In this work, the impact of the defect on the transmission of a mechanical wave in a periodic quasi-one-dimensional structure was investigated. The multilayer structure was made of PLA and air, while the defect layer was PNM-0.38PT with a significantly higher value of acoustic impedance in relation to the materials of the base structure. The influence of the position of the defect in the structure and its thickness was analysed. Transmission as a function of frequency was determined using the Transfer Matrix Method algorithm. The work showed the presence of band gaps in the analyzed structures. The influence of the symmetry of structures and substructures on the transmission of a mechanical wave was investigated. The influence of the number of layers with very low acoustic impedance (air) on the number of high transmission peaks with a small half-width was also demonstrated.

In the work, multi-criteria optimization of phononic structures was performed to minimize the transmission in the frequency range of acoustic waves, eliminate high transmission peaks with a small half-width inside of the band gap, and what was the most important part of the work – to minimize the number of layers in the structure. Two types of the genetic algorithm were compared in the study. The first one was characterized by a constant number of layers (GACL) of the phononic structure of each individual in each population. Then, the algorithm was run for a different number of layers, as a result of which the structures with the best value of the objective function were determined. In the second version of the algorithm, individuals in populations had a variable number of layers (GAVL) which required a different type of target function and crossover procedure. The transmission for quasi-one-dimensional phononic structures was determined with the use of the transfer matrix method algorithm. Based on the research, it can be concluded that the developed GAVL algorithm with an appropriately selected objective function achieved optimal solutions in a much smaller number of iterations than the GACL algorithm, and the value of the k parameter below 1 leads to faster achievement of the optimal structure.

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n x n system matrix A the sum of n-1 its entries is less than one. Key words: assignment, pole, zero, transfer matrix, linear, positive, system, state feedback

A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investi- gated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.

In this paper, we present a synthesis of the parameters of the fiber Bragg grating (FBG) and the reconstruction of the distributed strain affecting the grating, performed by means of its reflection spectrum. For this purpose, we applied the transition matrix method and the Nelder-Mead nonlinear optimization method. Reconstruction results of the strain profile carried out on the basis of a simulated reflection spectrum as well as measured reflection spectrum of the FBG indicate good agreement with the original strain profile; the profile reconstruction errors are within the single digit percentage range. We can conclude that the Nelder-Mead optimization method combined with the transition matrix method can be used for distributed sensing problems.

Mufflers are popular in the suppression of noise levels coming from various machinery. The most common parameters for the evaluation of the performance of mufflers are transmission loss, noise level, and insertion loss. The transmission loss is evaluated for tapered side outlet muffler using finite element analysis without considering the fluid-structure interaction. This study includes analytical modelling and acoustic modelling of the side outlet muffler and transmission loss is in excellent agreement with the reference paper. The feasibility of the acoustic model is also verified with the experimental work on simple expansion chamber muffler. The same finite element analysis is extended for the tapered side outlet muffler. The transmission loss of the tapered side outlet muffler in the given frequency range is found 8.96 dB better than the side outlet muffler. The acoustic pressure level and sound pressure level contours for the tapered side outlet muffler give a clear picture of wave propagation inside the muffler. The effect of the cut-off frequency on the transmission loss of the tapered side outlet muffler can be seen from the contours. This study can be helpful in the determination of the performance of the mufflers in terms of transmission loss, the performance of mufflers above cut-off frequency, and design improvements in the muffler to avoid the higher-order modes of the sound wave.

In this paper, we theoretically analyze the slow-light π-phase-shifted fiber Bragg grating (π-FBG) and its applications for single and multipoint/quasi-distributed sensing. Coupled-mode theory (CMT) and transfer matrix method (TMM) are used to establish the numerical modeling of slow-light π-FBG. The impact of slow-light FBG parameters, such as grating length (L), index change (Δn), and loss coefficient (α) on the spectral properties of π-FBG along with strain and thermal sensitivities are presented. Simulation results show that for the optimum grating parameters L = 50 mm, Δn = 1.5×10⁻⁴, and α = 0.10 m^-1, the proposed slow-light π-FBG is characterized with a peak transmissivity of 0.424, the maximum delay of 31.95 ns, strain sensitivity of 8.380 με^-1, and temperature sensitivity of 91.064 °C^-1. The strain and temperature sensitivity of proposed slow-light π-FBG is the highest as compared to the slow-light sensitivity of apodized FBGs reported in the literature. The proposed grating have the overall full-width at half maximum (FWHM) of 0.2245 nm, and the FWHM of the Bragg wavelength peak transmissivity is of 0.0798 pm. The optimized slow-light π-FBG is used for quasi-distributed sensing applications. For the five-stage strain quasi-distributed sensing network, a high strain dynamic range of value 1469 με is obtained for sensors wavelength spacing as small as 2 nm. In the case of temperature of quasi-distributed sensing network, the obtained dynamic range is of 133°C. For measurement system with a sufficiently wide spectral range, the π-FBGs wavelength grid can be broadened which results in substantial increase of dynamic range of the system.

Noise control is essential in an enclosed machine room where the noise level has to comply with the occupational safety and health act. In order to overcome a pure tone noise with a high peak value that is harmful to human hearing, a traditional reactive muffler has been used. However, the traditional method for designing a reactive muffler has proven to be time-consuming and insufficient. In order to efficiently reduce the peak noise level, interest in shape optimization of a Helmholtz muffler is coming to the forefront.

Helmholtz mufflers that deal with a pure tone have been adequately researched. However, the shape optimization of multi-chamber Helmholtz mufflers that deal with a broadband noise hybridized with multiple tones within a constrained space has been mostly ignored. Therefore, this study analyzes the sound transmission loss (STL) and the best optimized design for a hybrid Helmholtz muffler under a space- constrained situation. On the basis of the plane wave theory, the four-pole system matrix used to evaluate the acoustic performance of a multi-tone hybrid Helmholtz muffler is presented. Two numerical cases for eliminating one/two tone noises emitted from a machine room using six kinds of mufflers (muffler A~F) is also introduced. To find the best acoustical performance of a space-constrained muffler, a numerical assessment using a simulated annealing (SA) method is adopted. Before the SA operation can be carried out, the accuracy of the mathematical model has been checked using the experimental data. Eliminating a broadband noise hybridized with a pure tone (130 Hz) in Case I reveals that muffler C composed of a one- chamber Helmholtz Resonator and a one-chamber dissipative element has a noise reduction of 54.9 (dB). Moreover, as indicated in Case II, muffler F, a two-chamber Helmholtz Resonator and a one-chamber dissipative element, has a noise reduction of 69.7 (dB). Obviously, the peak values of the pure tones in Case I and Case II are efficiently reduced after the muffler is added.

Consequently, a successful approach in eliminating a broadband noise hybridized with multiple tones using optimally shaped hybrid Helmholtz mufflers and a simulated annealing method within a constrained space is demonstrated.

The notion of the normal transfer matrix and the notion of the structure decomposition of normal transfer matrix for 2D general model are introduced. Necessary and sufficient conditions for the existence of the structure decomposition of normal transfer matrix are established. A procedure for computation of the structure decomposition is proposed and illustrated by the numerical example. It is shown that the impulse response matrix of the normal model is independent of the polynomial part of its structure decomposition.