Rigid Mass Research Articles

Exact free vibration analysis for mechanical system composed of Timoshenko beams with intermediate eccentric rigid body on elastic supports: An experimental and analytical investigation

The purpose of this article is to investigate the changes in the magnitude of natural frequencies and their associated modal shapes of Timoshenko beam with respect to different system design parameters. This beam includes an intermediate extended eccentric rigid mass mounted on two elastic segments. The equilibrium equations which govern the transverse and rotational motions are derived. The application of the developed system frequency equation is demonstrated by several illustrative examples. Several end and intermediate conditions are considered. The influence of, rotary inertia, shear deformation, axial load, eccentric mass and elastic segments step ratio on the system natural frequencies and mode shapes are conducted. Several sets of new results are presented. Comparison of the present model results with the experimental data for shaft integrated with intermediate rigid mass demonstrates the accuracy of the analysis in practical applications. The present model is valid for several industrial applications, such as mechanical, structural, naval and for wider range of applications.

Numerical simulation on the seismic absorption effect of the cushion in rigid-pile composite foundation

In order to quantitatively study the seismic absorption effect of the cushion on a superstructure, a numerical simulation and parametric study are carried out on the overall FEA model of a rigid-pile composite foundation in ABAQUS. A simulation of a shaking table test on a rigid mass block is first completed with ABAQUS and EERA, and the effectiveness of the Drucker-Prager constitutive model and the finite-infinite element coupling method is proved. Dynamic time-history analysis of the overall model under frequent and rare earthquakes is carried out using seismic waves from the El Centro, Kobe, and Bonds earthquakes. The different responses of rigid-pile composite foundations and pile-raft foundations are discussed. Furthermore, the influence of thickness and modulus of cushion, and ground acceleration on the seismic absorption effect of the cushion are analyzed. The results show that: 1) the seismic absorption effect of a cushion is good under rare earthquakes, with an absorption ratio of about 0.85; and 2) the seismic absorption effect is strongly affected by cushion thickness and ground acceleration.

Closed-form modal analysis of flexural beam resonators ballasted by a rigid mass

The work deals with the study of free flexural vibrations of constant cross-section elastic beams ballasted by a rigid mass with rotary inertia at any longitudinal position. We analyse five sets of boundary conditions of the beam (fixed-free, fixed-fixed, fixed-pinned, pinned-pinned, and free-free) and hypothesize that the structure is perfectly rigid, where the rigid mass is applied. By employing the Euler–Bernoulli beam theory, a single parametric matrix is obtained, which provides the characteristic equation of motion of the structure. When applied to specific configurations, the proposed analytical model predicts the eigenfrequencies and eigenmodes of the beam as accurately as ad hoc analytical models available in the literature. The accuracy of the results is also confirmed by comparison with detailed two- and three-dimensional finite element analyses of a test case. By means of a three-dimensional finite element model, the applicability of the rigid mass hypothesis to continuous beams with a composite thickened portion is finally assessed.

Simple models for rope substructure mechanics: application to electro-mechanical lifts

Mechanical systems modelled as rigid mass elements connected by tensioned slender structural members such as ropes and cables represent quite common substructures used in lift engineering and hoisting applications. Special interest is devoted by engineers and researchers to the vibratory response of such systems for optimum performance and durability. This paper presents simplified models that can be employed to determine the natural frequencies of systems having substructures of two rigid masses constrained by tensioned rope/cable elements. The exact solution for free un-damped longitudinal displacement response is discussed in the context of simple two-degree-of-freedom models. The results are compared and the influence of characteristics parameters such as the ratio of the average mass of the two rigid masses with respect to the rope mass and the deviation ratio of the two rigid masses with respect to the average mass is analyzed. This analysis gives criteria for the application of such simplified models in complex elevator and hoisting system configurations.

33-1:Invited Paper: Development of AMOLED Display: From Rigid to Flexible

Recently, rigid AMOLED display industry has stepped into mass production stage progressively. Meanwhile, flexible display has attracted more attention for its great potential to generate novel product market. However, when it comes to the mass production, flexible AMOLED display still faces quite a few technological challenges. In this paper, a 4.6sdtp2016471408inch AMOLED display which can be rolled up under bending radius less than 3mm has been demonstrated, using process compatible to the current rigid AMOLED mass production line.

Structural consequences of cohesion in gravitational instabilities triggered by fluid overpressure: Analytical derivation and experimental testing

The critical taper theory of Coulomb wedges has been classically applied to compressive regimes (accretionary prisms/fold-and-thrust belts), and more recently to gravitational instabilities. Following the initial hypothesis of the theory, we provide an alternative expression of the exact solution for a non-cohesive wedge by considering the balance of forces applied to the external surfaces. Then, we use this approach to derive a solution for the case of cohesive wedges. We show that cohesion has conspicuous structural effects, including a minimum length required for sliding and the formation of listric faults. The stabilizing effect of cohesion is accentuated in the foremost thin domain of the wedge, defining a required Minimum Failure Length (MFL), and producing sliding of a rigid mass above the detachment. This MFL decreases with less cohesion, a smaller coefficient of internal friction, larger fluid overpressure ratio, and steeper upper and basal surfaces for the wedge. Listricity of the normal faults depends on the fluid overpressure magnitude within the wedge. For moderate fluid overpressure, normal faults are curved close to the surface, and become straight at depth. In contrast, where fluid overpressure exceeds a critical value corresponding to the fluid pressure required to destabilize the surface of a noncohesive wedge, the state of stress changes and rotates at depth. The faults are straight close to the surface and listric at depth, becoming parallel to the upper surface if the wedge is thick enough. We tested some of these structural effects of a cohesive wedge on gravitational instabilities using analogue models where cohesive material was subjected to pore-fluid pressure. The shape of the faults obtained in the models is consistent with the predictions of the theory.

Estimating the ride quality characteristics of vehicles with random decrement analysis of on-the-road vibration response data

ABSTRACTThis paper describes the application of a practical analytical technique based on the random decrement method to estimate the rigid sprung mass dynamic characteristics (frequency response function) of road vehicles using only vibration response data during constant-speed operation. A brief history and development of the random decrement technique is presented, along with a summary of work undertaken on optimal parameter selection to establish the random decrement signature. Two approaches to estimate the dynamic characteristics from the random decrement signature are described and evaluated. A custom, single-wheeled vehicle (physical quarter car) was commissioned to undertake a series of on-the-road experiments at various nominally constant operating speeds. The vehicle, also instrumented as an inertial profilometer, simultaneously measured the longitudinal pavement profile to establish the vehicle's actual dynamic characteristics during operation. The main outcome of the paper is that the random decrement technique can be used to provide accurate estimates of the sprung mass mode of the vehicle's dynamic characteristics for both linear and nonlinear suspension systems of an idealised vehicle.

Propagation of the compaction waves in a cellular block with varying cross-section

Current work aims to broaden our previous work on the compaction waves in a cellular block with varying cross-section under impact. Complement experiments were carried out to obtain the force signals of the foam specimen with varying cross-section in the dynamic crushing. Two impact scenarios were employed. In the first impact scenario, the foam block together with a back mass impinged onto a rigid target; and in the second scenario, a stationary foam block was impinged by a rigid mass. The foam/mass was fired from a gas gun barrel. The impact velocity was measured before the impact happened. The deformation processes were captured by a high speed camera and an aluminum bar was served as the rigid target. Two groups of semi-conductive strain gauges were attached at the surface of the bar to obtain the strain/stress signals. Typical force signals were analyzed together with their deformation processes.

Characterization of friction force and nature of bifurcation from experiments on a single-degree-of-freedom system with friction-induced vibrations

Experimental investigation is performed on a test set-up representing a single-degree-of-freedom friction-induced system. The experimental set-up consists of a rigid mass (oscillator) connected to a fixed support through a spring and the mass in frictional contact with a moving belt. The major objectives of the experiments are to characterize (i) the nature of friction-induced oscillations, (ii) the nature of bifurcation associated with frictional instability in the system, and (iii) the nature of friction force that is responsible for the oscillations observed from the experiment. The phase portrait of the system shows significant overshoot of the oscillator velocity above the belt velocity indicating the existence of hysteretic loop around zero relative velocity (pre-sliding regime). The bifurcation diagram clearly demonstrates the subcriticality of the Hopf bifurcation associated with the system negating all empirical friction models which yield supercritical Hopf bifurcation. The friction force-relative velocity curve shows significant hysteretic behavior, both in the pre-sliding as well as in the pure sliding domains. This observation hints towards a dynamic or an acceleration-dependent friction model as an appropriate choice for representing the friction force obtained from our experimental set-up.

Cyclic load testing of pre-stressed rock anchors for slope stabilization

The objective of this research was to assess the characteristics of seismic induced damage and the deformation patterns of pre-stressed cement-grouted cables that are used for rock slope stabilization projects subjected to quasi-static cyclic loading. The experimental configuration includes the installation of 15 pre-stressed cables in a slope model made of concrete blocks (theoretically rigid rock mass) on top of a pre-existing sliding surface. The study showed that: (i) The pre-stressed cables exhibited great seismic performance. Rapid displacement of the model blocks was observed after the complete loss of the initial pre-stress load under continued applied cyclic loads and exceedance of the state of equilibrium, which implies the higher the initial pre-stress load, the better the seismic performance of the rock anchor; (ii) The failure of the pre-stressed cables was due to fracture at the connection of the tendons and cable heads under cyclic loading. The sequence of failure had a distinct pattern. Failure was first observed at the upper row of cables, which experienced the most severe damage, including the ejection of cable heads. No evidence of de-bonding was observed during the cyclic loading; (iii) The stress distribution of the bond length for pre-stressed cables was highly non-uniform. High stress concentrations were observed at both the fixed end and the free end of the bond length both before and immediately after the state of equilibrium is exceeded. The results obtained can be used to evaluate the overall performance of pre-stressed rock anchors subject to seismic loading and their potential as rockfall prevention and stabilization measures.

Dynamic Response Analysis of an Asymmetric Coupled Vehicle-Track System Generated by Voided Elastic Two-Block Sleeper

Based on vehicle-track coupled dynamic theory, a three-dimensional asymmetric vehicle-track coupling vibration model is developed to investigate the effect of voided elastic two-block sleepers on vehicle and track system dynamic responses. For the vehicle system, one car body, two frames, and four wheel sets are assumed to be rigid, with 35 degrees of freedom (DOF). For the track system, the rails and the concrete two-block sleepers are the main vibration components. The rails are modelled as Timoshenko beams, and the concrete two-block sleepers are assumed to be rigid mass with vertical and lateral movement. The pads under the rails and the rubber boots under the sleepers provide greater vertical and lateral elasticity for the track. The Hertz nonlinear elastic contact theory is used to calculate the normal wheel/rail force. The wheel/rail tangent creep force is first calculated using Kalker’s linear creep theory and then modified by the Shen-Hedrick-Elkins theory. The results show that the asymmetric voided elastic two-block sleepers have greater effects on the dynamic responses for fasteners and sleepers than on the car body and the wheel/rail forces under measured geometric irregularity and random irregularity. Two or more voided sleepers will greatly affect the vehicle running safety.

Vibration control of a flexible structure with electromagnetic actuators

This work presents the model of a shear-frame-type structure composed of six flexible beams and three rigid masses. Fixed on the ground, outside the structure, two voltage-controlled electromagnetic actuators are used for vibration control. To model the flexible beams, unidimensional finite elements were used. Nonlinear equations for the actuator electromagnetic force, noise in the position sensor, time delays for the control signal update and voltage saturation were also considered in the model. For controlling purposes, a discrete linear quadratic regulator combined with a predictive full-order discrete linear observer was employed. Results of numerical simulations, where the structure is submitted to an impulsive disturbance force and to a harmonic force, show that the oscillations can be significantly reduced with the use of the electromagnetic actuators.

Analysis of geometric dispersion effect of impact-induced transient waves in composite rod using dynamic substructure method

Wave propagation in a composite rod is encountered in many contact-impact events. During the travelling of the impact-induced waves along the rod, geometric dispersion is possible when the diameter of the rod is of the same order as the wavelength. The aim of this paper is to develop an efficient method, namely dynamic substructure method to analyze the geometric dispersion of the waves in the problem of the finite-length composite rod coaxially struck by a moving rigid mass. For analyzing the geometric dispersion, a new rod element is presented through taking the lateral kinetic energy of the rod into account. The transient dynamic equation expressed by the reduced modal coordinates is derived by the Lagrange equation and the fixed-interface mode synthesis method. An adhesive contact model is used to account for contact constraint. The applications of the proposed method are demonstrated using 1) compress trapezoidal impulse and 2) impact-induced waves propagate in the large-diameter rod. In order to validate the feasibility of the proposed method, the comparison is also presented between the LS-DYNA3D solutions and the substructure solutions. It indicates that the proposed method is sufficiently accurate to compute the time history of contact force and to describe the geometric dispersion characteristics such as the attenuation of the amplitude of wavefront and the increasing of rise time. The error of the 2nd peak value of the contact force Fc2 is less than 5.0%, while the time cost of the proposed method are only 1.8% of those of the LS-DYNA3D program. Furthermore, numerical results show that the geometric dispersion results in “succession collisions” phenomenon become more complicated, and it experiences three times of the transitions from contact to separation.

Rapid, simple method for determining the porosity of mesoporous TiO2 films using a quartz crystal microbalance (QCM)

Two different mesoporous films of TiO2 were coated onto a QCM disc and fired at 450°C for 30min. The first film was derived from a sol–gel paste that was popular in the early days of dye-sensitised solar cells, i.e. dssc, research, a TiO2(sg) film. The other was a commercial colloidal paste used to make examples of the current dssc cell; a TiO2(ds) film. A QCM was used to determine the mass of the TiO2 film deposited on each disc and the increase in the mass of the film when immersed in water/glycerol solutions with wt% values spanning the range 0–70%. The results of this work reveal that with both TiO2 mesoporous films the solution fills the film's pores and acts as a rigid mass, thereby allowing the porosity of each film to be calculated as: 59.1% and 71.6% for the TiO2(sg) and TiO2(ds) films, respectively. These results, coupled with surface area data, allowed the pore radii of the two films to be calculated as: 9.6 and 17.8nm, respectively. This method is then simplified further, to just a few frequency measurements in water and only air to reveal the same porosity values. The value of the latter ‘one point’ method for making porosity measurements is discussed briefly.

Brittle and Ductile Behavior in Deep-Seated Landslides: Learning from the Vajont Experience

This paper analyzes the mechanical behavior of the unstable Mt. Toc slope before the 1963 catastrophic collapse, considering both the measured data (surface displacements and microseismicity) and the updated geological model of the prehistoric rockslide. From February 1960 up to 9 October 1963, the unstable mass behaved as a brittle–ductile ‘mechanical system,’ characterized by remarkable microseismicity as well as by considerable surface displacements (up to 4–5 m). Recorded microshocks were the result of progressive rock fracturing of distinct resisting stiff parts made up of intact rock (indentations, undulations, and rock bridges). The main resisting stiff part was a large rock indentation located at the NE extremity of the unstable mass that acted as a mechanical constraint during the whole 1960–1963 period, inducing a progressive rototranslation toward the NE. This large constraint failed in autumn 1960, when an overall slope failure took place, as emphasized by the occurrence of the large perimetrical crack in the upper slope. In this circumstance, the collapse was inhibited by a reblocking phenomenon of the unstable mass that had been previously destabilized by the first reservoir filling. Progressive failure of localized intact rock parts progressively propagated westwards as a consequence of the two further filling–drawdown cycles of the reservoir (1962 and 1963). The characteristic brittle–ductile behavior of the Vajont landslide was made possible by the presence of a very thick (40–50 m) and highly deformable shear zone underlying the upper rigid rock mass (100–120 m thick).

Stress waves in layered cellular materials—Dynamic compaction under axial impact

Theoretical analysis of the propagation of stress waves in layered cellular solids with different densities, and consequently strengths, is carried out to deepen the understanding of their dynamic compaction due to impact loading. The cellular topology is neglected and homogeneous properties are assumed. Two types of plastic waves are distinguished depending on the layers density arrangement. Only waves of strong discontinuity occur when the layers’ densities increase in the direction of propagation of the primary wave. Multiple reflections of the stress waves from the layer interfaces are identified and studied for this type of the layers density arrangement. Simultaneous propagation of a wave of strong discontinuity in the proximal layer and a simple wave in the subsequent layers occur when the layers’ densities decrease in the direction of propagation of the primary wave.Two types of loading conditions: an impact of a stationary cellular block by a rigid mass and an impact of a cellular block on a rigid wall are analysed. It is assumed that the constituent materials in the layered solids exhibit strain hardening. The plastic strain is sought as a function of the impact velocity and material properties when using the characteristic Hugoniot strain–velocity relationship. FE models using ABAQUS are constructed and numerical simulations are carried out to verify the predictions of the theoretical analysis. The potential of layered cellular materials to design more efficient structural components when subjected to intensive dynamic loading is briefly discussed when comparing the response of some layered configurations with their uniform density counterparts of equal mass.

Transmission of fore-and-aft vibration to the seat pan, the backrest and the headrest of a car seat

Measurements of the transmission of vibration from the floor beneath a seat to interfaces between the seat and the human body are used to characterise the dynamic performance of the seat. Most studies of seat transmissibility concern the transmission of vertical vibration through seat pan cushions, but fore-and-aft vibration at a seat pan and backrest can also cause discomfort. This study investigated the transmission of fore-and-aft vibration through a car seat to surfaces on the seat pan cushion, the backrest cushion and the headrest, and also to the seat frame at these three locations. The study sought to understand the influences of the seat frame and the cushion foam and to provide data for dynamic modelling of the seat. The fore-and-aft transmissibility of the seat was measured with 12 human subjects and an SAE J826 manikin, using 120-s periods of fore-and-aft random vibration (0.25-40 Hz) at three magnitudes (0.4 m/s2 r.m.s., 0.8 m/s2 r.m.s. and 1.2 m/s2 r.m.s.). With the manikin, there were three resonances (at 3.5 Hz, 12 Hz and 20 Hz) in the transmissibilities from the seat base to the seat pan frame and the seat pan cushion, and to the backrest frame and the backrest cushion. With the human subjects, the transmissibilities from the seat base to all six locations on the seat showed a principal resonance around 4 Hz. With increasing magnitude of the vibration, the principal resonance frequency in all the seat transmissibilities decreased. It is concluded that fore-and-aft resonances in the seat transmissibilities, especially to the backrest, are likely to affect vibration discomfort. There are large differences between the fore-and-aft transmissibility of a seat with a manikin and those with human subjects, consistent with the human body having dynamics very different from those of a rigid mass. Non-linearities in the seat transmissibilities with the manikin and with the human subjects may be explained by non-linearity in the biodynamics of the body and the responses of the seat and the manikin.

Parameter identification for vertical ground reaction forces on feet while running

The human foot is subjected to ground reaction forces during running. These forces have been studied for decades to reduce the related injuries and increase comfort. A four-degree-of-freedom system has been used in the literature to simulate the human body motion during the touch-down. However, there are still inconsistencies between the simulation results and experimental measurements. In this study, an optimization technique is proposed to obtain the required parameters to estimate the vertical ground reaction force using the measurements from actual runners. The touch-down velocities of the rigid and wobbling body masses were also treated as optimization variables. It was shown that the proposed parameters can be adjusted to represent a particular shoe type. Specifically, vertical ground reaction force parameters and touch-down velocities were obtained for shoes with various insole properties and cushioning technologies. The results of this study suggest that the human locomotion system reacts to the shoe properties by regulating the velocities of the body wobbling and rigid masses. The magnitude and the load rate obtained using the proposed parameters are consistent with the experimental data. It is shown that the viscoelastic properties of the shoe will significantly affect the load rate but not the load magnitude.

Propagation of compaction waves in cellular materials with continuously varying density

Theoretical analysis of the propagation of stress waves in cellular solids with non-uniform density, and consequently strength, is carried out to deepen the understanding of their dynamic compaction due to impact loading. Materials with continuously varying density in the direction of loading are considered when analysing the response to two types of loading conditions: an impact of a stationary cellular block by a rigid mass and an impact of a cellular block on a rigid wall. It is assumed that the local stress–strain characteristics of the graded materials exhibit strain hardening. The plastic strain field in the deformed graded cellular solid is sought here as a function of the impact velocity and material properties when using the Hugoniot material representation. It is shown that the initial density variation with respect to the boundaries of a finite thickness block has a significant effect on the history of the stresses and strains during the compaction process.FE models using ABAQUS are constructed and numerical simulations are carried out to verify the predictions of the theoretical analysis. Attention is paid to the energy absorption capacity of the materials depending on their initial density distribution when comparing their dynamic responses with the response of equivalent mass cellular block with uniform density. Significant advantages in using density graded cellular solids in finite thickness layers are not identified for the analysed loading rate.

Optimal wave shape with respect to efficiency in percussive drilling with detachable drill bit

The problem of finding the optimal incident wave of given duration that maximizes the efficiency of conversion of wave energy into work in percussive drilling with detachable drill bit is considered. The drill rod is modelled as 1D linearly elastic and the drill bit as a rigid mass. The bit/rock interaction is described by a history-dependent force versus penetration relation with different constant slopes for primary loading and unloading/reloading. A functional expressing the dependence of the efficiency on the shape of an arbitrary incident wave of given duration is derived and maximized. For short incident waves, there is a weak influence of the bit mass on the optimal wave shape which is nearly rectangular. For longer incident waves, there is a strong influence of the bit mass on the optimal wave shape which significantly differs from rectangular. The efficiencies for optimal waves approach those for rectangular waves for short waves. For long waves they approach or assume values which are independent of wave duration but decrease with increasing bit mass. Relative to commonly-used rectangular waves significant increase in efficiency can be achieved through optimization of the wave shape if the wave is not too short. Optimal incident waves can be realized accurately, e.g., by piezoelectric means.