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Ultrasonic-assisted plastic micro-forming is a research hotspot in metal-forming process. The friction characteristic is a key factor affecting the micro-forming properties of metal in ultrasonic-assisted micro-forming process. However, the existed researches were mostly focused on the friction characteristics of free surfaces, while few were studied on the friction characteristics between sample and mold cavity. In this paper, the micro double cup extrusion experiments of copper T2 were conducted to investigate the friction characteristics between sample and mold cavity with multiple ultrasonic vibration modes. Furthermore, the numerical model was developed to quantify the friction stress reduction caused by multiple ultrasonic vibration modes and estimate its contribution to decreasing the forming stress, which was usually considered mainly affected by acoustic softening, stress superposition, and friction reduction. The results show that the forming stress and the surface roughness of extruded samples are decreased sequentially with the multiple ultrasonic vibration modes of tool vibration (TV), workpiece vibration (WV), and compound vibration (CV). The cup height ratios of double cup extrusion are also increased sequentially with the ultrasonic vibration modes. But the increase of cup height ratio does not indicate the increase of friction coefficient. The friction stress reduction between sample and mold cavity is increased sequentially with TV, CV, and WV modes, and its contribution to decreasing the forming stress is 48%, 15%, and 49%, respectively.

The paper presents a numerical analysis of the free transverse vibration frequencies of the isotropic pentagonal plates of various thicknesses with one rigidly fixed edge and other edges free. The analysis is based on the finite element method and the reduced formula for calculating the frequencies of free vibrations of the isotropic pentagonal plate with free edges. The limits of application of the reduced formula are established, the coefficients of vibration mode and boundary conditions for the plates with various thickness-to-side ratios are determined. Deviations between the frequencies obtained using the finite element method and the reduced formula are identified. Free longitudinal vibration frequencies of the plates of various thicknesses are computed using the finite element method. Transverse and longitudinal vibration modes are obtained.

Subsoiling is an effective tillage technique for alleviating soil compaction, but the high traction resistance encountered at deeper working depths constrains its widespread application. To address this issue, a self-excited and forced intelligent vibrating subsoiler was developed. The subsoiler is equipped with a compound vibration mechanism that can adaptively switch between self-excited vibration and forced vibration modes based on real-time monitoring of soil resistance. Field experiments were conducted to evaluate the performance of the self-excited and forced vibrating subsoiling (SEFV). These experiments compared its performance with conventional subsoiling (CS) and self-excited vibrating subsoiling (SEV) at different working depths (35-45 cm) and forward speeds (2 and 4 km/h). The results showed that at 2 km/h, SEFV operated in self-excited vibration mode and reduced traction resistance by 12.4%-13.1% compared to CS, with no significant difference from SEV. At 4 km/h, the resistance reduction effect of SEFV became more pronounced with increasing depth. At 45 cm depth, SEFV reduced traction resistance by 9.9% and 18.9% compared to SEV and CS, respectively, as it switched to forced vibration mode to overcome the high soil resistance. SEFV also maintained high subsoiling depth stability (>90%) at both speeds and all depths tested, demonstrating its advantage over SEV under high resistance conditions. The intelligent control system based on resistance feedback enabled the SEFV to automatically adapt to variable soil conditions and optimize its vibration behavior for improved subsoiling performance and energy efficiency. This study provides new insights into the design of adaptive vibrating subsoilers for enhanced tillage operations.

This paper proposes a local resonance-type pentagonal phononic crystal beam structure for practical engineering applications to achieve better vibration and noise reduction. The energy band, transmission curve, and displacement field corresponding to the vibration modes of the structure are calculated based on the finite element method and Bloch-Floquet theorem. Furthermore, an analysis is conducted to understand the mechanism behind the generation of bandgaps. The numerical analysis indicates that the pentagonal unit oscillator creates a low-frequency bandgap between 60–70 Hz and 107–130 Hz. Additionally, the pentagonal phononic crystal double-layer beam structure exhibits excellent vibration damping, whereas the single-layer beam has poor vibration damping. The article comparatively analyzes the effects of different parameters on the bandgap range and transmission loss of a pentagonal phononic crystal beam. For instance, increasing the thickness of the lead layer leads to an increase in the width of the bandgap. Similarly, increasing the thickness of the rubber layer, intermediate plate, and total thickness of the phononic crystals results in a bandgap at lower frequencies. By adjusting the parameters, the beam can be optimized for practical engineering purposes.

BiCuSeO has recently been shown to be one of the best oxide-based thermoelectric materials. The electrical properties of this material have been widely studied; however, the reasons for its intrinsically low thermal conductivity have only been briefly discussed. In this paper, we calculated the band structure and the electrical properties of BiCuSeO. The phonon spectrum, mode Grüneisen parameters and the thermal properties were also investigated. Additionally, we proposed a new method for illustrating the interlayer interactions in this material. For the first time, using first principles calculations, we provide direct evidence of the structural in-layer and interlayer off-phase vibration modes, which contribute to the anharmonic vibrations and structural scattering of phonons and result in an intrinsic low lattice thermal conductivity for BiCuSeO.

A three-dimensional (3D) analytical formulation is proposed to put together magnetic, electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates. The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations. The second-order differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates. This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement. Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements. For these reasons, simply-supported boundary conditions are considered. Imposition of interlaminar continuity conditions on primary variables (displacements, magnetic potential, electric potential), and some secondary variables (transverse normal and transverse shear stresses, transverse normal magnetic induction/electric displacement) allows the implementation of the layer-wise approach. Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach. 3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature. A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios. For this benchmark, circular frequency values and related vibration modes through the transverse direction in terms of displacements, magnetic and electric potential, transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electro-elastic coupling and material and thickness layer effects. The present formulation has been entirely implemented in an academic Matlab (R2024a) code developed by the authors. In this paper, for the first time, the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix. The exponential matrix permits computing the secondary variable of the problem (stresses, electric displacement components and magnetic induction components) exactly, directly from constitutive and geometrical equations. In addition, the very simple and elegant formulation permits having a code with very low computational costs. The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.

Free vibrations are analyzed for isotropic plates in the form of isosceles triangles. We deduce the formula for the evaluation of the frequencies of free vibrations for plates of regular triangular shape with free edges and compute the coefficients of vibration mode and boundary conditions. The frequencies and modes of free vibrations of the isotropic thin isosceles triangular plates with free edges and different apex angles are computed by the finite-element method.

The present paper proposes a three-dimensional (3D) spherical shell model for the magneto-electro-elastic (MEE) free vibration analysis of simply supported multilayered smart shells. A mixed curvilinear orthogonal reference system is used to write the unified 3D governing equations for cylinders, cylindrical panels and spherical shells. The closed-form solution of the problem is performed considering Navier harmonic forms in the in-plane directions and the exponential matrix method in the thickness direction. A layerwise approach is possible, considering the interlaminar continuity conditions for displacements, electric and magnetic potentials, transverse shear/normal stresses, transverse normal magnetic induction and transverse normal electric displacement. Some preliminary cases are proposed to validate the present 3D MEE free vibration model for several curvatures, materials, thickness values and vibration modes. Then, new benchmarks are proposed in order to discuss possible effects in multilayered MEE curved smart structures. In the new benchmarks, first, three circular frequencies for several half-wave number couples and for different thickness ratios are proposed. Thickness vibration modes are shown in terms of displacements, stresses, electric displacement and magnetic induction along the thickness direction. These new benchmarks are useful to understand the free vibration behavior of MEE curved smart structures, and they can be used as reference for researchers interested in the development of of 2D/3D MEE models.

In structural health monitoring, because the number of sensors used is far lower than the number of degrees of freedom of the structure being monitored, the optimization problem of the location and number of sensors in the structures is becoming more and more prominent. However, spatial grid structures are complex and diverse, and their dynamic characteristics are complex. It is difficult to accurately measure their vibration information. Therefore, an appropriate optimization method must be used to determine the optimal positioning of sensor placement. Aiming at the problem that spatial grid structures have many degrees of freedom and the fact that it is difficult to obtain complete vibration information, this paper analyzed the typical EI method, MKE method, and EI-MKE method in the arrangement of the measuring points, and it was verified that the EI method was more suitable for the vibration detection of spatial grid structures through the example of a plane truss and spatial grid structures. Measuring points under the assumption of structural damage were explored, and it was proposed that there might have been a stable number of measuring points that could cover the possible vibration mode changes in the structures. At the same time, combined with the three-level improved Guyan recursive technique, in order to obtain better complete modal parameters, the influence of the number of measuring points on the complete vibration mode information was studied. It was concluded that MACd was better than MACn as the quantitative target.

A bi-directional linear ultrasonic motor (LUSM) based on multi-vibration of the piezoelectric (PZT) ceramic are proposed, designed, fabricated, and tested in this paper. The PZT ceramics with parallelogram cross-sections are positioned at both ends of the elastomer. Both torsional and longitudinal vibration modes co-occur when AC voltage is applied to PZT ceramics. In the elastomer, the longitudinal and bending modes are then formed. The motor can work on two hybrid vibration modes by changing the size of the stator and the voltage excitation scheme. The finite element method optimizes the motor design and modifies the motor size. The resonance frequencies of the two modes are extremely near, and the driving foot’s trajectory is acquired to evaluate the design’s reasonableness. A prototype is created, and an experimental investigation of the motor characteristics is presented. The results indicate that under a voltage of 1080 Vp-p, the proposed motor produces a forward velocity and thrust force of 37.04 mm/s and 0.22 N and a backward velocity and thrust force of 36.36 mm/s and 0.21 N.