Spatial Periodic Research Articles

Response Adjustability Analysis of Partial and Ordinary Differential Coupling System for Visco-Elastomer Sandwich Plate Coupled with Distributed Masses under Random Excitation via Spatial Periodicity Strategy

Vibration control of composite structures coupled with distributed masses under random excitations is a significant issue. In this paper, partial and ordinary differential coupling equations are obtained from a periodic sandwich plate coupled with supported masses under random excitation. An analytical solution to the coupling equations is proposed, and the stochastic response adjustability of the system with various periodic distributions of geometrical and physical parameters is studied. Spatial periodic layer thickness and core modulus of the sandwich plate are considered based on the active‐passive periodicity strategy. The periodically distributed masses are supported on the plate by coupling springs and dampers. Partial and ordinary differential coupling equations for the system including the periodic sandwich plate and supported masses are derived and then converted into unified ordinary differential equations for multi-mode coupling vibration. Generalized system stiffness, damping and mass are functions of the periodic parameters. Expressions of frequency response function and response spectral density of the system are obtained. Numerical results show the response adjustability via the spatially periodic geometrical and physical parameters. The results have the potential for application to dynamic control or optimization of sandwich structure systems.

Fourier transform analysis of irradiated Weiss oscillations

We present a theoretical approach to study the effect of microwave radiation on the magnetoresistance of a one-dimensional superlattice. In our proposal the magnetoresistance of a unidirectional spatial periodic potential (superlattice), is modulated by microwave radiation due to an interference effect between both space- and time-dependent potentials. The final magnetoresistance will mainly depend on the spatial period of the superlattice and the radiation frequency. We consider an approach to study these effects based on the fast Fourier transform of the obtained magnetoresistance profiles in function of the inverse of the magnetic field. Based on this theory we propose the design of a novel radiation sensor for the terahertz band.

Spatial Periodic Adaptive Control for Rotary Machine Systems

A spatial periodic adaptive control (SPAC) approach is developed to deal with rotary machine systems performing speed tracking tasks. Since the angular displacement is periodic when rotating by 2pi radians, most rotary machine systems present certain cyclic behaviors with a fixed periodicity which is either a fraction or multiple of 2pi . As a consequence, unknown system parameters and disturbances that characterize the system behaviors are also periodic in nature. By utilizing the spatial periodicity, the SPAC aims at improving the system performance. In the SPAC design, the dynamics of the rotary machine systems is first converted from the temporal to spatial coordinates in canonical form using the feedback linearization method. Then the new adaptive controller updates the parameters and the control signal periodically in a pointwise between two consecutive spatial cycles. Using a Lyapunov-Krasovskii functional, the convergence property of the SPAC can be analyzed for high order rotary systems and the periodic adaptation can be applied to rotary systems with pseudo-periodic parametric uncertainties. The effectiveness of the SPAC is verified through rigorous analysis and two numerical examples.

Weiss Oscillations Modulated by Microwave Radiation

We present a theoretical proposal to study the effect of microwave radiation on Weiss oscillations. We present a novel theoretical alternative to treat Weiss oscillations based on the effect that a unidirectional spatial periodic potential, i.e., a superlattice, produces on the scattering conditions of a two-dimensional electron system. In our proposal Weiss oscillations are modulated by microwave radiation due to an interference effect between both, spatial and time-dependent, periodic potentials. The final profile presented by the magnetoresistance depends mainly on the spatial period of the superlattice and the frequency of radiation. Depending on the values of these parameters, we predict that Weiss oscillations can reach dissipationless transport states.

Driving Weiss oscillations to zero resistance states by microwave Radiation

We present a theoretical model to study the effect of microwave radiation on Weiss oscillations. In our proposal Weiss oscillations, produced by a spatial periodic potential, are modulated by microwave radiation due to an interference effect between both, space and time-dependent, potentials. The final magnetoresistance depends mainly on the spatial period of the spatial potential and the frequency of radiation. Depending on the values of these parameters, we predict that Weiss oscillations can reach zero resistance states. On the other hand, these dissipationless transport states, created just by radiation, can be destroyed by the presence of a space-dependent potential.

Spatial Periodic Adaptive Control For Rotary Machine Systems

A spatial periodic adaptive control (SPAC) approach is developed to deal with rotary machine systems performing speed tracking tasks. Since the angular displacement is periodic when rotating by 2π radians, most rotary machine systems present certain cyclic behaviors with a fixed periodicity which is either a fraction or multiple of 2π. As a consequence, unknown system parameters and disturbances that characterize the system behaviors are also periodic in nature. By utilizing the spatial periodicity, the SPAC aims at improving the system performance. In the SPAC design, the dynamics of the rotary machine systems is first converted from the temporal to spatial coordinates. Then the new adaptive controller updates the parameters and the control signal periodically in a pointwise between two consecutive spatial cycles. Using a Lyapunov-Krasovskii functional, the convergence property of the SPAC can be analyzed for high-order rotary systems and the periodic adaptation can be applied to rotary systems with pseudo-periodic parametric uncertainties.

Analysis of transient response of saturated porous elastic soil under cyclic loading using element-free Galerkin method

A two-dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading. The procedure is based on the element-free Galerkin method and incorporated into the periodic conditions (temporal and spatial periodicity). Its shape function is constructed by moving least-square approximants, essential boundary conditions are implemented through Lagrange multipliers and the periodic conditions are implemented through a revised variational formulation. Time domain is discretized through the Crank–Nicolson scheme. Analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions. For only temporal periodic problems, a one-dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading. For both temporal and spatial periodic problems, a typical two-dimensional wave-induced transient problem with the seabed of finite thickness is analysed. Finally, a moving boundary problem is analysed. It is found that the current procedure is simple, efficient and accurate in predicting the response of soil layer under cyclic loading.

DEVELOPING CHAOS ON BASE OF TRAVELING WAVES IN A CHAIN OF COUPLED OSCILLATORS WITH PERIOD-DOUBLING: SYNCHRONIZATION AND HIERARCHY OF MULTISTABILITY FORMATION

The work is devoted to the analysis of dynamics of traveling waves in a chain of self-oscillators with period-doubling route to chaos. As a model we use a ring of Chua's circuits symmetrically coupled via a resistor. We consider how complicated are temporal regimes with parameters changing influences on spatial structures in the chain. We demonstrate that spatial periodicity exists until transition to chaos through period-doubling and tori birth bifurcations of regular regimes. Temporal quasi-periodicity does not induce spatial quasi-periodicity in the ring. After transition to chaos exact spatial periodicity is changed by the spatial periodicity in the average. The periodic spatial structures in the chain are connected with synchronization of oscillations. For quantity researching of the synchronization we propose a measure of chaotic synchronization based on the coherence function and investigate the dependence of the level of synchronization on the strength of coupling and on the chaos developing in the system. We demonstrate that the spatial periodic structure is completely destroyed as a consequence of loss of coherence of oscillations on base frequencies.