Unilateral Problem for a Viscoelastic Beam Equation Type p-Laplacian with Strong Damping and Logarithmic Source

In this manuscript, we investigate the unilateral problem for a viscoelastic beam equation of p-Laplacian type. The competition of the strong damping versus the logarithmic source term is considered. We use the potential well theory. Taking into account the initial data is in the stability set created by the Nehari surface, we prove the existence and uniqueness of global solutions by using the penalization method and Faedo-Galerkin’s approximation.

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

In this paper, dynamic response analysis of a forced fractional viscoelastic beam under moving external load is studied. The beauty of this study is that the effect of values of fractional order, the effect of internal damping, and the effect of intensity value of the moving force load on the dynamic response of the beam are analyzed. Constitutive equations for fractional order viscoelastic beam are constructed in the manner of Euler–Bernoulli beam theory. Solution of the fractional beam system is obtained by using Bernoulli collocation method. Obtained results are presented in the tables and graphical forms for two different beam systems, which are polybutadiene beam and butyl B252 beam.

A Class of Different Fractional-Order Chaotic (Hyperchaotic) Complex Duffing-Van Der Pol Models and Their Circuits Implementations

In this paper, we introduce three versions of fractional-order chaotic (or hyperchaotic) complex Duffing-van der Pol models. The dynamics of these models including their fixed points and their stability is investigated. Using the predictor-corrector method and Lyapunov exponents we calculate numerically the intervals of their parameters at which chaotic, hyperchaotic solutions and solutions that approach fixed points exist. These models appear in several applications in physics and engineering, e.g., viscoelastic beam and electronic circuits. The electronic circuits of these models with different fractional-order are proposed. We determine the approximate transfer functions for novel values of fractional-order and find the equivalent tree shape model (TSM). This TSM is used to build circuits simulations of our models}. A good agreement is found between both numerical and simulations results. Other circuits diagrams can be similarly designed for other fractional-order models.

Nonlinear dynamics of a base-isolated beam under turbulent wind flow

A homogeneous continuous viscoelastic beam, describing the dynamics of a base-isolated tower, exposed to a uniformly distributed turbulent wind flow, is studied. The beam is constrained at the bottom end by a nonlinear viscoelastic device, and it is free at the top end. Aeroelastic forces are computed by the quasi-static theory. The steady component of wind is responsible for a Hopf bifurcation, and the turbulent component induces parametric excitation. The interaction between the two bifurcations is investigated. Critical and post-critical behavior is analyzed by perturbation methods. The mechanical performances of the structure are discussed to assess the effectiveness of the viscoelastic isolation system.

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

The article deals with forced vibrations of a high-rise axisymmetric structure, represented as a viscoelastic beam of an annular section with a variable slope of the generatrices and variable thickness. The research was conducted to analyze the behavior of a high-rise structure for various kinematic effects. The task is to determine the displacements of the points of a high-rise structure at different time points under different kinematic effects. The methods were developed and a computer program was built; forced vibrations of high-rise axisymmetric structures under various kinematic actions, considering viscoelastic properties of the material, were investigated in linear, nonlinear, and viscoelastic formulations. The study of the dynamic behavior of a high-rise structure, taking into account the nonlinear and dissipative properties (different in nature) of the material, shows that the combined consideration of all these properties brings the resulting pattern closer to the one observed in reality. That is, the amplitude of the structure’s oscillations does not grow infinitely, but gradually decreases over time, and the maximum possible consideration of nonlinear and dissipative properties leads to the fastest damping of oscillations.