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Existence of non‐resonant solutions of time‐periodic type is established for the Kuznetsov equation with a periodic forcing term. The equation is considered in a three‐dimensional whole‐space, half‐space and bounded domain, and with both non‐homogeneous Dirichlet and Neumann boundary values. A method based on estimates for the corresponding linearization, namely the wave equation with Kelvin‐Voigt...
Lattice models are successfully used in modelling of fracture of brittle materials. To date, most of the lattice multi‐dimensional (2D and 3D) models known to the authors describe either in‐plane or three‐dimensional mechanics of the materials. Only a few lattice models are available in the literature for the description of the out‐of‐plane mechanics of plates. However, the parameters of those lattice...
The problem on buckling of a thin laminated non‐circular cylindrical shell under action of axial compressive forces non‐uniformly distributed along edges is considered. It is assumed that some layers are made of a “soft” material so that the reduced (effective) shear modulus for the entire package is much less than the reduced Young's modulus. The differential equations based on the generalized hypotheses...
This paper is concerned with the formal deduction of piezoelectric plate models in microstretch elasticity, by means of an asymptotic analysis with respect to a small parameter ε, being the thickness of the plate. Two different boundary conditions pertaining to electric quantities are considered, leading to two different models: the sensor model and the actuator model, respectively. Each of the two...
This paper proposes a simple two‐surface plasticity model for strain controlled conditions which includes only five material constants to describe the stable stress‐strain relationship under extensive non‐proportional loadings. In this model, the Mróz kinematic hardening rule is adopted to describe the instantaneous translation of the yield surface, and a larger radius of the limit surface is selected...
We prove the existence of minimisers for a family of models related to the single‐slip‐to‐single‐plane relaxation of single‐crystal, strain‐gradient elastoplasticity with ‐hardening penalty. In these relaxed models, where only one slip‐plane normal can be activated at each material point, the main challenge is to show that the energy of geometrically necessary dislocations is lower‐semicontinuous...
This paper investigates the global bifurcations and chaotic dynamics for nonlinear oscillations of symmetric cross‐ply composite laminated plates in case of 1:2 internal resonance. The higher‐dimensional Melnikov method and its extensions developed by Kovai and Wiggins is employed to analyze the global bifurcations for composite laminated plates. The explicitly sufficient conditions of the existence...
The feedback control algorithm is applied to provide stable propagation of the shock waves for nonlinear isothermal Euler equations even if the desired profile and velocity of the wave do not correspond to their analytical solution. Also the control algorithm helps to suppress scheme oscillations on the shock wave solutions, this is studied on an example of the Lax‐Wendroff second‐order scheme.
We present new solutions for the dynamics of a pendulum energy converter which is vertically excited at its suspension point. Thereby, we deal with a random excitation by a non‐white Gaussian stochastic process. We formulate the pendulum energy converter as a weakly perturbed Hamiltonian system. The random process across the energy levels of the Hamiltonian system is then approximated by a Markov...
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