In this stud y, we attempt to analyse free nonlinear vibrations of buckling in laminated composite beams. Two new methods are applied to obtain the analytical solution of the nonlinear governing equation of the problem. The effects of different parameters on the ratio of nonlinear to linear natural frequencies of the beams are studied. These methods give us an agreement with numerical results for the whole range of the oscillation amplitude.

The paper presents a method of how the nonlinear boundary condition [1] may be applied in nonlinear problems of electromagnetic field theory. It is introduced for problems with nonlinear conductivity. An analytical procedure has been constructed, which seeks to reduce calculations related with the nonlinear region. In order to verify the proposed solutions, two problems have been formulated: one of linear and the other of cylindrical symmetry. These have been additionally solved by the authors’ modification of the perturbation method that has been described in previous papers [7, 8, 10]. The electromagnetic field distribution obtained thereby has served as a referential result since it can obtain very accurate solutions [10]. Relative errors of electric and magnetic field strength are introduced to verify the results.

The task of electroacoustic devices is a transmission of audio signals. The transmitted signal should be distorted as little as possible. Nonlinear distortions are the distortions depending on signal level. The types of nonlinear distortions as well as their measures are presented in the paper. The weakest device in an electroacoustic chain is a loud-speaker. It causes the greatest degradation of the signal. It is usually the most nonlinear part of the electroacoustic system. The nonlinearities in loudspeakers are described in details. Other types of nonlinear distortions as transient intermodulation in power amplifiers and distortions caused by the A/C sampling are also presented.

The object of the present study is to investigate the influence of damping uncertainty and statistical correlation on the dynamic response of structures with random damping parameters in the neighbourhood of a resonant frequency. A Non-Linear Statistical model (NLSM) is successfully demonstrated to predict the probabilistic response of an industrial building structure with correlated random damping. A practical computational technique to generate first and second-order sensitivity derivatives is presented and the validity of the predicted statistical moments is checked by traditional Monte Carlo simulation. Simulation results show the effectiveness of the NLSM to estimate uncertainty propagation in structural dynamics. In addition, it is demonstrated that the uncertainty in damping indeed influences the system response with the effects being more pronounced for lightly damped structures, higher variability and higher statistical correlation of damping parameters.

In this paper, we present the general governing equations of electrodynamics and continuum mechanics that need to be considered while mathematically modelling the behaviour of electromagnetic acoustic transducers (EMATs). We consider the existence of finite deformations for soft materials and the possibility of electric currents, temperature gradients, and internal heat generation due to dissipation. Starting with Maxwell’s equations of electromagnetism and balance laws of nonlinear elasticity, we present the governing equations and boundary conditions in incremental form in order to solve wave propagation problems of boundary value type.

Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non- minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.

A heterogeneous Bertrand duopoly game with bounded rational and adaptive players manufacturing differentiated products is subject of investigation. The main goal is to demonstrate that participation of one bounded rational player in the game suffices to destabilize the duopoly. The game is modelled with a system of two difference equations. Evolution of prices over time is obtained by iteration of a two dimensional nonlinear map. Equilibria are found and local stability properties thereof are analyzed. Complex behavior of the system is examined by means of numerical simulations. Region of stability of the Nash equilibrium is demonstrated in the plane of the speeds of adjustment. Period doubling route to chaos is presented on the bifurcation diagrams and on the largest Lyapunov characteristic exponent graph. Lyapunov time is calculated. Chaotic attractors are depicted and their fractal dimensions are computed. Sensitive dependence on initial conditions is evidenced.

The acoustic properties of the sitar string are studied with the aid of a physical model. The nonlinearity of the string movement caused by the bridge acting as an obstacle to the vibrating string is of special interest. Comparison of the model's audio output to recordings of the instrument shows interesting similarities. The effects dispersion and bridge have on the sound of the instrument are demonstrated in the model.

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.

The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f(e) of the nonlinear parts satisfy the condition
k₁e  ≤ f(e) ≤ k₂e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (–¹/k₁,  –¹/k₂).

The paper focuses on different approaches to the safety assessment of concrete structures designed using nonlinear analysis. The method based on the concept of partial factors recommended by Eurocodes, and methods proposed by M. Holicky, and by the author of this paper are presented, discussed and illustrated on a numerical example. Global safety analysis by M. Holicky needs estimation of the resistance coefficient of variation from the mean and characteristic values of resistance, and requires two separate nonlinear analyses. The reliability index value and the sensitivity factor for resistance should be also identified. In the method proposed in this paper, the resistance coefficient of variation necessary to calculate the characteristic value of resistance may be adopted from test results and the resultant partial factor for materials properties, and may be calculated according to Eurocodes. Thus, only one nonlinear analysis from mean values of reinforcing steel and concrete is required.

The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.

The article is a continuation of a study on the synthesis of matching multi-terminal networks, also known as compensators. The reactive four-terminal-network compensators for linear loads were introduced in previous publications, but it appeared that they operate effectively with nonlinear loads too. The methods to create a compensator for a mono-harmonic source, which allows complete independence of input from output waveforms, ensuring optimal operating conditions for the source, are presented herein. The work for the first time presents the optimal four-terminal-network compensator applied to a nonlinear load.

Reliable evaluation of stress-strain characteristics can be done only in the laboratory where boundary conditions with respect to stress and strain can be controlled. The most popular laboratory equipment is a triaxial apparatus. Unfortunately, standard version of triaxial apparatus can reliable measure strain not smaller than 0.1 %. Such accuracy does not allow to determine stiffness referred to strain range most often mobilized in situ i.e. 10-3 ÷ 10-1%, in which stiffness distribution is highly nonlinear. In order to overcome this problem fundamental modifications of standard triaxial apparatus should be done. The first one concerns construction of the cell. The second refers to method of measurement of vertical and horizontal deformation of a specimen. The paper compares three versions of triaxial equipment i.e. standard cell, the modified one and the cell with system of internal measurement of deformation. The comparison was made with respect to capability of stiffness measurement in strain range relevant for typical geotechnical applications. Examples of some test results are given, which are to illustrate an universal potential of the laboratory triaxial apparatus with proximity transducers capable to trace stress-strain response of soil in a reliable way.

The implementation of a new, high-performance float flat glass manufacturing technology in Europe, in conjunction with the growing interest in new glass functions expressed by the construction industry, has led to significant developments in the theory of glass structures. Long time research conducted in the EU countries has been concluded by the technical document CEN/TC 250 N 1060, drawn up as a part of the work of the European Committee for Standardization on the second edition of Eurocodes (EC). The recommendations pertaining to the design of glass structures have been foreseen in the second edition of the Eurocodes, in particular the development of a separate design standard containing modern procedures for static calculations and stability of glass building structures (cf. works M. Feldmann, R. Kasper, K. Langosch and other).

In this paper new static analysis methods for glass plates made of monolithic and laminated glass, declared in th document CEN/TC 250 N 1060 (2014) and recommended in the national standarization document CNR-DT 210 (National Research Council of Italy, 2013) are presented. These static analysis methods are not commonly known in our national engineering environment, and thus require popularization and regional verification. Numerical and analytical simulations presented in this paper for rectangular plates made of monolithic and laminated glass and having various support conditions are of this character. The results of numerical calculations constitute a basis for the discussion of new static analysis methods for plates.