Deflection Angle Research Articles

Automated Fabrication of 3D Printed Magnetic Soft Robots With Programmable 3D Magnetizations

Magnetic soft robots (MSRs) are a viable tool for many biomedical applications, such as targeted drug delivery and minimally invasive surgery, since they can be actuated remotely using external magnetic fields. These robots are developed by programming ferromagnetic domains with specific magnetizations using magnetic particles embedded in a flexible substrate. Existing fabrication methods rely on partially automated or manual processes, which limit production rates and realistic design iterations. To address these challenges, a fully automated workflow that translates robot simulations into an instruction set for a stereolithography 3D printer is presented. In this process, a rotating permanent magnet is used to program 3D magnetizations by reorienting hard magnetic particles within a photosensitive resin. Geometric resolutions of 1.6 mm are achieved with a layer height of 0.1 mm, enabling the creation of structures 14 layers thick. Beam bending tests identify an optimal 6:1 resin‐to‐magnetic particle mass ratio, yielding a maximum deflection angle of 80°. Demonstrated applications include rolling and climbing locomotion in a maze and independent control of each arm in a multiarmed robot. By enabling fast, repeatable production of MSRs within 30 min, this automated system shortens the feedback loop from design to application, advancing their potential as a biomedical tool.

Mixing characteristics and co-flow behavior in interactive cascade ventilation: An Experimental Approach

Achieving optimal indoor air quality that is both healthy and comfortable remains a persistent pursuit. Interactive cascade ventilation (ICV) has demonstrated remarkable performance, harnessing a temperature gradient to reverse the direction of buoyancy flux. The aim of this study is to investigate the mixing characteristics and co-flow behavior of ICV. Experiments, informed by Abramovich's theory and the principles of similarity, are conducted using a scaled-down experimental setup. The research results indicate that varying the temperature difference between the upper and lower jets from 2°C to 7°C significantly influences the deflection angle. Notably, the lower jet exhibits a more pronounced decrease of 52%, suggesting that the warmer lower jets effectively uplift the cooler upper jets. It can counteract their descent, optimizing the use of cool air in occupied spaces. Additionally, analysis of different velocity ratios reveals a reduction in the deflection angle from 12.69° to 5.57° as the velocity ratio increases from 0.5 to 0.81. A modified jet equation has been derived, which delineates the central path of the jet trajectory. The insights obtained from this research serve to bolster the theoretical framework for optimizing critical supply air parameters within the ICV system, thereby significantly enhancing its ventilation performance. These findings elucidate the underlying mechanisms of ICV, leading to a more profound understanding of its operational dynamics.

Molecular dynamics study of heterogeneous nucleate boiling on metallic oxides

This study employs molecular dynamics (MD) simulations to investigate the nanoscale boiling of water on Al2O3, CuO, Fe2O3, TiO2, and ZrO2 substrates. By regulating the mechanical piston pressure and increasing the water film height above 10 nm, the simulations adhere to 1 atm and classical nucleation theory. Boiling performance is compared based on wettability, heat flux (HF), heat transfer coefficient (HTC), bubble volume percentage, bubble growth rate, and incipient explosive boiling time. CuO exhibits the highest HF at 33.46 GW/m2, while ZrO2 shows the lowest at 14.03 GW/m2. Al2O3, Fe2O3, and TiO2 have similar HTCs, ranging from 0.106 to 0.116 GW/m2/K. Fe2O3 demonstrates the highest bubble growth rate at 151.0 Å3/ps, indicating vigorous boiling activity. The surfaces of Al2O3, TiO2, and ZrO2 present a sawtooth structure that facilitates heat transfer and nucleation, explaining why Al2O3, despite its poor wettability, initiates explosive boiling the earliest. The proposed bubble atom insertion method offers a high-fidelity analysis of bubble dynamics. Principal axis deflection angles of bubble clusters are 0° and 90° for cross-type (Al2O3, Fe2O3, TiO2) and 45° and 135° for diagonal-type (CuO, ZrO2), indicating that bubbles nucleate and grow along the paths of oxygen atoms in these oxides.

Research on the Spiral Rolling Gait of High-Voltage Power Line Serpentine Robots Based on Improved Hopf-CPGs Model

The efficiency of helical locomotion in snake-like robots along high-voltage transmission lines is often hindered by low motion efficiency, high joint signal noise, and challenges in traversing obstacles. This study aims to address these issues by proposing a gait generation method that leverages a standardized Central Pattern Generator (CPG). We modify the traditional Hopf-CPG model by incorporating constraint functions and a frequency-tuning mechanism to regulate the oscillator, which allows for the generation of asymmetric waveform signals for deflection joints and facilitates rapid convergence. The method begins by determining initial and obstacle-crossing state parameters, such as deflection angles and helical radii of the snake-like robot, using the backbone curve method and the Frenet–Serret framework. Subsequently, a CPG neural network is constructed based on Hopf oscillators, with a limit cycle convergent speed adjustment factor and amplitude bias signals to establish a fully connected matrix model for calculating multi-joint output signals. Simulation analysis using Simulink–CoppeliaSim evaluates the robot’s obstacle-crossing ability and the optimization of deflection joint signal noise. The results indicate a 55.70% increase in the robot’s average speed during cable traversal, a 57.53% reduction in deflection joint noise disturbance, and successful crossing of the vibration damper. This gait generation method significantly enhances locomotion efficiency and noise suppression in snake-like robots, offering substantial advantages over traditional approaches.

Mean deflection angle, anterior and posterior length of the cranial base in Pakistani population with different sagittal skeletal malocclusion

Objective: To compare the mean deflection angles as well as the anterior and posterior lengths of the cranial base in different skeletal patterns. Method: The cross-sectional study was conducted at the Department of Orthodontics, Sharif Medical and Dental College, Jati Umrah, Lahore, Pakistan, from December 2022 to May 2023, and comprised orthodontic patients of either gender aged 8-20 years. Pre-treatment lateral cephalograms of the patients were traced on lead acetate tracing sheet with 0.03mm mechanical pencil. Outcome variables for the cranial base nasion-sella-articulare, nasion-sella-basion nasion-sella and sella-to-basion angles were recorded, and data was stratified for age and gender. Data was analysed using SPSS 23. Results: Of the 93 patients, 60(64.5%) were females and 33(35.5%) were males. The overall mean age was 15.6±3.0 years, 38(40.9%) aged 8-14 years and 55(59.1%) aged 15-20 years). Mean values of cranial base flexion nasion-sella-articulare and nasion-sella-basion and posterior cranial base length sella-to-basion were significantly different sagittal patterns (p<0.05). Gender-based differences in mean values of anterior and posterior cranial base lengths were significant (p<0.05). Conclusion: Cranial base flexion decreased significantly. Cranial base lengths were higher for males than females, while age had no effect on cranial base morphology. Key Words: Cranial base, Craniofacial, Growth and development, Malocclusion, Mandible, Maxilla, Prognathism and retrognathia.

Numerical Study on the Influence of Suction near Expansion Corner on Separation Bubble

Suction is an important control method in the shock wave and boundary layer interaction (SWBLI). Aimed at the problem of separation bubbles induced at the expansion corners, this study investigates the influence of suction on both the dimensions of bubble and the structure of the flow field at varying positions and back pressures under Ma = 2.73. As the upstream suction hole moves to the shoulder point, the size of the separation bubble decreases slightly. The decrease in back pressure leads to an increase in flow deflection angle αh. The low-kinetic-energy fluid in the boundary layer is removed and the thickness of the boundary layer decreases. Suction downstream of the shoulder point leads to an obvious change in separation bubble size. When the bleed position is upstream of the actual location of incident shock (Ddown = 2δ), the separation zone is located at the trailing edge of the hole, and the convergence of the separation shock wave (SS) and the barrier shock wave (BSW) leads to a large increase in the pressure plateau. At the downstream of the incident shock (Ddown = 5δ), the separation zone is situated at the leading edge of the hole, resulting in a substantial reduction in the size of the separation bubble. The flow reaches 88.5% of the theoretical expansion value at the shoulder point and directly turns into the bleeding area at the leeward side of the separation bubble. The deflection angle αh reaches the maximum of 46°, and the sonic flow coefficient Qsonic increases significantly. At the theoretical incident shock position (Ddown = 7δ), the separation zone is far from the suction hole position; the two are almost decoupled. The size of the bubble increases rapidly and the reattachment shock wave (RS) appears.

Experimental Investigation on a Trailing Edge Morphing Airfoil (TEMA) with Zigzag Rib Structure at Low Speed

Camber-morphing wing technology enables adaptive adjustments to wing curvature by optimizing aerodynamic performance and efficiency for varying flight conditions. This study emphasizes the novel Trailing Edge Morphing Airfoil (TEMA) design and analysis, showcasing its noteworthy aerodynamic characteristics. The design uses the parabolic morphing method to obtain TEMA profiles for deflection angles. The different shapes of the TEMA and base airfoil were analyzed using the XFOIL solver with a linear-vorticity stream function formulation. TEMA with a flexible zigzag section was developed using a 3D printing technique with TPU material. The rectangular wing model was developed using TEMA and tested in a low-speed subsonic wind tunnel with Reynolds numbers of 1.19 ×105, 2.54 × 105 and 3.18 x 105 for different angles of attack. The test cases had a combination of different Reynolds numbers, deflection angles, and angles of attack. The aerodynamic characteristics were calculated by measuring the pressure coefficient around the TEMA using an advanced pressure scanner. The results show that TEMA with a moderate deflection angle has the potential to improve the lift-to-drag ratios by around 30%. It was concluded that TEMA with +5° and +10° deflection angles demonstrated superior aerodynamic efficiency at the Reynolds numbers mentioned compared to the conventional NACA 2412 airfoil.

Improvement of Aerodynamic Performance of Bilaterally Symmetrical Airfoil by Co-Flow Jet and Adaptive Morphing Technology

For a special bilaterally symmetric airfoil (BSA), this paper designs an active flow control scheme based on the Co-Flow Jet (CFJ) and adaptive morphing technology, and establishes a numerical simulation method which is suitable for simulating aerodynamic characteristics. The accuracy and effectiveness of the numerical method has been verified through benchmark cases. This study investigates the effects of jet intensity, suction slot position and angle, and deflection angles of the leading and TE flap on the aerodynamic performance parameters and flow field structure of the bilaterally symmetric airfoil. The results show that the adaptive morphing technology can significantly improve the equivalent lift coefficient and equivalent lift-to-drag ratio of the bilaterally symmetric airfoil, without obviously increasing the CFJ power consumption coefficient. Selecting an appropriate CFJ intensity can achieve a relatively high equivalent lift-to-drag ratio with a low compressor power requirement. Moving the suction slot rearward can increase the lift coefficient, and placing it on the trailing edge (TE) flap can more efficiently delay flow separation, reduce power consumption, and increase the equivalent lift-to-drag ratio. The suction slot angle has little effect on the lift coefficient, but a larger suction slot angle can enhance the equivalent lift-to-drag ratio. Increasing the TE flap deflection angle enhances both the lift coefficient and drag coefficient, as well as the power consumption coefficient at high angles of attack. But it has little effect on the maximum equivalent lift-to-drag ratio. Increasing the leading edge flap deflection angle can improve the maximum equivalent lift-to-drag ratio while increasing the angle of attack corresponding to it. Overall, choosing a CFJ and adaptive morphing parameters by considering different factors can enhance the aerodynamic performance of the bilaterally symmetric airfoil.

On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions

In this paper, an analytic generalization of the weak field deflection angle (WDA) is derived by utilizing the current non-asymptotically flat generalization of the Gauss–Bonnet theorem. The derived formula is valid for any Schwarzschild-like spacetime, which deviates from the classical Schwarzschild case through some constant parameters. This work provided four examples, including Schwarzschild-like solutions in the context of Bumblebee gravity theory and the Kalb–Ramond framework, as well as one example from a black hole surrounded by soliton dark matter. These examples explore distinct mechanisms of Lorentz symmetry breaking, with results that are either new or in agreement with existing literature. The WDA formula provided a simple calculation, where approximations based on some conditions can be done directly on it, skipping the preliminary steps. For the shadow size analysis, it is shown how it depends solely on the parameter associated with the metric coefficient in the time coordinate. A general formula for the constrained parameter is also derived based on the Event Horizon Collaboration (EHT) observational results. Finally, the work realized further possible generalizations on other black hole models, such as RN-like, dS/AdS-like black hole solutions, and even black hole solutions in higher dimensions.

Conformal reconfigurable holographic metasurface for multifunctional radiation and scattering modulation.

A reconfigurable holographic metasurface (HM) with multifunctional modulation of radiation and scattering for conformal applications is designed in this paper. Based on optical holography theory, a holographic conformal modulation mechanism is proposed, and the conformal surface impedance distribution of HM is derived. To illustrate this mechanism, the designed conformal reconfigurable HM is used to demonstrate a series of radiation and scattering modulation functions, with its reconfigurable property enabling dynamic beam control. In radiation mode, beam scanning with wide angle from -50° to 50° is achieved. In scattering mode, specific responses are generated under different incident angles, including beam steering under oblique incidence within ±60°, multi-beam splitting within ±60° under normal incidence, and diffuse reflection. Low radar cross section (RCS) is exhibited over a wide frequency band from 7.2 to 25 GHz. The designed conformal reconfigurable HM shows high adaptability to cylindrical platforms, insensitivity to oblique incidence, and stability in beam deflection angles, which provides an innovative technical approach for information transmission and stealth in conformal devices.

Shadow and strong gravitational lensing of new wormhole solutions supported by embedding Class-I condition

This study deals with the new class of embedded wormhole solutions in the background of general relativity. Two newly calculated wormhole solutions satisfy all the required properties. The embedded diagrams for both calculated wormhole solutions are provided. All the energy conditions are discussed through their validity regions for the different ranges of involved parameters. In maximum regions, all energy conditions are violated. We investigate the shadow and strong gravitational lensing by the wormhole throat for the two new wormhole models, namely Model-I and Model-II. The present paper considers the wormhole throat to act as a photon sphere. We first derive null geodesics using the Hamilton-Jacobi separation method to investigate the shadow and strong gravitational lensing caused by the wormhole throat. We then numerically obtain the radius of wormhole shadow, strong deflection angle, and various lensing observables by taking the example of supermassive black M87* and Sgr A* in the context of both Model-I and Model-II. Keeping all other parameters fixed, it is observed that the parameters ζ1 and ζ2 for Model-I; and χ1 and χ2 for Model-II have significant effects on the wormhole shadow and strong gravitational lensing phenomena. Our conclusion is that it is possible to detect relativistic images, such as Einstein rings, produced by wormholes with throat radii of rth=3M. The stability analysis via Tolman–Oppenheimer–Volkov equation is included for both wormhole solutions. Additionally, current technology enables us to test hypotheses related to astrophysical wormholes.

Analysis of trajectory transection rate on four-lane divided rural highway curves

Objective The study aims to develop continuous trajectory profiles along curves with minimal error. It also focuses on formulating a percentage trajectory transection rate model as a function of geometric parameters (e.g., radius and curve length) for through and passing maneuvers on four-lane divided highways. Additionally, the study sought to identify the critical maneuver between through and passing on horizontal curves of four-lane divided highways. Methods A total of 15 horizontal curve sites on a four-lane divided rural highway in plain terrain were selected. An instrumented vehicle, equipped with a GPS data logger and cameras, was used for data collection. Naturalistic driving data from 34 drivers’ trips across the curves were collected for analysis, ensuring free-flow conditions. This dataset was used to develop continuous trajectory profiles, with GPS positioning errors minimized by calibrating the profiles at the Point of Curvature (PC) and Point of Tangency (PT) using the vanishing point method. Moreover, multiple linear regression technique was used to develop the mean percentage trajectory transection rate models i.e., for through (PTTR μC_T ) and passing (PTTR μC_P ) maneuvers. Results The trajectory profiles were effectively developed using the vanishing point method, which restricts the mean absolute error to 16 cm. The developed models revealed that curve length significantly influences PTTR in through maneuvers, while deflection angle, approach tangent length and curve length are the most critical factors in passing maneuvers. Notably, curve length emerged as a common predictor for both maneuvers. Additionally, a 15% higher trajectory transection rate was observed in passing maneuvers. Conclusions Combining geometric features such as curve length, deflection angle, and approach tangent length provides a more comprehensive understanding of drivers’ trajectory behavior, especially during passing maneuvers. The developed models can serve as a supplemental tool in geometric design to minimize lateral deviations and trajectory transitions across horizontal curves on four-lane divided highways. Passing maneuvers are riskier than through maneuvers, often involving lane changes and unpredictable paths. This highlights the need for roadway departure safety measures such as raised pavement markings, centerline rumble strips, and passing restrictions at specific curves.

Root-soil interface friction jointly amplified by high root density and shear deflection

Plant roots significantly enhance the stability of shallow slopes. However, the mechanism of the root-soil interaction at root-bundle scale remains unclear. The objective of this study is to reveal the factors that control root-soil interface frictional stress at root-bundle scale. Through theoretical analysis, it is clarified that spatiotemporal inhomogeneity exists in root-soil interface frictional stress, and it could be amplified by root density and root deflection angle. Large-scale shear tests with 160 mm and 10 mm shear zones were then conducted to verify this hypothesis, where variations in shear zone thicknesses corresponded to different shear deflections. The number of roots was measured within the sheared zone. Results reveal that the average root-soil interface frictional stress of rooted soils with 10 mm shear zone is 66% higher than that for rooted soils with 160 mm shear zone. During the shear process, the state of roots transitions from stretching to sliding, accompanied by increasing root-soil interface friction. This study confirms that root-soil interface frictional stress is jointly amplified by root density and root deflection angle, providing robust evidence for constructing physics-based mechanical reinforcement models.

The Effect of Airflow-Assisted Parameters on Droplet Deposition on Soybean Leaves at the V7 Growth Stage

In agricultural production, the underside of crop leaves and the middle-lower canopy are key areas where pests and diseases typically develop at early stages. Increasing droplet deposition in these critical regions is essential for improving pesticide efficacy and crop yield. This study aims to optimize airflow-assisted parameters to enhance spray operation quality. By extracting the physical characteristics of soybean leaves at the V7 growth stage and conducting theoretical analysis, the study explored the factors influencing leaf orientation and droplet deposition, as well as the coupling relationship between these two aspects. A one-way fluid–structure coupling model was established using COMSOL software 6.1 to simulate the interaction between airflow and soybean leaves. The simulation results showed that airflow caused 71.1% of upper leaves, 66.7% of middle leaves, and 43.3% of lower leaves to have a flipping angle greater than 10°, with most flipped leaves (61.9%) concentrated on the windward side. Using droplet deposition on the middle-lower canopy and the underside of leaves as evaluation indices, a numerical simulation orthogonal experiment was conducted. The results indicated that the optimal operational parameters were an initial airflow speed of 20 m/s, an outlet-to-canopy distance of 0.45 m, and a forward airflow deflection angle of 32°. This optimal parameter combination improved droplet deposition. Field experiments confirmed these results, showing that compared to the spraying without optimization, droplet deposition on the lower and middle canopy and the underside of the leaves increased by 2.1 times and 2.3 times, respectively.

GaAs gradient metasurface for vortex beam emission with high deflection angles.

This study experimentally demonstrates metasurfaces capable of producing output emissions with deflection angles greater than 75 degrees. These metasurfaces are composed of high-aspect-ratio gallium arsenide (GaAs) nano-resonators on double-sided polished GaAs substrates, operating reflectively at a wavelength of 650 nm. Beyond deflecting the incident light beam, the metasurfaces are successfully shown to generate high-deflection-angle, doughnut-shaped emissions by incorporating vortex beam (VB) structured light with a topological charge of up to 8. The broadband capabilities of these metasurfaces are also explored in this work. This work significantly advances the manipulation of structured light. Achieving high deflection angles opens new pathways for developing compact optical systems that leverage the unique properties of vortex beams in a range of applications.

Glucose Sensor Design Based on Monte Carlo Simulation.

Continuous glucose monitoring based on the minimally invasive implantation of glucose sensor is characterized by high accuracy and good stability. At present, glucose concentration monitoring based on fluorescent glucose capsule sensor is a new development trend. In this paper, we design a fluorescent glucose capsule sensor with a design optimization study. The motion trajectory of incident light in the fluorescent gel layer is simulated based on the Monte Carlo method, and the cloud maps of light intensity with the light intensity distribution at the light-receiving layer are plotted. Altering the density of fluorescent molecules, varying the thickness of tissue layers, and adjusting the angle of incidence deflection, the study investigates the influence of these parameter changes on the optimal position of reflected light at the bottom. Finally, the simulation results were utilized to design and fabricate a fluorescent glucose capsule sensor. Rabbit subcutaneous tissue glucose level tests and real-time glucose solution concentration monitoring experiments were performed. This work contributes to the real-time monitoring of glucose levels and opens up new avenues for research on fabricating glucose sensors.

Coupled differential-algebraic equations framework for modeling six-degree-of-freedom flight dynamics of asymmetric fixed-wing aircraft

This study presents a comprehensive mathematical framework for modeling the flight dynamics of a six-degree-of-freedom fixed-wing aircraft as a rigid body with three control surfaces: rudder, elevators, and ailerons. The framework consists of 35 differential-algebraic equations (DAEs) and requires 30 constants to be specified. It supports both direct and inverse flight dynamics analyses. In direct dynamics, the historical profiles of control inputs (deflection angles and engine thrust) are specified, and the resulting flight trajectory is predicted. In inverse dynamics, the desired flight trajectory and an additional constraint are specified to determine the required control inputs. The framework employs wind axes for linear-momentum equations and body axes for angular-momentum equations, incorporates two flight path angles, and provides formulas for aerodynamic force and moment coefficients. Key advantages include improved computational efficiency, elimination of Euler angle singularities, and independence from symmetry assumptions with regard to the aircraft’s moments of inertia. The model also accounts for nonlinear air density variations with altitude, up to 20 km above mean sea level, making it suitable for accurate and efficient flight dynamics simulations.

Enhancing primordial B-mode detection: comprehensive delensing pipelines for improved sensitivity to r

Recognizing the impact of contamination from weak gravitational lensing B-modes induced by Large Scale Structure, we examine delensing methods to enhance sensitivity to the tensor-to-scalar ratio r in primordial B-mode detection experiments. This study presents a realistic pipeline to improve r constraints using foreground-cleaned maps with negligible residuals. The pipeline, based on simulations, is adaptable for future experiments. We focus on two delensing approaches: (1) subtracting the gradient-order lensing B-mode template, computed by convolving the E-mode with the lensing potential, from the observed B-mode signal; and (2) remapping observations using the estimated inverse deflection angle. For parameter constraints, we employ three models to reduce r uncertainty and bias, finding consistent uncertainties across models, though biases vary due to the multipole-dependence of the delensing fraction. We demonstrated this pipeline using simulated observation maps from future CMB polarization experiments, which included current representative ground-based small aperture telescopes (sub-1m), next-generation ground-based large aperture telescopes (6m), and highly competitive future space-based medium aperture missions (3m). Results show a delensing efficiency of 40% with the small-aperture telescope alone, increasing to 65% when combined with the large-aperture telescope, and 80% with the satellite mission. These lead to reductions in r uncertainty by 46% for ground-based and 63% for space missions. The most promising method adds the lensing template B-mode as an additional frequency channel, minimizing bias on r.

Measuring line-of-sight distances to haloes with astrometric lensing B-mode

Relative astrometric shifts between multiply lensed images provide a valuable tool to investigate haloes in the intergalactic space. In strong lens systems in which a single lens plays the primary role in producing multiple images, the gravitational force exerted by line-of-sight (LOS) haloes can slightly change the relative positions of multiply lensed images produced by the dominant lens. In such cases, a LOS halo positioned sufficiently far from the dominant lens along the LOS can create a pattern in the scaled deflection angle that corresponds to the B-mode (magnetic or divergence-free mode). By measuring both the B-mode and E-mode (electric or rotation-free mode), we can determine the LOS distance ratios, as well as the `bare' convergence and shear perturbations in the absence of the dominant lens. However, scale variations in the distance ratio lead to mass-sheet transformations in the background lens plane, introducing some uncertainty in the distance ratio estimation. This uncertainty can be significantly reduced by measuring the time delays between the lensed images. Additionally, if we obtain the redshift values of both the dominant and perturbing haloes, along with the time delays between the multiply lensed images that are affected by the haloes, the B-mode can break the degeneracy related to mass-sheet transformations in both the foreground and background lens planes. Therefore, measuring the astrometric lensing B-mode has the potential to substantially decrease the uncertainty in determining the Hubble constant.

Investigation of a flat-type piezoelectric motor using in-plane vibrations.

This paper presents a flat-type piezoelectric motor utilizing in-plane vibration modes. Two piezoelectric ceramic plates in combination with a brass metal sheet were used to construct the stator. The superposition of two second order in-plane vibration modes can generate a traveling-wave inside the stator. The greatest advantage of the proposed motor lies in its sheet structure configuration, which significantly reduces the overall size of piezoelectric motors exploiting in-plane vibrations, particularly in terms of thickness. Meanwhile, the stator also demonstrates greater vibration displacements when compared to higher-order operating modes. Through discussing the impact of stator structure parameters on the vibration deflection angle θ, the excitation ways of operating modes were investigated. Subsequently, the finite element method was utilized to explore both the static and dynamic vibration properties of the stator. Simulation results suggest that at a steady state, stator driving points achieve vibrations at the micro-meter level, satisfying actual application requirements. Finally, a prototype motor was fabricated. Driven by two-phase alternating voltage with a frequency of 69.4kHz, the no-load speed and stall torque of the prototype motor are 52rpm and 3.2mNm, respectively.