Search Results (27)

This paper investigates the vibration characteristics of tensioned umbrella-shaped membrane structures with complex curvature under heavy rainfall. To solve the geometrical problem of the complex curvature of a membrane surface, we set the rule of segmentation and simplify the shape by dividing it into multi-segment conical membranes. The generatrix becomes a polyline with a constant surface curvature in each segment, simplifying calculations. The equivalent uniform load of different rainfall intensity is determined by the theory of the stochastic process. The governing equations of the isotropic damped nonlinear forced vibration of membranes are established by using the theory of large deflection by von Karman and the principle of d’Alembert. The equations of the forced vibration of the membrane are solved by using Galerkin’s method and the small-parameter perturbation method, and the displacement function, vibration frequency, and acceleration of the membrane are obtained. At last, the influence of the height–span ratio, number of segments, pretension and load on membrane displacement, vibration frequency, and acceleration of the membrane surface are analyzed. Based on the above data, the general law of deformation of the umbrella-shaped membrane under heavy rainfall is obtained. Data and methods are provided for the design and construction of the membrane structure as a reference. Moreover, we propose methods to enhance calculation accuracy and streamline the computational process. Full article

The ultimate goal of research on seismic mitigation technologies is engineering application. However, current studies primarily focus on the application of dampers in planar structures, while actual engineering structures are three-dimensional (3D) in nature. A type of damper, making up tuned mass dampers (TMDs) and inerters, has excellent vibration mitigation performance and needs brackets to connect to structures. In this work, a coupled dynamic model of an energy dissipation system (EDS) comprising a TMD, an inerter, a bracket, and a 3D building structure is presented, along with analytical solutions for stochastic seismic responses. The main work is as follows. Firstly, based on D’Alembert’s dynamics principle, the seismic dynamic equations of an EDS considering a realistic damper and a 3D structure are formulated. The general dynamic equations governing the bidirectional horizontal motion of the EDS are further derived using the dynamic finite element technique. Secondly, analytical expressions for spectral moments and variances of seismic responses are obtained. Finally, four numerical examples are presented to investigate the following: (1) verification of the proposed response solutions, showing that the calculation time of the proposed method is approximately 1/500 of that of the traditional method; (2) examination of spatial effects in 3D structures under unidirectional excitation, revealing that structural seismic responses in the direction along the earthquake ground motion is approximately 10⁴ times that in the direction perpendicular to the ground motion; (3) investigation of the spatial dynamic characteristics of a 3D structure subjected to unidirectional seismic excitation, showing that the bracket parameters significantly affect the damping effects on an EDS; and (4) application of the optimization method for the damper’s parameters that considers system dynamic reliability and different weights of the damper’s parameters as constraints, indicating that the most economical damping parameters can achieve a reduction in displacement spectral moments by 30–50%. The proposed response solutions and parameter optimization technique provide an effective approach for evaluating stochastic seismic responses and optimizing damper parameters in large-scale and complex structures. Full article

In the context of holonomic systems, the identification of virtual displacements is clear and consolidated. This provides the possibility, once the class of displacements have been coupled with Newton’s equations, for us to write the correct equations of motion. This method combines the d’Alembert principle with Lagrange formalism. As far as nonholonomic systems are concerned, the conjecture that dates back to $\check{\mathrm{C}}$etaev actually defines a class of virtual displacements through which the d’Alembert–Lagrange method can be applied again. A great deal of literature is dedicated to the $\check{\mathrm{C}}$etaev rule from both the theoretical and experimental points of view. The absence of a rigorous (mathematical) validation of the rule inferable from the constraint equations has been declared to have expired in a recent publication; one of our objectives is to produce a critical comment on this stated result. Finally, we explore the role of the $\check{\mathrm{C}}$etaev condition within the significant class of nonholonomic homogeneous constraints. Full article

The D’Alembert–Lagrange principle is a fundamental concept in analytical mechanics that simplifies the analysis of multi-degree-of-freedom mechanical systems, facilitates the dynamic response prediction of structures under various loads, and enhances the control algorithms in robotics. It is essential for solving complex problems in engineering and robotics. This theoretical study aims to highlight the advantages of using acceleration energy to obtain the differential equations of motion and the generalized driving forces, compared to the classical approach based on the Lagrange equations of the second kind. It was considered a mechanical structure with two degrees of freedom (DOF), namely, a planar robot consisting of two homogeneous rods connected by rotational joints. Both the classical Lagrange approach and the acceleration energy model were applied. It was noticed that while both approaches yielded the same results, using acceleration energy requires only a single differentiation operation, whereas the classical approach involves three such operations to achieve the same results. Thus, applying the acceleration energy method involves fewer mathematical steps and simplifies the calculations. This demonstrates the efficiency and effectiveness of using acceleration energy in dynamic system analysis. By incorporating acceleration energy into the model, enhanced robustness and accuracy in predicting system behavior are achieved. Full article

This paper proposes a kinetostatic approach for analyzing the joint torques of a redundant snake robot. The method is suitable for weightless space environments. With the high degree of freedom and flexible cable actuation, the redundant snake robot is well-suited for utilization in space-weightless environments. This method reduces computational cost by using the multiplication of matrices and vectors instead of inverse matrices. Taking advantage of the velocity screw (twist) and force screw (wrench), this strategy provides an idea for redundant serial robots to achieve the calculation of joint torques. This methodology is straightforward for programming and has good computational efficiency. The instantaneous work performed by the actuation is expressed with the force screw. According to the principle of virtual work, the kinetostatic equation of the robot can be obtained and the torque required for each joint can be determined. Meanwhile, to solve the inertia force generated by joint acceleration, D’Alembert’s principle is adopted to transform the dynamic problem into a static problem. Through kinetostatic analysis of a redundant snake robot, this paper shows the approach of establishing the kinetostatic model to calculate the torque in screw form. At the same time, the actuation distribution of the redundant snake robot is also cracked effectively for practical purposes. Due to the difficulty of achieving weightless space environments, this paper validates the method by using ADAMS simulation without gravity in the simulation. Full article

The experimental determination of cutting forces during milling is an important aspect followed in the manufacturing process and involves the use of specialized devices known as dynamometers. These can be made in the laboratory, depending on the type of measurements to be made, or they can be commercial, purchased from specialized companies. In this paper, such a dynamometer made by the authors in the laboratory is analyzed. For the elastic elements, octagonal rings are used. The main problem in the case of these dynamometers, namely the determination of the stiffness of the rings, is solved analytically, using the FEM for comparison, and then experimentally validated. The dynamic model, created based on the obtained values using d’Alembert’s principle, allows for simulating the behavior of this dynamometer in practical applications and determining the field in which it can be used. The frequencies and natural modes of vibration are determined, and the values obtained are compared with those obtained using ANSYS software 2021 R2. Full article

A fast spraying speed, wide working area, and easy operation are the operational advantages of high-clearance boom sprayers. To address the issue of spray boom mechanical vibration affecting the spraying effect, a double-link trapezoidal boom suspension is designed for the 3WPYZ sprayer. This suspension can achieve passive vibration reduction, active balance, and ground profiling. The kinematic model of the boom suspension is established based on D’Alembert’s principle and the principle of multi-body dynamics, and the design factors affecting the stability of the boom are determined. Through orthogonal experimental design and virtual kinematics simulation, the influence of the boom length and orifice diameter of each part on the swing angle and the natural frequency of the boom suspension is investigated. Design-Expert 8.0.6 software is used to analyze and optimize the test results. The optimization results show that, when the connecting boom length L_AB is 265 mm, the inner boom suspension boom length L_AD is 840 mm, the outer boom suspension boom length L_BC is 1250 mm, and the throttle hole diameter d is 4 mm; the maximum swing angle of the boom suspension is reduced by 53.02%. In addition, the natural frequency of the boom is reduced from 1.3143 rad/s to 1.1826 rad/s, and the dynamic characteristic optimization effect is remarkable. The modal analysis results show that the first sixth-order vibration test frequency of the boom sprayer suspension designed in this paper meets the requirements and avoids the influence of external factors. Field tests show that, when the sprayer is excited by the environment at 3.5° to 4°, the boom suspension can reduce the vibration transmitted by the body to a reasonable range. The static analysis shows that the structural design of this study reduces the stress at the connection of the end boom suspension, the maximum displacement, and the maximum stress of the inner boom suspension. The test results of the dynamic characteristics of the implement are basically consistent with the virtual model simulation test results, thus achieving the optimization objectives. Full article

The present paper describes, in a theoretical fashion, a variational approach to formulate fourth-order dynamical systems on differentiable manifolds on the basis of the Hamilton–d’Alembert principle of analytic mechanics. The discussed approach relies on the introduction of a Lagrangian function that depends on the kinetic energy and the covariant acceleration energy, as well as a potential energy function that accounts for conservative forces. In addition, the present paper introduces the notion of Rayleigh differential form to account for non-conservative forces. The corresponding fourth-order equation of motion is derived, and an interpretation of the obtained terms is provided from a system and control theoretic viewpoint. A specific form of the Rayleigh differential form is introduced, which yields non-conservative forcing terms assimilable to linear friction and jerk-type friction. The general theoretical discussion is complemented by a brief excursus about the numerical simulation of the introduced differential model. Full article

Transverse cracking is thought of as the typical distress of asphalt pavements. A faster detection technique can provide pavement performance information for maintenance administrations. This paper proposes a novel vehicle-vibration-based method for transverse cracking detection. A theoretical model of a vehicle-cracked pavement vibration system was constructed using the d’Alembert principle. A testing system installed with a vibration sensor was put in and applied to a testing road. Then, parameter optimization of the Short-time Fourier transform (STFT) was conducted. Transverse cracking and normal sections were processed by the optimized STFT algorithm, generating two ideal indicators. The maximum power spectral density and the relative power spectral density, which were extracted from 3D time–frequency maps, performed well. It was found that the power spectral density caused by transverse cracks was above 100 dB/Hz. The power spectral density at normal sections was below 80 dB/Hz. The distribution of the power spectral density for the cracked sections is more discrete than for normal sections. The classification model based on the above two indicators had an accuracy, true positive rate, and false positive rate of 94.96%, 92.86%, and 4.80%, respectively. The proposed vehicle-vibration-based method is capable of accurately detecting pavement transverse cracking. Full article

Liquid films are an important part of liquid metal granulation in the process of centrifugal spray forming. The size of the granulated particles has an important influence on the density, grain size and microstructure uniformity of the deposited blanks. The particle size is closely related to the flow characteristics of liquid films. Therefore, enhancing our understanding of the flow characteristics of liquid films can provide guidance for forming blanks. In this study, force analysis of a liquid film on the surface of a high-speed rotating centrifugal disc used in centrifugal spray-forming technology was carried out using D’Alembert’s principle and Newton’s law of viscosity. Then, combined with the principle of mass conservation, a theoretical model of the smooth flow of the liquid metal film was established. The experimental values obtained by Leshev were compared with our values to verify the correctness and accuracy of the model. Through the model, the influencing factors of the liquid film flow were obtained, such as the centrifugal disc speed, centrifugal disc radius, inlet volume flow rate and kinematic viscosity. Taking A390 aluminum alloy as the research object, the influence of the process parameters on the thickness, velocity and trajectory of the liquid film was revealed theoretically, and the relationship between the process parameters and the trajectory length and liquid film thickness was clarified. Modeling and analysis can not only help us to understand the flow of a liquid film, but also help us to predict the relevant parameters, which is convenient for the accurate and rapid regulation of the process to obtain the desired flow parameters. Therefore, the research content of this paper is of great significance for the preparation of billets with a uniform microstructure and excellent mechanical properties. Full article

The current problems associated with the maintenance of hard coal longwall mining depend on the application or use of extraction technologies. In order to make the best use of these technologies, a new approach based on simulation studies is necessary. This paper aims to develop a mathematical model for the powered roof support’s operation. The three groups of professionals involved in the testing of the roof support were involved in the work on changing the hydraulic system of the powered roof support stand. These professionals were powered roof support’s designers, researchers and users. The research subject was the development of a mathematical model as a starting point for conducting simulations. The model is based on d’Alembert’s principle and the equation of the balance of flow rates. Based on the developed model, it is possible to determine the pressure in the space under the piston of the hydraulic prop. The results obtained in the simulations are the basic assumptions for the development of a prototype that would solve the current problems in the hydraulic systems of powered roof supports. The adopted research methodology assumed the development of a mathematical model, simulation in the MATLAB environment and verification of the model on a test stand. The obtained results of simulation tests based on the developed mathematical model were confirmed in bench tests. Simulation and bench tests determined the correctness of the assumptions made for the development of the prototype model. Based on the analysis of the results, the nature of the work of the future prototype has been predetermined. The next stage will be the testing of the prototype, which is to be included in the hydraulic system of the prop of powered roof support in the future. The model mentioned before is the baseline model, and it will be modified depending on the application of the future design in real conditions. Simulation studies of powered roof support will allow the structure that is used currently to be optimised, so as to adapt it to increasingly difficult working conditions. Full article

Solving the stability region in the plane motion of vehicles has become a hot research topic in vehicle handling stability under extreme conditions, but there is still a lack of research on the stability region under steering and braking conditions. In this paper, a five-degree-of-freedom (5DOF) nonlinear dynamic model of a vehicle with braking torque introduced is established, and the model is transformed into an equivalent system by using the D’Alembert principle. Then, the equilibrium points of the equivalent system are solved by using an improved hybrid algorithm combining the genetic algorithm (GA) and sequential quadratic programming (SQP) method. According to the bifurcation characteristics of the equilibrium points, the boundary of the stability region at the given initial longitudinal velocity is determined, and the three-dimensional stability region is fitted. Finally, the stability region of the equivalent system and the original system are analyzed by the energy dissipation method, and the stability region determined by the equilibrium point bifurcation method is verified by simulation. The results show that as the braking torque increases, the number of equilibrium points increase to three from one, the equilibrium bifurcation method proposed in this paper can effectively solve the stability region of the equivalent system, and the solution results are consistent with the original system stability region. When the limited braking torque is 500 N·m and the initial longitudinal velocity increases from 30 m/s to 50 m/s, the absolute value of the front wheel steering angle at the boundary point changes from less than 0.02 rad to more than 0.02 rad. Full article

An approach is presented to investigate the 1:2 internal resonance of the sling and beam of a suspension sling–beam system. The beam was taken as the geometrically linear Euler beam, and the sling was considered to be geometrically nonlinear. The dynamic equilibrium equation of the structures was derived using the modal superposition method, the D’Alembert principle and the Hamilton principle. The nonlinear dynamic equilibrium equations of free vibration and forced oscillation were solved by the multiple-scales method. We derived the first approximation solutions for the single-modal motion of the system. Numerical examples are provided to verify the correctness of formula derivation and obtain the amplitude–time response of free vibration, the primary resonance response, the amplitude–frequency response, and the amplitude–force response of forced oscillation. According to the analysis, it is evident that the combination system exhibits robust nonlinear coupling properties due to the presence of internal resonance, which are useful for engineering design. Full article

Considering the effect of the bridge deck’s bending stiffness and the indirect effect of adjacent cables (CEB), this paper aims to propose a refined model to reliably analyze the complex internal resonance mechanism of the tower–multicable–beam coupled system (MCS) under nonlinear geometric conditions. To accurately analyze the dynamic behavior, the shear difference effect is applied to simulate the continuous rigidity of the single beam. The dynamic equations of the whole resonance system are derived based on the D’Alembert Principle and the Finite Difference Method, the Galerkin Method and verified by the case study. The results of the numerical simulation based on the Fourth Runge–Kutta Method show that the dynamic parameter of each component is closely related to the coupled resonance of the system. The dynamic behavior under two conditions, tower–cable 1:1 resonance (TCR) or cable–beam 1:2 resonance (CBR), is deeply analyzed. Additionally, the excitation effect of the maximum amplitude by two excitation approaches, the initial displacement or initial velocity, both show a linear increase. The mutual transmission process of vibration excitation on the cable through the bridge beam or the tower as the medium is also further discussed. Full article

Runway roughness is one of the most critical performance factors for runway evaluation, which directly impacts airport operation safety and pavement preservation cost. Properly evaluated runway roughness could optimize the decision-making process for runway preservation and therefore reduce the life cycle cost of the runway pavement asset. In this paper, the excitation effect of runway roughness is analyzed using a coupled aircraft/runway system. The coupled system is composed of a two degrees-of-freedom (2-DOF) aircraft model and a typical asphalt runway structure model established under runway roughness random excitation in this work. The dynamic differential equations for the coupled system are derived based on D’Alembert’s principle. The system’s vibration responses are determined via the pseudo excitation method and three response laws, i.e., the center of gravity acceleration (CGA), the dynamic load coefficient (DLC) of the landing gear, and the runway structural displacement, which are investigated under different modes. The results show that the first-order mode of the runway structure, vertical deformation, is the most significant of the four modes. Moreover, uneven excitation has a significant effect on the distribution of the aircraft’s vibration response. Compared with a single aircraft system, the developed coupled aircraft/runway system has different dynamic responses, and the degree of difference depends on the taxiing speed. The coupled effect on the CGA increases significantly with an increase in speed, with up to a 7.3% percentage difference. The coupled effect on the DLC first increases and then decreases as the aircraft speed increases, reaching a maximum of about 6% percentage difference at 120 km/h. Full article