Equivalent Mechanical Model Research Articles

Dynamics Modelling and Simulation for Deployment Characteristics of Mesh Reflector Antennas

The dynamics of mesh reflectors are characterized by large deformation when antennas undergo a large motion in the deployment process. In this work, absolute node coordinate formulation (ANCF), with the merit of precise description of large deformation, is employed to consider the flexibility of the reflector net. From a practical perspective, the effect of the torsional spring is incorporated into the dynamic governing equations by an equivalent mechanical model. Deployment simulation of the mesh reflector antennas is performed by a numerical procedure. It can be found that with the action of a degenerative driven force caused by the friction effect, the deployed process of antennas exhibits a character of asynchronous deployment. Additionally, a significant increase in tension during the final period of deployment has an intense influence on smooth deployment.

Artificial thermal strain method: A novel approach for the analysis and fast prediction of the thermal distortion

Abstract Understanding the thermal distortion induced by arc welding, laser, or induction heating is a challenge in academia and industry. This study presents the artificial thermal strain (ATS) method which was modified from strain as boundary (SDB) method, based on inherent strain theory, and its equivalent mechanical model to analyse the distortion mechanism. Experiments and numerical simulation of multi-pass laser bending of alloy 304 L were conducted, wherein the various kinds of inherent strain distributions and the boundary of effective inherent strain were examined. Further, the mechanism of bending angle reduction under lower line energy was evaluated by considering the inherent strain redistribution at each pass. The results indicate that the bending angle reduction in multi-pass laser scanning is determined by the size of the inherent strain area at low line energy. Moreover, a simplified plastic finite element model based on the ATS method was developed to predict the welding deformation of plate curvature induced by parallel laser scanning. Additionally, only 210 elements and 7 s was cost to perform with the deformation analysis, which indicates that the ATS model is effective in predicting thermal distortion. Meanwhile, the ATS method can provide theoretical guidance and fast prediction for the actual thermal processing in large welded structure and additive manufacturing in the future.

Sloshing Dynamics in 2D Multi-Baffled Containers Under Low-Gravity Conditions

The sloshing free vibrations and the Equivalent Mechanical Model (EMM) parameters are determined for 2D multi-baffled containers under low-gravity conditions using Boundary Element Method (BEM) and potential flow model of the fluid. The presented model is applicable to any values of the acceleration of gravity and surface tension and to constant cross-section containers with arbitrary geometry, and baffle arrangement and shape. The results for a simple rectangular container are validated compared to the analytical values and very good agreement is achieved. Some baffled containers are also analyzed and their sloshing natural frequencies and EMM parameters are presented under low and zero-gravity conditions. Moreover, the effect of baffle characteristics on these parameters is investigated in a wide range of the acceleration of gravity and some conclusions are outlined.

A smooth polynomial shaped command for sloshing suppression of a suspended liquid container

A smooth polynomial shaped command with an adjustable command time length is proposed for eliminating the residual vibrations of a multi-mode system. The ability of eliminating jerks and vibrational modes, regardless of their number, offers the most advantage of the proposed command. A numerical simulation is conducted to test the command’s effectiveness by eliminating the residual sloshing oscillations of a liquid-filled container conveyed by an overhead crane in a rest-to-rest manoeuvre. The governing equations of the liquid free-surface level are derived by modelling the sloshing dynamics by a series of mass–spring–damper harmonics. The proposed model accounts for the coupling between the pendulum dynamics and the sloshing equivalent mechanical model. The command’s robustness to the system parameters’ uncertainties, liquid depth and cable length, are investigated as well. The ability of adjusting the command length and retaining higher sloshing modes in command-designing are also outlined.

Equivalent Axial Stiffness of Horizontal Stays

Cable-stayed structures are widely employed in several fields of civil, industrial, electrical and ocean engineering. Typical applications are cable-stayed building roofs, bridges, guyed masts, overhead electrical lines, and floating device anchorages. Since the cable behavior is often highly nonlinear, suitable equivalent mechanical cable models are often adopted in analyzing this kind of structures. Usually, like in the classical Dischinger’s approach, stays are treated as straight rods offering an equivalent axial tangent stiffness, so that each of them can be substituted with an appropriate equivalent nonlinear spring or truss element. Formulae expressing equivalent stiffness provided by classical methods are satisfactory only when the cable is highly stressed, and therefore its sag is small with respect to its chord; on the contrary, when the cable is slack, they give often contradictory or meaningless results. Aiming to remove that limitation, a more refined approach based on the application of the virtual work principle is discussed. Important products of that original rational criterion are accurate and closed form innovative expressions of the tangent stiffness of the cable, whose field of application is independent on the sag to chord ratio of the cable, as well as on the magnitude of the normal stresses. Referring to some relevant case studies, the results obtained applying these new formulae are critically discussed for cables made of different materials, also in comparison with the approximate expressions provided by simplified methods.

Study on the Calculation Method of Stress in Strong Constraint Zones of the Concrete Structure on the Pile Foundation Based on Eshelby Equivalent Inclusion Theory.

In view of the strong constraint zones of the concrete structure on the pile foundation, there are some differences between the calculation results of the isotropic equivalent pile foundation by the volume replacement ratio method and the actual engineering. In this paper, referring to the relevant algorithm of rock mass with anchor, the anchor and rock mass are, respectively, compared to pile and surrounding soil foundation. Eshelby equivalent inclusion theory is introduced into the equivalent mechanical model of soil foundation with pile, and a new equivalent pile foundation algorithm considering anisotropic elastic constant is compiled by Fortran. Three kinds of calculation methods are used to calculate the stress field of the concrete structure of the large pump station on the pile foundation during the construction period, and the stress in the strong constraint zones of the concrete structure are mainly analyzed. It is found that the calculation accuracy of Algorithm 3 is the highest, and the calculation results of Algorithm 2 can be modified by the coefficients to achieve the calculation accuracy of Algorithm 3 and the calculation efficiency is actually improved. Finally, the accuracy of the proposed method is verified by the engineering measured data.

Command Shaping for Sloshing Suppression of a Suspended Liquid Container

AbstractThe residuals of liquid free-surface wave oscillations induced by a rest-to-rest crane maneuver of a suspended liquid container are eliminated using a command-shaped profile. The dynamics of liquid sloshing are modeled using an equivalent mechanical model based on a series of mass-spring-damper systems. The proposed model considers the excited frequencies of the container swing motion and liquid sloshing modes. The objective is to design a discrete-time shaped acceleration profile with a variable command length that controls the moving crane-jib, while suppressing the sloshing modes. Simulations are conducted to illustrate the command effectiveness in eliminating liquid sloshing with a wide variation range of system and command-designing parameters; liquid depth, cable length, command duration, and the employing of higher sloshing modes in representing the sloshing dynamics. The command sensitivity of the input command to changes of the system parameters are treated as well. A refined and smooth input command based on suppressing the residuals of multimodes is also introduced. Furthermore, the command effectiveness was supported by a comparison with the time-optimal flexible-body control and multimode zero vibration input shaper.

Response of an Annular Tuned Liquid Damper Equipped With Damping Screens

Abstract Annular tuned liquid dampers (TLDs) may be installed in slender structures with limited floor space, in which people and utilities must pass through the core, such as a wind turbine or observation tower. This study investigates an annular-shaped TLD equipped with damping screens. A linearized equivalent mechanical model capable of capturing the fundamental sloshing mode response of an annular TLD is presented. An experimental shake table testing program is completed to assess the performance of the model. Thirty-six frequency sweep tests consisting of various TLD configurations, excitation amplitudes, and excitation directions are completed. Good agreement is observed between the linearized equivalent mechanical model and experimental wave heights, sloshing forces, and energy dissipated per cycle that have been filtered to include only the fundamental sloshing mode response. The model is also observed to be in good agreement with experimental data for different excitation directions. The model is coupled to a generalized structure to investigate the response of a structure equipped with an annular TLD. The annular TLD is found to reduce the response of a generalized offshore wind turbine structure undergoing harmonic force excitation. The annular TLD provides performance comparable to an optimal linear tuned mass damper (TMD) with the same properties for a range of force excitation amplitudes.

Equivalent Mechanical Model for Conducting Polypyrrole Actuator

Conducting polypyrrole actuators are widely used in sensors and bionic robots because of their high conductivity, flexibility and biocompatibility. Based on the theory of cantilever beam, the equivalent mechanical model of conducting polypyrrole actuator is built, and the bending characteristics of different length actuators under different voltage are studied by using the bending characteristics test system of polypyrrole actuator, and the functional relationship between voltage and bending displacement. By lifting the weight with the actuator, it is verified that the free end of the actuator can withstand the force.

A cost-effective voice coil motor-based portable micro-indentation device for in situ testing

Abstract To evaluate the mechanical properties of structures in service, a portable micro-indentation device was developed and built. The basic design principle of the indentation device, i.e. measurement of the indentation depth and the indentation force with sufficient accuracy, was discussed. To avoid using load cell to decrease the machine compliance, a new method that using the current through voice coil motor to calculate the indentation force was proposed. After analyzing the equivalent mechanical model of the developed device, an eddy current displacement sensor was installed on the device to improve the measurement accuracy of indentation depth. Indentation tests were performed on polymethylmethacrylate (PMMA) and unplasticized polyvinyl chloride (UPVC) with the developed device and the commercial indentation device ZHU2.5 to demonstrate the validity and accuracy of the developed micro-indentation device.

Theoretical and Experimental Parametric Study on Tuned Liquid Sloshing Damper

This paper presents a parametric study on tuned liquid sloshing damper (TLD), which has been carried out theoretically and experimentally. Theoretically, the governing differential equation of the equivalent mechanical model is solved using Fourier expansion-based differential quadrature method. The obtained solution shows good agreement with the experimental results. Experimentally, a simple test rig is designed and constructed in order to acquire free vibration of a pendulum like platform with an attached liquid slosh damper. Different parameters, i.e. the liquid filling ratio, the liquid viscosity and the tank shapes, are studied theoretically and experimentally in order to investigate the damping capacity of the supplementary damper. It can be concluded that Fourier expansion-based differential quadrature method has been reliable and efficient in solving the proposed problem, as the liquid viscosity increases damping capacity increases for all shapes of the tanks, the rectangular tank is the most effective shape on damping capacity with respect to the considered shapes. Filling ratio plays an important role in controlling both of settling time and damping coefficient, where 16% filling ratio provides the most damping capacity. Generally, the TLD has been more effective for structures with low damping ratios where structural acceleration decreases with the introduction of the TLD.

Composite equivalent mechanical models for large-amplitude liquid sloshing in axisymmetrical tanks

Equivalent mechanical models are widely used to describe the dynamics of liquid sloshing in aerospace engineering, but the traditional equivalent mechanical models based on linear theory have poor applicability and accuracy in large-amplitude sloshing. The composite equivalent modeling method suitable for large-amplitude sloshing in normal and low-gravity is proposed in this paper. By considering the change of liquid equilibrium position in sloshing, the large-amplitude motion of the liquid relative to the tank is decomposed into bulk motion following the equivalent gravity and additional small-amplitude sloshing, thus greatly expands the application scope of the linear equivalent mechanical model. Taking the axisymmetrical tanks as examples, the liquid dynamic equilibrium position following the equivalent gravity under large-amplitude sloshing is determined, and the composite equivalent mechanical model in the form of a spherical pendulum is established. For spherical tanks, all liquid is assumed to be involved in bulk motion and the model parameters are found constant during sloshing. For non-spherical tanks such as cylindrical and Cassini tanks, liquid near the tank wall is assumed motionless relative to the tank, and the time-dependent model parameters are approximated by linear interpolation based on equivalent gravity and inclination of the liquid surface. Based on the spherical pendulum model, the dynamic equation of the equivalent system is derived, thus the slosh forces, moments and positions of the liquid center of mass under large translational and rotational excitations are calculated in 3D axisymmetrical tanks. To verify the validity of the modeling method and the accuracy of the composite model, the results of the composite equivalent mechanical model, the traditional equivalent mechanical model as well as the computational fluid dynamics (CFD) software are compared and analyzed. As shown by the results, the composite equivalent mechanical model proposed can accurately predict the dynamic responses of large-amplitude liquid sloshing in axisymmetrical tanks.

Dynamic characteristics and reliability analysis of ball screw feed system on a lathe

For ball screw feed system on a lathe, the randomness of geometric parameters deriving from the inevitable manufacturing and assembly errors significantly affected the system dynamic characteristics and turning accuracy. In this study, a novel lumped dynamic model accounting for the analytical piecewise restoring force function involving the overall axial deformation is proposed. The equivalent mechanical model of bearing joints including the change of nominal contact angle is made a reasonable simplification to facilitate acquisition of the system analytical equation of motion. Additionally, the approximate analytical solution of the proposed equation is obtained by the modified Lindstedt–Poincaré method (MLP). The advanced first order second moment method (AFOSM) is employed to evaluate the reliability of dynamic response error. Furthermore, the numerical simulation aims to demonstrate the capabilities of the MLP and AFOSM method in the practical applications. Eventually, the effects of external excitation, sliding platform position, and nominal contact angles on the dynamic response are discussed and the reliability and sensitivity analysis in accordance with actual turning accuracy level is presented.

Mass-Spring-Damping Theory Based Equivalent Mechanical Model for Cylindrical Lithium-ion Batteries under Mechanical Abuse

An equivalent mechanical model with the equivalent physical meaning of mass-spring-damping is proposed for cylindrical lithium-ion batteries through experiments and theory. The equivalent mechanical model of a cylindrical lithium-ion battery consists of a spring-damping parallel unit. Therefore, a spring-damping parallel unit connecting a damping unit in series is selected to construct the constitutive characteristics of the battery under mechanical abuse. Comparison results show that the equivalent mechanical model can more effectively describe the mechanical properties of the batteries than most cubic fitting models, of which the average relative error of the equivalent mechanical model under different states-of-charge is less than 6.75%. Combined with the proposed equivalent mechanical model, the failure process of the batteries was simulated and analyzed using LS-Dyna and HyperWorks. Under rigid rod tests, failure occurred at the core and bottom of the batteries; under hemispherical punch tests, failure occurred at the core and top, consistent with the experimental results. The average prediction error for the failure displacement under different abuse conditions is less than 4% in the simulations. The equivalent mechanical model requires only a few parameters and can be recognized easily. In the future, the model can be used in safety warning devices based on mechanical penetration.

연료 슬로싱 효과를 고려한 위성 기동 간의 SAR 안테나 반사판의 진동 분석

Sloshing refers to the movement of a liquid free surface caused by disturbances of a liquid partially filled in a container. Sloshing generates forces and moments owing to the pressure distribution on the liquid free surface, which affect the dynamic stability of the vessel. An equivalent mechanical model that exerts the same amount of force and moment on the vessel wall as sloshing is used to analyze the sloshing effect on the vessel. This phenomenon also occurs in the fuel tank of a satellite structure that controls the attitude using a propulsion system with a liquid propellant. A satellite with a deployable synthetic-aperture radar (SAR) antenna, which is made of a thinner and lighter material, is likely to be more susceptible to various disturbances, including liquid sloshing. In this study, an analysis of a deployable SAR antenna reflector vibrating from the liquid fuel sloshing between the changes in the satellite’s attitude was conducted. The equivalent mechanical model is used to simulate the sloshing effect, and the vibrations of the reflector are compared and analyzed with and without the sloshing effect for the specified torque input.

Equivalent mechanical model of rectangular container attached to a pendulum compared to experimental data and analytical solution

A tuned liquid damper (TLD) is a passive control device that transfers kinetic energy from the main structure to a liquid sloshing in a tank. The mechanical description of a sloshing liquid contained in a tank requires an intricate mathematical formulation. An alternative technique describes the TLD dynamic behavior as an equivalent mechanical model comprising a series of pendulums or mass–spring systems attached to the tank walls. To validate this approach, this paper compares the discrete model to experimental results and an analytical solution for a rectangular container attached to a pendulum (pendulum-slosh problem). At first, the fundamental oscillation period of the discrete model, representing a rectangular tank, is compared to experimental data and a classic analytical solution. Finally, we compare the pendulum-slosh problem modeled as a discrete model with the analytical solution and experimental results.

Investigation on the equivalent mechanical longitudinal fluid sloshing model for a partially filled tank vehicle

This paper aims to investigate the equivalent mechanical model of longitudinal fluid sloshing for a partially filled tank vehicle. A one-degree-of-freedom (1DOF) mass-spring-damping (MSD) equivalent mechanical model proposed in the literature is first evaluated. To improve the precision of the MSD model, two 2DOF models those are the serial 2DOF (2DOF-S) model and the parallel 2DOF (2DOF-P) model, and a hybrid 3DOF (3DOF-H) model have been proposed, formulated and evaluated. Comparisons demonstrate that the 3DOF-H model can provide rather satisfying precision in broad ranges of tank ellipticity and fill level. Finally, the proposed 3DOF-H MSD sloshing model is further evaluated from the viewpoint of vehicle dynamics response. It is revealed that it is easy to integrate the 3DOF-H model with vehicle dynamics to build a fluid tank vehicle model which can reflect the basic dynamics property of a tank vehicle.

Series-Type Pendulum Tuned Mass Damper-Tuned Sloshing Damper

Abstract A pendulum-type tuned mass damper (TMD)-tuned sloshing damper (TSD) system is proposed as a cost-effective device to reduce wind-induced structural motion. Lagrange's principle is employed to develop an equivalent mechanical model for the system. The sloshing liquid provides additional gravitational restoring force to the pendulum TMD but does not provide a corresponding increase to its inertia. As a result, the natural frequency of the pendulum TMD is increased due to the TSD degree-of-freedom. Shake table testing is conducted on several pendulum TMD-TSD systems that are subjected to harmonic base excitation at discrete frequencies near the natural frequency of the pendulum TMD. The modeled and experimental results are in reasonable agreement when the liquid is not shallow or the response amplitude is not large. The pendulum TMD-TSD is coupled to a linear structure, and it is demonstrated through an analytical study that the device provides performance that is comparable to a traditional TMD. The proposed system is advantageous because it does not require a viscous damping system that is often one of the most costly components of traditional TMDs.

Equivalent Mechanical Model for Cylindrical Lithium-ion Battery Under Mechanical Abuse and Soft Short-circuit Failure Warning

Based on the analysis of the experimental data for cylindrical lithium-ion battery under mechanical abuse, an equivalent mechanical model of spring-damping parallel unit connects a damping unit in series is proposed in this paper. By combining the equivalent mechanical model with the Crushable-Foam material model, the experiments and simulations on the flat plate tests, rigid rod tests and hemispherical punch tests are performed, the prediction error of the simulation model to the failure displacement is less than 11%. After that, the equivalent mechanical model is analyzed, a soft short-circuit failure prediction model is proposed. A failure warning system is designed according to the prediction model, and the warning system can prompt the soft short-circuit failure of the battery in time and has a certain safety margin.

Dynamic characteristics of liquid sloshing in cylindrical tanks filled with porous media

The dynamic characteristics of liquid sloshing in cylindrical tanks filled with porous media are analyzed in this paper. As the tank is subjected to the small external excitations, the flow is assumed to be in Darcy’s flow regime, and then the porous medium can provide damping effect linearly proportional to the fluid velocity. Based on the pore flow theory, the linear equivalent mechanical model with the damping effect due to porous medium is established. This equivalent model consists of a rigidly fixed mass and infinite sets of mass-damping-spring systems, which can exert the same total dynamic force as the linearized actual fluid field. The equivalent system can explain the dynamic characteristics of each modal response of sloshing in a cylindrical porous-medium tank. Therefore it is more convenient to analyze the sloshing behavior from the structural dynamic analysis point of view. By this model, the natural frequency and damping ratio of the cylindrical porous-medium tank are revealed. Both parameters are related to the tank dimensions, porosity and permeability of the porous medium.