Summary This article compares the 2‐D and 0‐D analytical models for the slotless double‐sided inner armature linear permanent magnet synchronous machines (SDSIALPMSMs). The sub‐domain method is implemented to achieve the 2‐D analytical model. In this method, the cross‐section of the motor is divided into eleven sub‐regions and the Maxwell equations are determined for each sub‐region. In the presented 0‐D model, a magnetic equivalent circuit (MEC) is derived to compute the maximum magnetic flux density in the air‐gap. In both approaches, the magnetic flux density is analytically calculated to predict the inductance, induced voltage, flux linkage and electromagnetic forces. Ultimately, the results of both analytical models are validated against those of the 3‐D finite‐element method (FEM) analysis. These results confirm the superiority of the 2‐D analytical model compared with that of the 0‐D in the terms of the accuracy of the magnetic flux density, induced voltage, self and mutual inductances as well as the tangential and normal electromagnetic forces. Also, less computational time of the described 2‐D analytical model is recognized as a merit compared with FEM models.

Laminated composite beams with non-uniform thickness are being used as primary structural elements in a wide range of advanced engineering applications. Tapered composite structures, formed by terminating some of the plies, create geometry and material discontinuities that act as sources for delamination initiation and propagation. Any small damage or delamination in these structures can progress rapidly without any visible external signs. Due to this reason early detection of damage in these systems during their service life is receiving increasing attention. The presence of a crack in a component or structure leads to changes in its global dynamic characteristics results in decreases in the natural frequencies and modifications of the mode shapes of the component or structure. The present work aims to investigate the influences of delamination on the natural frequencies, frequency and voltage responses of smart non-uniform thickness laminated composite beams. In order to guarantee the continuity of curvature at element interfaces, particularly at ply drop-off locations, a higher-order finite element model by considering the electro-mechanical coupling effect is used which can accurately and efficiently represents the dynamic responses of the structure for forced/random stimuli and provide accurate results using fewer elements.

Slotless double-sided outer armature permanent-magnet (PM) linear motors (SDOPMLs) have high efficiency and low detent force. Despite their simple control strategy and easy manufacturing process, finding an accurate model of these motors to calculate the machine quantities is challenging. It is particularly critical for obtaining the optimum design of these machines which may include too many iterations in a short time. To overcome this challenge, a 2-D analytical model based on the subdomain method is presented to determine the magnetic flux density components for the motor under the study. According to this analytical procedure, the motor cross-section is divided to 11 sub-regions, then the superposition theorem is utilized to analyze the flux density distribution in all sub-regions due to various magnetization patterns, (i.e., parallel, two-segment Halbach, ideal Halbach, and bar magnet in shifting directions) as well as armature reaction current, respectively. According to the calculated magnetic flux density components, machine quantities like flux linkage, induced voltage, inductances, and electromagnetic force components are explained. Also, the obtained analytical results are compared with those of the finite-element method (FEM) to confirm the accuracy of the proposed model. The proposed model can be used in the design and optimization stage of the linear slotless motor against the numerical model to save time. Finally, a comparative study between the performance of the single-sided and double-sided slotless PM linear motors in the same volume is implemented. This comparison shows the advantage of the double-sided motor in terms of the unbalanced magnetic force (UMF).

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