Simple Mechanical Model Research Articles

Simplified Models to Capture the Effects of Restraints in Glass Balustrades under Quasi-Static Lateral Load or Soft-Body Impact

Structural glass balustrades are usually composed of simple glass panels which are designed under various restraint solutions to minimize large out-of-plane deflections and prematurely high tensile/compressive stress peaks under lateral loads due to crowd. Linear supports, point-fixing systems, and others can be used to create geometrical schemes based on the repetition of simple modular units. Among others, linear restraints that are introduced at the base of glass panels are mechanically described in the form of ideal linear clamps for glass, in which the actual geometrical and mechanical details of real fixing components are reduced to rigid nodal boundaries. This means that, from a modelling point of view, strong simplifications are introduced for design. In real systems, however, these multiple components are used to ensure appropriate local flexibility and adequately minimize the risk of premature stress peaks in glass. The present study draws attention to one of these linear restraint solutions working as a clamp at the base of glass panels in bending. The accuracy and potential of simplified mechanical models in characterizing the effective translational and rotational stiffness contributions of its components are addressed, with the support of efficient and accurate Finite Element (FE) numerical models and experimental data from the literature for balustrades under double twin-tyre impact. Intrinsic limits are also emphasized based on parametric calculations in quasi-static and dynamic regimes.

Relative assessment of cloth mask protection against ballistic droplets: A frugal approach.

During the COVID-19 pandemic, the relevance of evaluating the effectiveness of face masks–especially those made at home using a variety of materials–has become obvious. However, quantifying mask protection often requires sophisticated equipment. Using a frugal stain technique, here we quantify the “ballistic” droplets reaching a receptor from a jet-emitting source which mimics a coughing, sneezing or talking human–in real life, such droplets may host active SARS-CoV-2 virus able to replicate in the nasopharynx. We demonstrate that materials often used in home-made face masks block most of the droplets. Mimicking situations eventually found in daily life, we also show quantitatively that less liquid carried by ballistic droplets reaches a receptor when a blocking material is deployed near the source than when located near the receptor, which supports the paradigm that your face mask does protect you, but protects others even better than you. Finally, the blocking behavior can be quantitatively explained by a simple mechanical model.

Simplified analytical solution for responses of fault-crossing tunnels with flexible joints under fault movement

An approach is developed for estimating the responses of a tunnel with multiple flexible joints under fault movements. Initially, a new simplified mechanical model of flexible joints is built, and a closed-form solution for a tunnel with multiple flexible joints is derived using Green’s function method. Then, the explicit solution of a tunnel with flexible joints subjected to fault movement is subsequently obtained and verified by comparing its results with those from the numerical modeling. Finally, the responses caused by different factors, i.e., fault displacement, lining stiffness, surrounding rock property in the fault zone and joint stiffness, are investigated in detail to provide a better understanding of the mechanical mechanism of flexible joints. The results show the differences in displacement and rotation induced by flexible joints can be quantitatively calculated by the proposed solution in different cases. The flexible joint is capable of reducing the internal forces of the lining and the influence ranges of fault dislocation on tunnel responses. A lower joint stiffness increases the displacement difference monotonically and efficiently reduces the internal forces of the lining. The proposed analytical solution can be used to predict the seismic responses of fault-crossing tunnels with multiple flexible joints under fault movement in engineering design.

A simple mechanical model of the drumroll

We propose an experiment in which the sound of a drumroll is recorded and analysed according to a simple mechanical model in which the inelastic restitution coefficient of the collision between the stick and drum surface, as well as the ongoing kinematics of the drumstick, are considered. The agreement shows that this model is well suited for describing the most relevant features of drumstick behaviour during this type of motion.

Mechanical model for the analysis of ship collisions against reinforced concrete floaters of offshore wind turbines

This paper presents a simplified mechanical model to study ship collisions against Reinforced Concrete (RC) floaters of Floating Offshore Wind Turbines (FOWTs). The model accounts for the deformability of both striking ships and struck RC structures, including a method to evaluate the elastic–plastic response of RC slabs with normal horizontal restraints, while considering contact area effects and punching shear failure. In the proposed model, the internal mechanics are coupled to the external body dynamics, whilst the hydro-mechanical effects acting on the collided bodies such as hydrostatic restoring, viscous, and wave damping forces are accounted for by the large rotations rigid-body dynamics solver MCOL. A parametric analysis is conducted on the model to study its sensitivity to changes in impact energy, impact location, reinforcement ratios, wall thicknesses, and striker rigidities, whose outcomes are compared with Non-Linear Finite Element (NLFE) simulations. The results show that the proposed model can accurately capture the penetrations in both structures, their body dynamics, and the contact force through the collision at a significantly lower computational cost than their NLFE counterpart.

A simple classroom exercise for teaching principles of ultrasound diagnostic using two springs

We present a novel method for demonstrating the physical principles of ultrasound imaging at a level suitable for educational programmes up to the university level, using a simple mechanical model that is very inexpensive and accessible to a broad variety of educational institutions. The method revolves around the use of one or two steel springs that can be extended on a flat surface. The spring represents a tissue and the longitudinal wave traveling along the spring represents the propagation of an ultrasound wave in tissue. This method allows students to gain direct experience with wave propagation, reflection and transmission in tissue as well as insight into the physical processes underlying ultrasound imaging. These include equally the ultrasound diagnostic device measurement of the depth of various tissue boundaries, modelled as a simple measurement of the time elapsed between the emission of a wave and the detection of a wave reflected from an object intersecting the spring. An ultrasound device probes the boundary between a formation (an organ or a lesion) and surrounding tissue by registering the amplitude of reflection on the formation, which is proportional to a difference in acoustic impedance between the formation and the tissue. The amplitude of the reflected wave in our apparatus is also proportional to acoustic impedance between the spring and an object like a plastic ruler intersecting the spring, whose stiffness and consequently acoustic impedance can be adjusted by its offset. It is also easy to clearly see the reflected wave on the boundary of two coupled springs (two tissues) with different acoustic impedances. We represent a series of representative measurements using our mechanical model demonstrating its good precision.

Seismic Response of a Large LNG Storage Tank Based on a Shaking Table Test

In order to study the dynamic response of the LNG storage tank under the action of seismic load and the seismic isolation effect of the lead-core rubber bearing, this paper establishes the experimental storage tank model with reference to the structural form of the large-scale LNG storage tank, and the seismic response of the test tank is obtained using a shaking table test. Simplified mechanical models of non-isolated and isolated storage tanks are proposed and the seismic responses of the corresponding storage tanks are calculated using the Newmark-beta method. Under the action of seismic waves with different acceleration peaks, the results show that (a) more excitation directions of the seismic wave can lead to the greater acceleration and displacement response of the tank and (b) the isolation bearing has a damping effect on the acceleration response of the storage tank, but it has an amplifying effect on the displacement of the storage tank. Comparing the results of the simplified model and the shaking table test, it is found that the change trend of the acceleration response of the experimental results and simplified mechanical models is the same. The spectral characteristic curve of them is not large, which verifies the effectiveness of the simplified model.

Mechanical models for predicting the strength and stiffness of a beam-to-column adhesively-bonded connection between pultruded profiles

This paper presents two simple analytical expressions to predict the strength and stiffness of an adhesive beam-to-column connection between glass pultruded profiles (GFRP) subjected to shear and bending loads (vertical load applied at the free end of the beam). The joint configuration is characterized by a tubular column made of a commercially available hollow profile with a square cross section (90 mm × 90 mm × 8 mm) and two U-profiles (150 mm × 45 mm × 8 mm) arranged in the form of a built-up beam. The mechanical behaviour of this type of connection is governed by shear and bending stresses acting on the beam, with the latter becoming torsional stresses inside the adhesive layers and responsible for the failure of the connection.Regarding the strength prediction, a simple mechanical model based on the scheme of a single lap joint subjected to a traction force is presented. While, for the stiffness prediction, a simple formula for evaluating the adhesive layer deformability is proposed. With the latter, and by means of the Principle of the Virtual Power, the vertical displacement (corresponding to the vertical load applied) is evaluated and, consequently, the stiffness of the joint predicted.A comparison with the experimental results available in current literature has made it possible to verify the effectiveness of the proposed formulations which involve relatively few geometrical and mechanical parameters.

Mechanical model for the motion of RPV internals affecting neutron flux noise

In the decade after 2000, the amplitude of the neutron flux fluctuations in German 1300 MWe class PWR built by Kraftwerk Union (KWU) increased and later decreased significantly. To further investigate the hypothesis that changes in the mechanical properties of the fuel assemblies (FAs) and subsequent stronger mechanical oscillations of fuel assemblies and other RPV internals are responsible for the observations and to find possible excitation mechanisms, a simple mechanical model is developed. It describes the dynamic motion response of the mechanically coupled system of Reactor Pressure Vessel (RPV), core barrel and a row of fuel assemblies and takes reactive fluidic forces into account. To determine the components to be considered in this model, RPV internals with an effect on neutron flux are identified in a prior step.The dynamic answers of the model to generic excitation scenarios and parametric studies reveal distinct properties of the system. They indicate 1) that fluidic near-field coupling can equalize the fuel assemblies’ reaction amplitudes within a certain region regardless of their individual stiffnesses, 2) that the fluid must be part of the oscillation, 3) that a non-periodicity might stem from a superposition and interaction of several oscillators, 4) that a local excitation source does not spread or synchronize over the whole core, 5) that a neglection or separate consideration of the RPV and core barrel may be justified in some cases. The findings altogether affirm that core-wide oscillations of the fluid flow leading to a simultaneous oscillation of individual fuel assembly groups, possibly including bidirectional effects between fluid and structure, in combination with the changes of the fuel assemblies’ mechanical properties, might be responsible for the temporary increase of neutron flux fluctuations observed in PWR built by KWU.A variant of the mechanical model was studied in a full core investigation with coupled neutron kinetics simulations. These simulations qualitatively reproduce important features of measurement data, while being overall too small in amplitude to explain the observations quantitatively, which confirmed the necessity of considering further effects.

Sloshing effect analysis of liquid storage tank under seismic excitation

Sloshing wave height is a main parameter in the seismic design of liquid storage tanks, and severe sloshing may lead to the liquid leakage or buckling of the steel tank wall. To accurately evaluate the sloshing wave height of the tank under earthquake action, a total of three shaking table tests were conducted on the liquid storage tanks, and numerical simulation methods based on the direct coupling method as well as the bidirectional coupling method were implemented. The sloshing height results from tests and simulations were compared with the values obtained from the theoretical formula, and the applicability of various calculation methods was analyzed. Thereafter, the theoretical formula of the simplified mechanical model and the bidirectional coupling method were adopted to predict the sloshing wave height of tanks with various dimensions, and the theoretical formula was further modified. Simultaneously, the influence of pulse-like ground motion on sloshing effect and hydrodynamic pressure of large-scale liquefied natural gas (LNG) storage tanks was examined. Additionally, the GB 50341–2014, API 650–2013, and Eurocode 8–2006 were utilized to assess the sloshing wave height of large storage tanks subjected to seismic ground motion, and the applicability of the computed results has been further discussed. Based on the above research, practical design recommendations were proposed in this work, which can provide a guidance for the seismic design of storage tanks.

Potentials and Limits of Simplified Models for Linearly Restrained Glass Balustrades under Static Loads and Impact

Glass balustrades are designed to prevent large deflections and high stress peaks under conventional lateral loads. In practice, linear restraints are generally described in the form of ideal linear clamps for glass, to replace the actual geometrical and mechanical properties of restraint components. This means that strong simplifications are introduced in place of multiple details and components expected to offer local flexibility and prevent premature stress peaks in glass. In this paper, attention is given to linear restraints that are commonly described in terms of “clamp” boundaries for glass panels under lateral loads. The use of simplified mechanical models to characterize the actual stiffness and linear restraints and components is addressed, with the support of refined Finite Element numerical models and literature experimental data for balustrades under twin-tyre impact.

A Joint State-Parameter Identification Algorithm of a Structure with Non-Diagonal Mass Matrix Based on UKF with Unknown Mass

Inaccurate mass estimates have been recognized as an important source of uncertainty in structural identification, especially for large-scale structures with old ages. Over the past decades, some identification algorithms for structural states and unknown parameters, including unknown mass, have been proposed by researchers. However, most of these identification algorithms are based on the simplified mechanical model of chain-like structures. For a chain-like structure, the mass matrix and its inverse matrix are diagonal matrices, which simplify the difficulty of identifying the structure with unknown mass. However, a structure with a non-diagonal mass matrix is not of such a simple characteristic. In this paper, an online joint state-parameter identification algorithm based on an Unscented Kalman filter (UKF) is proposed for a structure with a non-diagonal mass matrix under unknown mass using only partial acceleration measurements. The effectiveness of the proposed algorithm is verified by numerical examples of a beam excited by wide-band white noise excitation and a two-story one-span plane frame structure excited by filtered white noise excitation generated according to the Kanai–Tajimi power spectrum. The identification results show that the proposed algorithm can effectively identify the structural state, unknown stiffness, damping and mass parameters of the structures.

Qualitative Modelling the Dancing Volvox with Two-Body System: Comparing Simple Mechanics with Observation Video

Volvox cells normally construct a spherical colony of hundred of cells and moving together to perform their basic needs. More than moving a single colony, two attached volvox colonies can ‘dance’ and move together. This system can be modeled as a two-body system, where its center of mass (COM) is performing simple translational (TRAN) motion, while the two colonies center is rotating around the COM with roll (ROLL) or spin (SPIN) motions. From the available observation video, about 10 s or 325 frames can be isolatedfor Sobel edge detection to get a clear picture of the dancing motion of two volvox colonies. It has been observed that the dancing volvox has a superposition motion of the other motion (TRAN, ROLL, SPIN), which has been compared qualitatively with the simple mechanics model of the two-body system. From the model, the translational velocityis about 1.25 m/s, and its roll and spin angular velocity are about 0.785 and 3.063 rad/s, respectively. The results of the study concluded that the mode of motion of the two Volvox colonies was a combination of spin and translational motion.

Analytical truss model with an extended strut for conventionally reinforced concrete coupling beams with span-to-height ratios larger than 1.75

Conventionally reinforced concrete coupling beams are widely used in coupled shear wall structures to improve the structural lateral stiffness and energy dissipation capacity. Therefore, it is of great significance to develop a simple mechanical analytical model that can accurately predict the shear strength and deformation of conventionally reinforced concrete coupling beams. In the previous work, the authors proposed an analytical truss model for coupling beams with the span-to-height ratio l/h ≤ 1.75. However, due to the changes in the load-transfer mechanism, the model is not suitable for coupling beams with l/h > 1.75. By comparing existing test results of coupling beams with different span-to-height ratios and numerical results provided by a refined finite element simulation, the evolution of the load-transfer mechanism with the variation of l/h is identified. On this basis, an analytical truss model that is consist of a novel extended strut and several secondary conventional struts is proposed. The proposed model is verified to predict the shear strength of 23 existing coupling beams well, with l/h > 1.75, and the coefficient of variation (COV) is of 0.092. In contrast, the design codes ACI 318–19 and GB 50010–2010 provide less accurate predictions (their COVs are 0.263 and 0.195, respectively). Moreover, the calculated shear force-transverse displacement skeleton curves using the proposed model are in good agreement with the test results. On the other hand, by simplifying the calculation process of this model, a simplified model is put forward for practical engineering application, resulting in a slight loss of accuracy (the COV is 0.109). In order to prevent the insufficient ductility of coupling beams with l/h > 1.75 with this simplified model, a standardized design method is also proposed.

Quantum cosmological backreactions. II. Purely homogeneous quantum cosmology

This is the second paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory. The purpose of the present paper is twofold. On the one hand, it illustrates the formalism of space adiabatic perturbation theory (SAPT) for two simple quantum mechanical toy models. On the other, it proves the main point, namely that backreactions lead to additional correction terms in effective Hamiltonians that one would otherwise neglect in a crude Born-Oppenheimer approximation. The first model that we consider is a harmonic oscillator coupled to an anharmonic oscillator. We chose it because it displays many similarities with the more interesting second model describing the coupling between an inflaton and gravity restricted to the purely homogeneous and isotropic sector. These results have potential phenomenological consequences in particular for quantum cosmological theories describing big bounces such as Loop Quantum Cosmology (LQC).

Quantitative analysis of the morphing wing mechanism of raptors: Analysis methods, folding motions, and bionic design of Falco Peregrinus

Raptors can change the shape and area of their wings to an exceptional degree in a fast and efficient manner, surpassing other birds, insects, or bats. Some researchers have focused on the functional properties of muscle skeletons, mechanics, and flapping robot design. However, the wing motion of the birds of prey has not been measured quantitatively, and synthetic bionic wings with morphing abilities similar to raptors are far from reality. Therefore, in the current study, a 3D suspension system for holding bird carcasses was designed and fabricated to fasten the wings of Falco Peregrinus with a series of morphing postures. Subsequently, the wing skeleton of the falcon was scanned during extending motions using the computed tomography (CT) approach to obtain three consecutive poses. Subsequently, the skeleton was reconstructed to identify the contribution of the forelimb bones to the extending/folding motions. Inspired by these findings, we propose a simple mechanical model with four bones to form a wing-morphing mechanism using the proposed pose optimisation method. Finally, a bionic wing mechanism was implemented to imitate the motion of the falcon wing—divided into inner and outer wings with folding and twisting motions. The results show that the proposed four-bar mechanism can track bone motion paths with high fidelity.

Study on distortion energy and stability of gob floor based on stress deviator field

AbstractTo analyze the plastic failure process and mechanism of gob floor in the process of close‐distance coal seams mining, a simplified mechanical model of the lateral abutment pressure of the gob was proposed to derive the stress of surrounding rock. The distribution characteristics of gob floor stress deviator were obtained, and the effect of geological parameters (coal depth H and horizontal lateral pressure coefficient λ) were studied. By combining Mohr–Coulomb theory, the influence of surrounding rock cohesion c, internal friction angle φ, different coal seam depths H and different horizontal lateral pressure coefficients λ on the distribution of plastic zone of gob floor was obtained. The results showed that the distribution of the plastic zone under different geological factors is roughly the same as that of the stress deviator. This also proves that the excavation of the rock layer causes the redistribution of stress, which leads to the plastic failure of the surrounding rock. To verify the rationality of the proposed model, industrial experiments and simulation experiments were carried out. The results of on‐site investigation showed that the stability and integrity of surrounding rock in the concentration area of stress deviator is far less than that in the low concentration area. In addition, the acoustic wave test and the displacement field monitoring result of surrounding rock in the simulation experiments of a similar model are basically consistent with the distribution of the stress deviator field. These results agree well with the distribution of stress deviator obtained by theoretical calculation.

A reduced 1D stochastic model of bleb-driven cell migration

Blebs are pressure-driven protrusions that have been observed in cells undergoing apoptosis, cytokinesis, or migration, including tumor cells that use blebs to escape their organs of origin. Here, we present a minimal 1D model of bleb-driven cell motion that combines a simple mechanical model with turnover kinetics of the actin cortex and adhesions between the membrane and the cortex. The deterministic version of this model is used to study the properties of individual blebbing events. We further introduce stochastic turnover of the adhesions, which allows for spontaneous initiation of repeated blebbing events, thus leading to sustained cell travel. We explore how the main parameters of the system control the properties of the blebbing events and the speed of cell travel. Finally, we derive a further simplification by deriving a Langevin approximation to this stochastic model.

Musculoskeletal Modeling of the Wrist via a Multi Body Simulation.

In this study, three different musculoskeletal modeling approaches were compared to each other. The objective was to show the possibilities in the case of a simple mechanical model of the wrist, using a simple multi-body-simulation (MBS) model, and using a more complex and patient-specific adaptable wrist joint MBS model. Musculoskeletal modeling could be a useful alternative, which can be practiced as a non-invasive approach to investigate body motion and internal loads in a wide range of conditions. The goal of this study was the introduction of computer-based modelling of the physiological wrist with (MBS-) models focused on the muscle and joint forces acting on the wrist.

Static effect of assembled beam bridge under statistical and stable traffic flow load

The live load effect of bridge structure caused by traffic flow load is the largest in the sum of all live load effects. Study on the strain and deflection of the assembled beam bridge under the statistical stable traffic flow load can reveal the static effect and dynamic response law of the structure, and then evaluate the service performance of the structure. In this paper, the advanced bridge structure health monitoring technology is used to collect and analyze the traffic flow load parameters. First, according to the probability distribution function of each parameter in the traffic flow load model, the statistical stable traffic flow load is synthesized and the simplified bridge mechanical model is applied. Second, the variance and relative entropy are used to judge the statistical stability of the expectation, variance and probability density function of the static effect. Finally, the evolution law of the expectation, variance and probability density function of the static effect at different locations on the prefabricated beams of the whole bridge deck is analyzed when the static effect reaches the state of statistical stability.