delta(13)C measured in the wool can predict muscle delta(13)C distribution, suggesting that wool is a valuable matrix for meat authentication.     

Energy Based Stochastic Estimation of Nonlinear Oscillators with Parametric Random Excitation

A new energy-based system identification method is developed, applicable in situations where the dynamic response of a structure is measurable but the excitation is unmeasurable and describable only in terms of a stochastic process. It is shown that, in the case of a non-linear single degree of freedom system subjected to purely parametric, non-white random excitation, the power spectrum of the excitation can be identified through an estimation of the diffusion coefficient relating to the energy envelope of the response process. Through an estimation of the drift coefficient an identification of the system damping is also possible. The method is validated through application to simulated data relating to a Duffing oscillator with non-linear damping.     

A discrete approach for a generalized Beck’s column in parametric resonance

A Galerkin projection based on non-standard bases is conceived to derive an equivalent discrete model of a continuous system under non-conservative forces. The problem of deriving a discrete model capable of describing critical and post-critical scenarios for non-selfadjoint systems is discussed and an heuristic rule for a proper choice of trial functions is given. The procedure is utilized to analyze the effect of non-conservative autonomous and non-autonomous (pulsating) forces acting on a linearly damped Beck’s column involving geometrical nonlinearities. The linear and nonlinear behaviours arising from the analysis of the proposed discrete model are in good agreement with those observed through the unavoidably more involved direct continuous approach. Critical scenarios for the autonomous and non-autonomous cases are investigated and the multiple scales method is applied in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. A comparison between critical and post-critical continuous and discrete model is performed adopting two control parameters, namely the amplitudes of the static and dynamic components of the forces, playing the role of detuning and bifurcation parameters, respectively.