Shape optimization on mufflers within a limited space volume is essential for industry, where the equipment layout is occasionally tight and the available space for a muffler is limited for maintenance and operation purposes. To proficiently enhance the acoustical performance within a constrained space, the selection of an appropriate acoustical mechanism and optimizer becomes crucial. A multi-chamber side muffler hybridized with reverse-flow ducts which can visibly increase the acoustical performance is rarely addressed; therefore, the main purpose of this paper is to numerically analyze and maximize the acoustical performance of this muffler within a limited space.

In this paper, the four-pole system matrix for evaluating the acoustic performance - sound transmission loss (STL) - is derived by using a decoupled numerical method. Moreover, a simulated annealing (SA) algorithm, a robust scheme in searching for the global optimum by imitating the softening process of metal, has been used during the optimization process. Before dealing with a broadband noise, the STL's maximization with respect to a one-tone noise is introduced for the reliability check on the SA method. Moreover, the accuracy check of the mathematical models with respect to various acoustical elements is performed.

The optimal result in eliminating broadband noise reveals that the multi-chamber muffler with reverse-flow perforated ducts is excellent for noise reduction. Consequently, the approach used for the optimal design of the noise elimination proposed in this study is easy and effective.

A substantial quantity of research on muffler design has been restricted to a low frequency range using the plane wave theory. Based on this theory, which is a one-dimensional wave, no higher order wave has been considered. This has resulted in underestimating acoustical performances at higher frequencies when doing muffler analysis via the plane wave model. To overcome the above drawbacks, researchers have assessed a three-dimensional wave propagating for a simple expansion chamber muffler. Therefore, the acoustic effect of a higher order wave (a high frequency wave) is considered here. Unfortunately, there has been scant research on expansion chamber mufflers equipped with baffle plates that enhance noise elimination using a higher-order-mode analysis. Also, space-constrained conditions of industrial muffler designs have never been properly addressed. So, in order to improve the acoustical performance of an expansion chamber muffler within a constrained space, the optimization of an expansion chamber muffler hybridized with multiple baffle plates will be assessed. In this paper, the acoustical model of the expansion chamber muffler will be established by assuming that it is a rigid rectangular tube driven by a piston along the tube wall. Using an eigenfunction (higher-order-mode analysis), a four-pole system matrix for evaluating acoustic performance (STL) is derived. To improve the acoustic performance of the expansion chamber muffler, three kinds of expansion chamber mufflers (KA-KC) with different acoustic mechanisms are introduced and optimized for a targeted tone using a genetic algorithm (GA). Before the optimization process is performed, the higher-order-mode mathematical models of three expansion chamber mufflers (A-C) with various allocations of inlets/outlets and various chambers are also confirmed for accuracy. Results reveal that the STL of the expansion chamber mufflers at the targeted tone has been largely improved and the acoustic performance of a reverse expansion chamber muffler is more efficient than that of a straight expansion chamber muffler. Moreover, the STL of the expansion chamber mufflers will increase as the number of the chambers that separate with baffles increases.

In order to enhance the acoustical performance of a traditional straight-path automobile muffler, a multi-chamber muffler having reverse paths is presented. Here, the muffler is composed of two internally parallel/extended tubes and one internally extended outlet. In addition, to prevent noise transmission from the muffler’s casing, the muffler’s shell is also lined with sound absorbing material. Because the geometry of an automotive muffler is complicated, using an analytic method to predict a muffler’s acoustical performance is difficult; therefore, COMSOL, a finite element analysis software, is adopted to estimate the automotive muffler’s sound transmission loss. However, optimizing the shape of a complicated muffler using an optimizer linked to the Finite Element Method (FEM) is time-consuming. Therefore, in order to facilitate the muffler’s optimization, a simplified mathematical model used as an objective function (or fitness function) during the optimization process is presented. Here, the objective function can be established by using Artificial Neural Networks (ANNs) in conjunction with the muffler’s design parameters and related TLs (simulated by FEM). With this, the muffler’s optimization can proceed by linking the objective function to an optimizer, a Genetic Algorithm (GA). Consequently, the discharged muffler which is optimally shaped will improve the automotive exhaust noise.

There has been considerable research done on multi-chamber mufflers used in the elimination of industrial venting noise. However, most research has been restricted to lower frequencies using the plane wave theory. This has led to underestimating acoustical performances at higher frequencies. Additionally, because of the space-constrained problem in most plants, the need for optimization of a compact muffler seems obvious. Therefore, a muffler composed of multiple rectangular fin-shaped chambers is proposed. Based on the eigenfunction theory, a four-pole matrix used to evaluate the acoustic performance of mufflers will be deduced. A numerical case for eliminating pure tones using a three-fin-chamber muffler will also be examined. To delineate the best acoustical performance of a space-constrained muffler, a numerical assessment using the Differential Evolution (DE) method is adopted. Before the DE operation for pure tone elimination can be carried out, the accuracy of the mathematical model must be checked using experimental data. The results reveal that the broadband noise has been efficiently reduced using the three-fin-chamber muffler. Consequently, a successful approach in eliminating a pure tone using optimally shaped three-fin-chamber mufflers and a differential evolution method within a constrained space has been demonstrated.

Most researchers have explored noise reduction effects based on the transfer matrix method and the boundary element method. However, maximum noise reduction of a plenum within a constrained space, which frequently occurs in engineering problems, has been neglected. Therefore, the optimum design of multi-chamber plenums becomes essential. In this paper, two kinds of multi-chamber plenums (Case I: a two-chamber plenum that is partitioned with a centre-opening baffle; Case II: a three-chamber plenum that is partitioned with two centre-opening baffles) within a fixed space are assessed. In order to speed up the assessment of optimal plenums hybridized with multiple partitioned baffles, a simplified objective function (OBJ) is established by linking the boundary element model (BEM, developed using SYSNOISE) with a polynomial neural network fit with a series of real data – input design data (baffle dimensions) and output data approximated by BEM data in advance. To assess optimal plenums, a genetic algorithm (GA) is applied. The results reveal that the maximum value of the transmission loss (TL) can be improved at the desired frequencies. Consequently, the algorithm proposed in this study can provide an efficient way to develop optimal multi-chamber plenums for industry.

The paper is an exploration of the optimal design parameters of a space-constrained electromagnetic vibration-based generator. An electromagnetic energy harvester is composed of a coiled polyoxymethylen circular shell, a cylindrical NdFeB magnet, and a pair of helical springs. The magnet is vertically confined between the helical springs that serve as a vibrator. The electrical power connected to the coil is actuated when the energy harvester is vibrated by an external force causing the vibrator to periodically move through the coil. The primary factors of the electrical power generated from the energy harvester include a magnet, a spring, a coil, an excited frequency, an excited amplitude, and a design space. In order to obtain maximal electrical power during the excitation period, it is necessary to set the system’s natural frequency equal to the external forcing frequency. There are ten design factors of the energy harvester including the magnet diameter (Dm), the magnet height (Hm), the system damping ratio (ζsys), the spring diameter (Ds), the diameter of the spring wire (ds), the spring length (ℓs), the pitch of the spring (ps), the spring’s number of revolutions (Ns), the coil diameter (Dc), the diameter of the coil wire (dc), and the coil’s number of revolutions (Nc). Because of the mutual effects of the above factors, searching for the appropriate design parameters within a constrained space is complicated. Concerning their geometric allocation, the above ten design parameters are reduced to four (Dm, Hm, ζsys, and Nc). In order to search for optimal electrical power, the objective function of the electrical power is maximized by adjusting the four design parameters (Dm, Hm, ζsys, and Nc) via the simulated annealing method. Consequently, the optimal design parameters of Dm, Hm, ζsys, and Nc that produce maximum electrical power for an electromagnetic energy harvester are found.