Mathematical Modeling of Complex Oscillations of Flexible Micropolar Mesh Cylindrical Panels

Russian Physics Journal - A new mathematical model of oscillations of mesh micropolar geometrically nonlinear cylindrical panels under the action of a normal alternating distributed load has been...     

Wavelet-Based Analysis of Parametric Vibrations of Flexible Plates

Wavelet-based methods are reviewed, and their advantages in comparison to standard approaches are outlined. Then, a wavelet analysis is performed to investigate parametric vibrations of flexible plates under a sinusoidal load. In particular, a scenario leading from regular motion to chaos is analyzed     

Bifurcations of a Thin Plate-Strip Excited Transversally and Axially

The complex vibrations and bifurcations of plates modeled as systemswith infinite degrees-of-freedom are considered. Both theBubnov–Galerkin with high-order approximations and finite differencemethods with approximation O(h ⁴)are applied. In addition, the calculation ofthe Lyapunov exponents of the system is performed, and the results arecompared to those derived by Bennetin's method. Some examples of newnonlinear phenomena exhibited by the considered systems are reported.     

Feigenbaum Scenario Exhibited by Thin Plate Dynamics

The dimensionless partial differential equations governing thedynamics of a thin flexible isotropic plate with an external load arederived and investigated. The period doubling bifurcations, as well asthe chaotic dynamics, are detected and analyzed. The algorithms leadingto the reduction of the original equations to those of a difference setof ordinary differential and algebraic equations are proposed, comparedto other known methods, and then applied to the problem.Among others, it is shown that, in spite of the system complexity, theFeigenbaum scenario exhibited by one-dimensional maps also governs theroute to chaos in the continuous system under consideration.     

Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

Nonlinear Dynamics - The dependence of the quality factor of nonlinear microbeam resonators under thermoelastic damping for Timoshenko beams with regard to geometric nonlinearity has been studied....     

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions(symmetric and non-symmetric)are studied in this work.Reliability of the obtained results is verified by the finite difference method(FDM)and the finite element method(FEM)with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes(regular and non-regular).The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.     

Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena

The Euler–Bernoulli kinematic model as well as the von Kármán geometric non-linearity are used to derive the PDEs governing flexible beam vibrations. The beam is embedded into a 2D temperature field, and its surface is subjected to action of the electric potential. We report how an increase of the exciting load amplitude yields the beam turbulent behavior, and how the temperature changes a scenario from a regular/laminar to spatio-temporal/turbulent dynamics. Both classical Fourier analysis and Morlet wavelets are used to monitor a strong influence of temperature on regular and chaotic beam dynamics.     

Cyanoarylporphyrazines with High Viscosity Sensitivity: A Step towards Dosimetry-Assisted Photodynamic Cancer Treatment

Despite the significant relevance of photodynamic therapy (PDT) as an efficient strategy for primary and adjuvant anticancer treatment, several challenges compromise its efficiency. In order to develop an “ideal photosensitizer” and the requirements applied to photosensitizers for PDT, there is still a need for new photodynamic agents with improved photophysical and photobiological properties. In this study, we performed a detailed characterization of two tetracyanotetra(aryl)porphyrazine dyes with 4-biphenyl (pz II) and 4-diethylaminophenyl (pz IV) groups in the periphery of the porphyrazine macrocycle. Photophysical properties, namely, fluorescence quantum yield and lifetime of both photosensitizers, demonstrate extremely high dependence on the viscosity of the environment, which enables them to be used as viscosity sensors. Pz II and pz IV easily enter cancer cells and efficiently induce cell death under light irradiation. Using fluorescence lifetime imaging microscopy, we demonstrated the possibility of assessing local intracellular viscosity and visualizing viscosity changes driven by PDT treatment with the compounds. Thus, pz II and pz IV combine the features of potent photodynamic agents and viscosity sensors. These data suggest that the unique properties of the compounds provide a tool for PDT dosimetry and tailoring the PDT treatment regimen to the individual characteristics of each patient.     

Routes to chaos in continuous mechanical systems: Part 2. Modelling transitions from regular to chaotic dynamics

In second part of the paper both classical and novel scenarios of transition from regular to chaotic dynamics of dissipative continuous mechanical systems are studied. A detailed analysis allowed us to detect the already known classical scenarios of transition from periodic to chaotic dynamics, and in particular the Feigenbaum scenario. The Feigenbaum constant was computed for all continuous mechanical objects studied in the first part of the paper. In addition, we illustrate and discuss different and novel scenarios of transition of the analysed systems from regular to chaotic dynamics, and we show that the type of scenario depends essentially on excitation parameters.