Search Results (249)

The Dynamic Stiffness Matrix (DSM) of a structure is a frequency-dependent stiffness matrix relating the actions (forces and moments) and displacements (translations and rotations) when the structure vibrates at a given frequency. The DSM may be used to find the natural frequencies, modes, and structural response. For many structures, including skeletal frames of prismatic members, exact transcendental expressions for the DSM are readily available. This paper presents a mathematical proof of a linear determinantal relationship between the DSM of a skeletal frame when it is undamaged, cracked, and hinged at the crack location. The rotational stiffness or flexibility of the crack also appears as a linear term. This relationship gives, for the first time, an explicit equation to directly calculate the stiffness of the rotational spring representing a crack from measured natural frequencies for any potential crack location. Numerical examples demonstrate that computing the DSM of the intact and hinged structures gives an efficient solution method for the inverse problem of identifying crack location and severity. This paper also shows that an approximate DSM based on a finite element model can be used in the same way, making this procedure more versatile. Furthermore, new approximate expressions for the natural frequencies of structures with very small or very severe cracks are derived. An interesting relationship between the square of the bending moment in an undamaged beam and the determinant of the DSM of a hinged beam is also derived. This relationship, which can also be inferred from previous work, leads to a better understanding of the effect of crack location in specific vibration modes. Full article

The presence of a bogie in three-axle vehicles when moving along a curved trajectory leads to deterioration in its handling and maneuverability. The paper developed a mathematical model of the elastic bogie wheel while moving along a curvilinear trajectory, according to which the bogie wheel simultaneously participates in curvilinear and plane-parallel motion with a slip angle. Such movement of the bogie wheels develops significant lateral and longitudinal forces on the steered wheels, which leads to the movement of the steered wheels with slip, redistribution of the load on them, tire twisting, and a decrease in the steering angle of the outside steered wheel due to the elasticity of the steering trapezoid. Based on the mathematical model of the bogie wheel, an analytical dependence was obtained to determine the minimum turning radius of a three-axle vehicle. The reliability of the analytical dependencies characterizing the movement of the bogie wheel along a curvilinear trajectory was determined by comparing the minimum turning radii of a three-axle vehicle with the intermediate axle lowered and raised. It has been established that the minimum turning radius of a vehicle with a bogie increases compared to a two-axle vehicle and depends on the cornering stiffnesses of the tires of the bogie and steered wheels, the bogie and vehicle wheelbases, the kinematic and elastic parameters of the steering trapezoid, the direction of turning of the steered wheels, and the load on the steered and the bogie wheels. Full article

The practice of operating hydraulic machines and equipment shows that failures can occur earlier than the specified lifespan. At the same time, at the stage of carrying out strength calculations of the designed machines and equipment, significant safety margins are incorporated into parts and units. That is, calculated machine lifespans often exceed actual values. Accurate data require full-scale lifespan testing or observations of operation. However, resource tests are economically expensive, since they require a significant amount of energy, and, as a result, lead to a negative impact on the environment. It is possible to level out the listed shortcomings during resource tests by using energy-efficient and energy-saving technologies, such as energy recovery. This study enhances energy efficiency and assesses engineering systems during equipment design. In particular, we present a hydromechanical drive design for testing reciprocating hydraulic machines. The study analyzes energy-saving and energy recovery methods during operation. On the basis of the analysis and previously conducted studies, we developed a mathematical model for hydraulic equipment testing. The developed model is based on the volumetric stiffness theory, enabling analysis of the design and functional characteristics of test stand components on their dynamic behavior and energy efficiency. Full article

To investigate the seismic performance of steel tube-reinforced concrete (ST-RC) columns after fire on one side, this study employs numerical simulation and theoretical analysis methods. A numerical analysis model of ST-RC columns post-fire is established using ABAQUS to simulate and analyze their seismic performance under cyclic loading. The characteristics of the hysteresis curves of ST-RC columns after fire on one side under cyclic loading are described in detail. Comparisons are made between the skeleton curves, ductility, stiffness degradation, and energy dissipation capacity of ST-RC columns under three conditions: unexposed to fire, exposed to fire on all sides, and exposed to fire on one side. Finally, multiple influencing factors, including heating time, slenderness ratio, section size, core area ratio, external concrete strength, reinforcement ratio, and load ratio, are selected for parametric analysis of the ductility coefficient, stiffness, and viscous damping coefficient. Mathematical formulas for the ductility coefficient, stiffness, and viscous damping coefficient of ST-RC columns after fire on one side under cyclic loading are derived through regression analysis. The results show that the seismic performance of ST-RC columns is attenuated after fire on one side, and the ductility and initial stiffness of ST-RC columns decreases by 5.62% and 24.69%, respectively, compared with those without fire. The energy dissipation capacity of the ST-RC column increases significantly when it enters the plastic deformation stage under the action of reciprocating load. Full article

Viscoelastic materials are commonly used in civil engineering, biomedical sciences, and polymers, where understanding their creep and relaxation behaviors is essential for predicting long-term performance. This paper introduces an operator-based method for modeling viscoelastic materials, providing a unified framework to describe both creep and relaxation functions. The method utilizes stiffness and compliance operators, offering a systematic approach for analyzing viscoelastic problems. The operator-based method enhances the mathematical duality between the creep and relaxation functions, providing greater physical intuition and understanding of time-dependent material behavior. It directly reflects the intrinsic properties of materials, independent of input and output conditions. The method is extended to dynamic problems, with complex modulus and compliance derived through operator representations. The fractal tree model, with its constant loss factor across the frequency spectrum, demonstrates potential engineering applications. By incorporating a damage-based variable coefficient, the model now also accounts for the accelerated creep phase of rocks, capturing damage evolution under prolonged loading. While promising, the current method is limited to one-dimensional problems, and future research will aim to extend it to three-dimensional cases, integrate experimental validation, and explore broader applications. Full article

Polyurethane grouting technology is widely employed to maintain critical transportation infrastructure, including pavements, airports, and railways. After injection, foamed polyurethane bonds with surrounding aggregates to form a polyurethane–aggregate composite material (PACM). The gradation of aggregates in PACM, stress levels, and loading frequencies significantly influence fatigue performance under cyclic traffic loading. This study investigates the fatigue behavior of three distinct PACM gradation types through three-point bending fatigue tests under varying stress levels and loading frequencies. Results reveal that the finer gradations of PACM tend to exhibit higher flexural stiffness and longer fatigue life but also greater sensitivity to stress levels. Conversely, coarser gradations show lower stiffness but improved energy dissipation characteristics. Additionally, the flexural stiffness modulus, fatigue life, and cumulative dissipated energy decrease with increasing stress levels, while they grow with higher loading frequencies. In contrast, the dissipated angle follows an opposite trend. Additionally, mathematical models were developed to describe the evolution of dissipated energy, uncovering a three-stage pattern dominated by a prolonged plateau phase accounting for over 80% of the fatigue process. Based on this characteristic plateau, fatigue life prediction models were established for each gradation type, achieving high prediction accuracy with relative errors below 10%. These findings not only highlight the significant impact of aggregate gradation on PACM fatigue performance but also provide practical tools for optimizing material design in pavement maintenance. Full article

To address the limitations of single-chamber soft grippers, such as constant curvature, insufficient motion flexibility, and restricted fingertip movement, this study proposes a soft gripper inspired by the structure of the human hand. The designed soft gripper consists of three fingers, each comprising three soft joints and four phalanges. The air chambers in each joint are independently actuated, enabling flexible grasping by adjusting the joint air pressure. The constraint layer is composed of a composite material with a mass ratio of 5:1:0.75 of PDMS base, PDMS curing agent, and PTFE, which enhances the overall finger stiffness and fingertip load capacity. A nonlinear mathematical model is established to describe the relationship between the joint bending angle and actuation pressure based on the constant curvature assumption. Additionally, the kinematic model of the finger is developed using the D–H parameter method. Finite element simulations using ABAQUS analyze the effects of different joint pressures and phalange lengths on the grasping range, as well as the fingertip force under varying actuation pressures. Bending performance and fingertip force tests were conducted on the soft finger actuator, with the maximum fingertip force reaching 2.21 N. The experimental results show good agreement with theoretical and simulation results. Grasping experiments with variously sized fruits and everyday objects demonstrate that, compared to traditional single-chamber soft grippers, the proposed humanoid joint-inspired soft gripper significantly expands the grasping range and improves grasping force by four times, achieving a maximum grasp weight of 0.92 kg. These findings validate its superior grasping performance and potential for practical applications. Full article

This paper presents the development of empirical mathematical models of draught force, F_x, and vertical force, F_y, acting on duckfoots attached to the tines with different stiffness and working in various soil conditions. The models consider technical variables such as stiffness, k, tool depth-to-width ratio, d/w, tool movement speed, v, and soil moisture content, MC, which have not been thoroughly analysed in the literature. The correlation coefficients for predicting F_x and F_y values were 0.4996 and 0.6227, respectively. Statistical analysis confirmed the significant effect of these parameters on the forces acting on the tools, with the variables d/w and v having the most critical impact on F_x and F_y. The SLSQP (sequential least squares programming) optimisation method was used to determine the optimal values of technical variables. The maximum value of F_x was 438.55 N, and the minimum was 98.98 N, with variable values at the edges of the studied ranges. Similarly, F_y values of 135.25 N and −84.55 N, respectively, were obtained. The optimisation results showed good fitness with experimental results, and the negative relative errors (from −1.72% do −4.81%), indicating overestimating, confirmed the accuracy of the model’s predictions. The justification of the research results allowed us to conclude that there is no basis for rejecting the explanatory hypotheses. The developed models have a generalisable value in the analysed ranges, and further research should focus on creating more universal, theoretical models of soil–tool interactions. Full article

The global response characteristics of rotor/stator rubbing systems are critical for the optimal design and safe operation of rotating machinery. Based on the mathematical model, numerical simulation and theoretical analysis have been widely carried out to study the regions of different responses, which have not been globally explored and evaluated by experiments with the unified parameters of a mathematical and physical model. Thus, the existence conditions of the global responses of a rubbing rotor are experimentally investigated and then quantitatively compared with theoretical solutions and dynamic simulation results. With the equivalent stiffness and the kinetic dry friction identified by the aid of a new voltage divider, the rubbing rotors are accurately tested by the new experimental technique and dynamically simulated by rigid-flexible coupling technique. From the comparison results of orbit and full spectrum, it is shown that the response characteristics of no rub motion, synchronous full annular rub, partial rub, and dry friction backward whirl obtained by experiment and dynamic simulation are in good agreement with theoretical solutions. Then, it is also concluded that all boundaries of the existence/co-existence regions of the whirling motions are proved to be valid. Moreover, stick-slip oscillation is detected in the rotor/stator testing system. Full article

One of the challenging aspects of designing body-in-white stiffness test rigs is measuring test accuracy. This paper proposes a method of integrating the body-in-white stiffness test rig and the body-in-white into an overall model for the optimization design. It establishes an optimization mathematical model based on the overall structure of the stiffness test rig, taking into account the factors affecting the accuracy of the test results of the body-in-white stiffness test rig. The stiffness test rig’s testing accuracy can be significantly increased by designating the degrees of freedom at each connection position as discrete variables. The Hybrid and Adaptive Metamodeling Method (HAM) is used to optimize the mathematical model. This approach uses and integrates three distinct metamodels with various attributes. The body-in-white torsional stiffness test result error is only 1.1%, and the body-in-white bending stiffness test result error is only 3.4%, owing to the optimization result that was used to design and manufacture a set of body-in-white stiffness test rigs and use them for a body-in-white stiffness test verification. Full article

This study proposes a frequency-based finite element updating method for an effective physics-based digital twin (DT). One approach to constructing a physics-based DT is to develop a mechanics-based mathematical model that accurately simulates the behavior of an actual structure. The proposed method utilizes finite element updating, adjusting model parameters to improve model accuracy. Unlike simple modal analysis, which focuses on vibration characteristics, this method recognizes that accurate dynamic transient-based vibration analysis requires considering the damping effect, as well as mass and stiffness, during the updating process. Moreover, a frequency-based analysis is employed instead of the computationally expensive time-based analysis for more efficient dynamic modeling. By transforming data into the frequency domain, the method efficiently represents dynamic behavior within relevant frequency ranges. We further enhance the computational efficiency using the model reduction technique. To validate the method’s accuracy and efficiency, we compare the analysis results and computation time using a numerical example of the control rod drive mechanism. The proposed method shows significantly reduced computation time, by a factor of 8.9 compared to conventional time-based methods, while preserving high accuracy. Therefore, the proposed method can effectively support the development of physics-based DTs. Full article

This research aims to advance the understanding and application of dynamic models for gears within agricultural machinery drive trains by developing analytical solutions. Despite the significant advancements in vibration analysis, there is a notable scarcity of comprehensive research that addresses the analytical modeling of gear dynamics, particularly using advanced mathematical techniques such as the multiple scale method (MSM). A new approach to modeling gear meshing is introduced, where the Fourier expansion of a rectangular signal is utilised to simulate the time-varying mesh stiffness (TVMS). Such an approach allows the use of the MSM as an efficient tool to obtain solutions for parametrically induced vibrations. A dynamic model of a simple helical gear system is introduced in the form of Hill’s equation, and a sensitivity analysis is conducted for the main parameters of the system based on the solution obtained with the MSM. The results show the high credibility of the provided method when compared with a well-known state-of-the-art model and that the model reacts to parameter variations as expected. Additionally, an analysis of the energy harvesting possibilities is presented, which shows that, for the default parameter values, the harvester should be tuned to 5694.31 Hz to generate the maximum energy. It is concluded that the proposed model and MSM approach can serve as suitable tools for gear analysis, and the future paths for research are defined. Full article

This paper deals with developing a comparative study of the principal time-domain system identification methods suitable for performing an experimental modal analysis of structural systems. To this end, this work focuses first on analyzing and reviewing the mathematical background concerning the analytical methods and the computational algorithms of interest for this study. The methods considered in the paper are referred to as the AutoRegressive eXogenous (ARX) method, the State-Space ESTimation (SSEST) method, the Numerical Algorithm for Subspace State-Space System Identification (N4SID), the Eigensystem Realization Algorithm (ERA) combined with the Observer/Kalman Filter Identification (OKID) method, and the Transfer Function ESTimation (TFEST) method. Starting from the identified models estimated through the methodologies reported in the paper, a set of second-order configuration-space dynamical models of the structural system of interest can also be determined by employing an estimation method for the Mass, Stiffness, and Damping (MSD) matrices. Furthermore, in practical applications, the correct estimation of the damping matrix is severely hampered by noise that corrupts the input and output measurements. To address this problem, in this paper, the identification of the damping matrix is improved by employing the Proportional Damping Coefficient (PDC) identification method, which is based on the use of the identified set of natural frequencies and damping ratios found for the case study analyzed in the paper. This work also revisits the critical aspects and pitfalls related to using the Model Order Reduction (MOR) approach combined with the Balanced Truncation Method (BTM) to reduce the dimensions of the identified state-space models. Finally, this work analyzes the performance of all the fundamental system identification methods mentioned before when applied to the experimental modal analysis of flexible structures. This is achieved by carrying out an experimental campaign based on the use of a vibrating test rig, which serves as a demonstrative example of a typical structural system. The complete set of experimental results found in this investigation is reported in the appendix of the paper. Full article

This work focuses on small bearingless permanent magnet synchronous motors (BPMSMs). In order to enhance its torque control stiffness and improve the stability of its torque and magnetic levitation force dynamic waveforms, a novel six-phase distributed single-winding BPMSM with 12 slots and 2 poles (six-phase DSW-12/2-BPMSM) is proposed and researched in this work. First, the structure and working principle of the six-phase DSW-12/2-BPMSM are analyzed. Subsequently, considering the relative permeability of permanent magnets, mathematical models of the inductance matrix, electromagnetic torque and radial magnetic levitation force are established. Then, using the finite element method (FEM), the control characteristics of the electromagnetic torque and magnetic levitation force of the six-phase DSW-12/2-BPMSM are analyzed, and the mathematical model is verified. Finally, FEM simulation analysis and comparisons are conducted with a commonly used six-phase centralized single-winding BPMSM with 6 slots and 2 poles (six-phase CSW-6/2-BPMSM). The research results show that the established mathematical model is effective and accurate compared with the six-phase CSW-6/2-BPMSM. The six-phase DSW-12/2-BPMSM has greater torque control stiffness, its dynamic waveforms of torque and radial magnetic levitation force have higher quality and stability, and the coupling degree between its torque and radial magnetic levitation force is lower. Full article

This research paper presents the findings of a design optimization analysis conducted on additive-manufactured thermoplastic sandwich structures with hexagonal honeycombs subjected to quasi-static three-point bending. Based on experimental results, finite element analysis, and analytical models, the relationship between four selected design variables (i.e., cell wall length ratio, cell wall angle, cell wall thickness, and skin thickness) and the structure’s mass, flexural stiffness, and maximum load capacity was determined. The influence of each design variable on the aforementioned structural properties was mathematically represented using three scaling laws to formulate a multi-objective optimization problem. Two conflicting objective functions, one for the mass and the other for the reciprocal of the maximum load capacity, along with a nonlinear constraint equation for the minimum allowed flexural stiffness of the sandwich structure were developed. The optimal values of the design variables were determined using two optimization methods, the Pareto optimal front and genetic algorithm, and by applying the Improved Minimum Distance Selection Method (IMDSM). Optimized designs were obtained for different values of flexural stiffness. It was found that, independently of the stiffness constraint value, the optimal value of the cell wall length ratio was 0.2 and the optimal cell wall thickness was 1.4 mm, which correspond to the minimum cell wall length ratio and maximum cell wall thickness considered in this study, respectively. On the other hand, if higher flexural stiffness is required for the structure, both cell wall angle and skin thickness must be increased accordingly. Furthermore, an increase in flexural stiffness is accompanied by an increase in both the mass and maximum load capacity of the structure. Full article