Vertical Pendulum Research Articles

High resolution inclinometer based on vertical pendulum and fiber Bragg grating Fabry–Perot cavity

In this paper, an inclinometer based on a vertical pendulum and a fiber Bragg grating Fabry–Perot cavity (FBG-FP) is proposed. A low-damping rotation structure is used to reduce the mechanical frictions of the pendulum system and induce a wavelength shift of FBG-FPs. We find that the sensitivity can be maximized by optimizing the parameters of the inclinometer. Using a high-resolution demodulation system, a sensitivity of 179.9 pm/(°), and a resolution better than 0.02″ can be achieved. Experiments also show that the proposed inclinometer has good linearity and repeatability.

О МОДЕЛИРОВАНИИ ПЛЯСКИ ПРОВОДОВ ВОЗДУШНЫХ ЛЭП И ПАРАМЕТРИЧЕСКОМ АНАЛИЗЕ ЭФФЕКТИВНОСТИ МАЯТНИКОВЫХ ГАСИТЕЛЕЙ

The paper presents the results of a numerical simulation of the galloping of overhead transmission lines conductors (TLC) with pendulum dampers in order to analyze the efficiency of their application. Studies show that during galloping, along with the pronounced vertical movements of the conductors, there are synchronized torsional vibrations associated with them. Twisting of the conductors leads to an additional increase in the lifting aerodynamic forces and, as a result, the amplitudes of the vibrations in comparison with the clean vertical movement of the conductors. Therefore, the control of torsional vibrations is one of the effective ways to protect the transmission lines conductors from low-frequency oscillations. For this purpose, pendulum dampers of various structural schemes are used. Wires are considered as absolutely flexible threads, which have elasticity for tension and torsion. The tension within the span is considered constant. It is assumed that the points of the conductor axis move only in a plane that is perpendicular to the longitudinal axis. The equations of dynamics in partial derivatives describing translational and torsional vibrations of a wire are written. To account for the dampers, the conductor is divided into sections between which the dampers are placed. The equations of dampers motion under the action of the conductors are written. The numerical integration procedure is based on the finite-difference analogue of the obtained oscillation equations. As a result of the numerical experiments for single conductors, the scheme is justified for the joint installation of vertical and horizontal pendulums and their parameters, under which low-frequency oscillations of conductors of the most dangerous forms of galloping are successfully damped. The initial installation angles are determined for horizontal pendulums which are most effective for detuning torsional and transverse oscillations.

Linear Quadratic Regulator Design for Position Control of an Inverted Pendulum by Grey Wolf Optimizer

In this study, a linear quadratic regulator (LQR) based position controller is designed and optimized for an inverted pendulum system. Two parameters, vertical pendulum angle and horizontal cart position, must be controlled together to move a pendulum to desired position. PID controllers are conventionally used for this purpose and two different PID controllers must be used to move the pendulum. LQR is an alternative method. Angle and position of inverted pendulum can be controlled using only one LQR. Determination of Q and R matrices is the main problem when designing an LQR and they must be minimized a defined performance index. Determination of the Q and R matrices is generally made by trial and error method but finding the optimum parameters using this method is difficult and not guaranty. An optimization algorithm can be used for this purpose and in this way; it is possible to obtain optimum controller parameters and high performance. That’s why an optimization method, grey wolf optimizer, is used to tune controller parameters in this study.

Implementation Assessment of a Wave Energy Converter, Based on Fully Enclosed Multi-axis Inertial Reaction Mechanisms

This paper examines the implementation of a standalone 1 MW Wave Energy Converter (WEC), based on a novel concept of a class of WECs, consisting in fully enclosed appropriate internal body configurations, which provide inertial reaction against the motion of an external vessel. Acting under the excitation of the waves, the external vessel is subjected to a simultaneous surge and pitch motion in all directions, ensuring maximum wave energy capture. The internal body is suspended from the external vessel body in such an appropriate geometrical configuration, that a symmetric four bar mechanism is essentially formed. The first advantage of this suspension geometry is that a linear trajectory results for the center of the mass of the suspended body with respect to the external vessel, enabling the introduction of a quite simple form of a Power Take-Off (PTO) design. The simplicity and symmetry of the suspension geometry and of the PTO, ensure a quite simple and robust technological implementation. Mass and inertia distribution of the internal body are optimized, ensuring maximal conversion and storage of wave energy. As a result, the internal body assembly is essentially, dynamically equivalent to a vertical physical pendulum. However, the resulting equivalent pendulum length and inertia can far exceed those that can be achieved by a simple horizontal or vertical pendulum, suspended or inverted, leading to a significant reduction of the suspended mass.

On Advanced Versions of Wave-Power Plants

The modern electric-power industry, which is based on thermal-power plants, is causing difficult environmental problems on a planetary scale. Leading industrialized countries are developing power industry based on renewable energy sources (RESs) using the energy of the Sun, rivers, oceans, wind, and geothermal energy of the Earth. The energy density of sea waves is much higher than that of solar radiation and wind. However, solar- and wind-power plants have gained more widespread use than have wave ones. The reason for this is the absence of a cheap and effective way of converting the sea-wave energy into electricity. Existing wave-power plants are inferior to other types of power plants using renewable sources of energy in mass and size and, therefore, in the cost of electricity. The paper considers a layout allowing for a significant reduction in the mass and dimensions of a wave-power plant. The wave-power plant is housed in the hull of a moored twin-hull ship. By means of cables and a vertical pendulum, the energy of waves is converted first into mechanical shaft-rotation energy and then into the electrical energy. The use of a tackle pulley allows increasing the generator rotor speed to hundreds of rpm and reducing the pendulum mass. All the electrical equipment of the power plant is arranged inside the twin-hull ship. Results of use of the wave-power-plant model in a wave-simulator tank are presented.

The response of quadrangular plates to blast load resulting from the detonation of encased buried charges

In real-life situation, especially in the numerous regions where conflicts exist, improvised explosive devices can be made of varying explosives encased in different containers detonated under varying conditions. This article reports on a series of experiments that was carried out to investigate the response of quadrangular plates to buried encased charges with a view to simulate the detonation of landmines buried in sand and compared with different loading conditions. Four loading scenarios, namely, bare and encased charges detonated in air and bare and encased charges buried under sand, were investigated. The results were evaluated and compared to the data obtained from bare charges detonated in air in terms of plate deformation and impulse imparted onto the target plate. A vertical ballistic pendulum was used to measure the impulse imparted onto the target plates by the different charges. The results showed that the presence of the steel casing in buried charge tests caused more damage to the test plate. An increase in the midpoint deflection of the test plate was observed despite a slightly reduced impulse imparted onto the plate. Larger impulse was imparted onto the target plate by buried bare charges compared to bare charges detonated in air. Midpoint deflection and impulse decreased with an increasing stand-off distance for all the different loading scenarios.

Sand ejecta kinematics and impulse transfer associated with the buried blast loading: A controlled laboratory investigation

An experimental test facility has been developed for performing laboratory studies on shallow buried blast loading. The shock tube based test facility offers an alternative method for generating blast wave in a controlled and repeatable manner, without the use of explosives. In this paper, we consider a spherical expanding blast wave of moderate shock strength with relatively low driving pressure. A confined dry sand bed prepared with a constant density, is exposed to a blast wave from the embedded shock tube. The principal objective of this paper is to understand the various events involved during the interaction of leading blast wave with the soil medium, followed by the expansion of the entrained gas. The process initiates with the formation of stress wave in the sand media, followed by the gas bubble expansion and terminates with sand ejection. The variation in the output of the sand ejecta is investigated with the help of high speed photography. The velocity of the sand ejecta front is found to decrease with the increase in the burial depth (DoB). Further, the impulse (using vertical pendulum) and peak pressure (using transducers) imparted to the rigid target are evaluated. The target is located at different stand-off distances (SoD) above the top surface of the sand bed. It is found that the peak pressure values are influenced by the presence of dome-cap of the ejecta, expanding vertically upwards generating a point-load impact. Irrespective of the depth of burial (DoB = 32mm–64mm), maximum impulse is observed around the zone of bubble expansion (close to the sand bed surface). Sand ejecta does however have a greater influence on the impulse at higher SoDs (> 40mm). Moreover, the maximum momentum transfer is observed when SoD to DoB ratio is 2.5. In conclusion, the shock-driven sand test facility is found to be a simple and efficient tool to study the complex dynamics of sand ejecta, including the post- impact on the target structures.

Design, Development, and Testing of a Scaled Vertical Axis Pendulum Wave Energy Converter

Vertical axis pendulum wave energy converters are a relatively unknown type of point absorber whose ostensive robustness and simplistic design merit further exposure and investigation. To this end, an exploratory empirical study of such a converter—one that is a small-scale generic prototype—is presented in this work. The prototype was deployed at Oregon State University's O.H. Hinsdale Wave Research Laboratory and subjected to varying wave environments and operational conditions. The exploratory study was governed by evaluating how the prototype's net mean power output responded to the varied wave environments and operational conditions. These varied environments and conditions included the following: 1) the number of mooring lines; 2) the amount of wave scatter; 3) the wave direction; 4) the pendulums’ inertial characteristics; and 5) the amount of torsional loading applied to a pendulum's swing (simulating electric power generation). Results from the study give a general analysis of how a representative, but generic, vertical axis pendulum wave energy converter performs in irregular waves with different deployment configurations. Likewise, the results promote pathways for further vertical axis pendulum wave energy converter research and development.

A preliminary numerical study on the time-varying fall attitudes and aerodynamics of freely falling conical graupel particles

The flow fields and dynamic motions of conical graupel of diameters 0.5–5mm falling in air of 800hPa and −8°C are studied by solving the transient Navier-Stokes equations numerically for flow past the conical graupel and the body dynamics equations representing the 6-degrees-of-freedom motion that determines the position and orientation of the graupel in response to the hydrodynamic force of the flow fields. The shape of conical graupel made through a simple but practical existing mathematical equation allows us to have an uneven mass distribution, which is generally believed to have great influence on ice particles' orientations while falling when inertial force becomes increasingly dominant over other effects. The simulated motions include vertical fall, lateral translation, sailing, rotation and pendulum swing. The computed flow fields are characterized in terms of streamtrace patterns as well as the vorticity magnitude fields, and the corresponding motions of the conical graupel is physically featured by looking upon the graupel surface distributions of pressure coefficient, torques contributed by both pressure as well as viscous effects. Tumbling doesn't occur when an initial orientation of the graupel is either 20° or 160° about Y axis, and the torque contributed by the pressure effect is dominant over that contributed by the viscous effect.

Structural Desigh and Motion Analysis of Universal Mobile Quadruped Robot

Abstract According to bionics and simplified octopus structure, this paper designed a universal mobile quadruped robot and adopted Denavit-Hartenberg system to analyze the single leg kinematics of a robot, obtaining its kinematics equation. Also, through the method of separating variables, this paper solved its inverse kinematics and got the joint angle. A walking gait is planned and the joint angle of vertical pendulum stance phase and swing phase of the robot in walking are calculated. MATLAB is used to simulate the relevant joint angles of the robot, so as to analyze its movement change. Experimental results further verified the universal motion of robots.

Development and demonstration of a gravity gradiometer onboard an autonomous underwater vehicle for detecting massive subseafloor deposits

Gravity surveys are used to detect underground density structures. Hybrid survey configurations using a gravimeter and a gravity gradiometer are particularly effective in this regard. A gravity gradiometer was developed for use in hybrid gravity surveys of massive subseafloor deposits. Its performance was evaluated in an ocean-based trial using an autonomous underwater vehicle (AUV). The gradiometer consisted of two identical vertical long-period pendulums, acting as gravity sensors, with a separation of 0.44m. The self-noise of the gradiometer was estimated to be 6 E (6×10−9/s2) at 2–50mHz, with which the gravity gradient signal could be detected when the AUV was above a typical ore deposit. The gravity gradiometer was mounted on a forced gimbal vertically controlled by fiber optic gyroscopes and tiltmeters. The ocean-based trial observation performed at a depth of approximately 1300m in Sagami Bay using the AUV Urashima (JAMSTEC) showed that the system operated steadily on a moving platform except during periods of extreme motion, such as turning and pitching. The resulting gravity gradient was highly affected by the motion of the platform and the estimated resolution was 3×102 E, which was mainly limited by the noise of the recording system.

Comparison of VP broadband tiltmeter and VS vertical pendulum tiltmeter

Vertical pendulum (VP) tiltmeter is a kind of earthquake precursor observation equipment, which is used to record the interaction force associated with astronomical tidal tilts caused. Currently, VP broadband tiltmeter and vertical sensor (VS) vertical pendulum tiltmeter are primarily used. In this paper, we compare the two different instruments by using four aspects—mechanical structure, circuitry, zeroing, and bandwidth—based on their working principles and applications. We conclude that VP broadband tiltmeter is more superior compared with VS vertical pendulum tiltmeter because of its higher bandwidth and degree of automation.

Impulse transfer during sand impact with a cellular structure

Compressible cellular metal sandwich structures made from a 3D assembly of square cross section 6061 T6 aluminum alloy tubes, and face sheets of the same alloy have been attached to a vertical pendulum and impacted by synthetic wet sand with an incident velocity of ∼300 ms−1. The transmitted impulse of samples with thick (relatively rigid) and thin face sheets are compared to that transferred by an incompressible solid aluminum test block of the same dimensions. A discrete particle-based simulation method was used to simulate the experiments and to investigate the soil particle – structure interaction with the cellular structures. The simulated results agreed very well with experimental data; both showed that the impulse transferred to cellular structures with a 22 MPa core strength was 10–15% less than that transferred to a solid block of similar dimensions. However, the simulations reveal that the some of this apparent mitigation resulted from a subtle sand interaction between the bottom of the test structure and the sand box used for the tests. When this sand box effect was eliminated in the simulations, a small impulse reduction from cellular structures with thin face sheets was still observed. However, this was found to be a result of dynamic deflection of the edges of the front face sheet. When this effect was eliminated (by the use of a rigid front face), the simulations showed a small (5%) impulse reduction occurred for cellular structure whose compressive strength was much less than the pressure applied by the sand. This was a consequence of rapid core compression which increased the travel distance (and lateral spreading) of late arriving sand during the sand loading process. Weak cellular structures, that suffered significant crushing, also reduce the impulse transfer rate.

Impulse transfer during sand impact with a solid block

A vertical pendulum apparatus has been used to experimentally investigate the impulse and pressure applied by the impact of wet synthetic sand upon the flat surface of a back supported solid aluminum test block. The transferred impulse and maximum pressure applied to the sample were both found to decrease with increasing standoff distance between the bottom of the sand layer and the impact face of the solid block. A particle based simulation method was used to model the sand's acceleration by the explosive and its impact with the test structure. This method was found to successfully predict both the impulse and pressure transferred during the tests. Analysis of the experimentally validated simulations indicates that the momentum transmitted to the test structure is approximately equal to the free field momentum of the incoming sand, consistent with the idea that the sand stagnates against a planar surface upon impact. The decrease in transferred impulse with increasing standoff distance arises from a small reduction in sand particle velocity due to momentum transfer to air particles, and an increase in lateral spreading of the sand particles as the standoff distance increased. This spreading results in a smaller fraction of the sand particles impacting the (finite) area of the test sample impact face.

Linear active disturbance rejection control of underactuated systems: The case of the Furuta pendulum

An Active Disturbance Rejection Control (ADRC) scheme is proposed for a trajectory tracking problem defined on a nonfeedback linearizable Furuta Pendulum example. A desired rest to rest angular position reference trajectory is to be tracked by the horizontal arm while the unactuated vertical pendulum arm stays around its unstable vertical position without falling down during the entire maneuver and long after it concludes. A linear observer-based linear controller of the ADRC type is designed on the basis of the flat tangent linearization of the system around an arbitrary equilibrium. The advantageous combination of flatness and the ADRC method makes it possible to on-line estimate and cancels the undesirable effects of the higher order nonlinearities disregarded by the linearization. These effects are triggered by fast horizontal arm tracking maneuvers driving the pendulum substantially away from the initial equilibrium point. Convincing experimental results, including a comparative test with a sliding mode controller, are presented.

Early results of micro-deformation measurements in Magdalena Jama (Slovenia) by a vertical static pendulum

Vertical static pendulums have been installed in mines or caves in Central Europe since 2007. Two-dimensional optical measurement of the tilt of a rock mass and continuous fully digital on-line evaluation of results makes possible the detection of a small tilt of the surroundings with a resolution of tens of nanoradians or the deformation of the surroundings in the horizontal plane with resolution of hundreds of nanometres. The paper describes the measurement device and the first results of the measurements in Magdalena Jama, which is part of the Postojna Cave System (Slovenia). The correlation of deformation between distant stations shows the existence of stress variations that are not only of local origin (high floods, local seismicity, and aseismic deformations). The stress field has a wider, and not only regional, character with effects that can be observed very far from the origin.

A laboratory-scale buried charge simulator

An experimental technique has been developed in order to mimic the effect of landmine loading on materials and structures to be studied in a laboratory setting, without the need for explosives. Compressed gas is discharged beneath a sand layer, simulating the dynamic flow generated by a buried explosive. High speed photography reveals that the stages of soil motion observed during a landmine blast are replicated. The effect of soil saturation and the depth of the sand layer on sand motion are evaluated. Two series of experiments have been performed with the buried charge simulator to characterise subsequent impact of the sand. First, the time variation in pressure and impulse during sand impact on a stationary target is evaluated using a Kolsky bar apparatus. It is found that the pressure pulse imparted to the Kolsky bar consists of two phases: an initial transient phase of high pressure (attributed to wave propagation effects in the impacting sand), followed by a lower pressure phase of longer duration (due to lateral flow of the sand against the Kolsky bar). Both phases make a significant contribution to the total imparted impulse. It is found that wet sand exerts higher peak pressures and imparts a larger total impulse than dry sand. The level of imparted impulse is determined as a function of sand depth, and of stand-off distance between the sand and the impacted end of the Kolsky bar. The second study uses a vertical impulse pendulum to measure the momentum imparted by sand impact to a target which is free to move vertically. The effect of target mass upon imparted momentum is investigated. It is concluded that the laboratory-scale sand impact apparatus is a flexible tool for investigating the interactions between structures and dynamic sand flows.

The influence of the height of burial of buried charges – Some experimental observations

This paper presents the results of an experimental investigation to determine the effect of the height of burial (the amount of sand beneath the buried charge) on a buried charge in terms of impulses imparted onto a rigid steel target plate (suspended from a vertical pendulum). The 40 mm rigid target plate of exposed area 400 mm × 400 mm is located at a constant stand-off distance of 47 mm above the surface of the sand. Tests conducted at a height of burial of 0 mm (placed flush on a steel base plate) resulted in the largest impulse transfer for all depth of burial (amount of sand above the buried charge) values tested. The optimal depth of burial for impulse transfer was observed to occur within 50–70 mm irrespective of the height of burial (0–110 mm). Semi-infinite height of burial conditions are attained when any further increase in the height of burial does not influence the impulse transfer to the target plate. The height of burial representing semi-infinite conditions observed in the experiments is a function of the depth of burial.

New Highway Power Generation Device Based on Auto Wake

With the increasingly serious environment pollution and energy shortage problem of further deepening, how to use more effective and more environmental protection equipment of the new energy conversion and utilization of become social the public and the government attaches great importance to the problem. According to the high speed highway car wake contains huge wind, the wind power generation unit born. The vertical shaft by double S rotor, wind deflector, variable speed clutch institutions, centripetal vertical pendulum and low speed generator composition , realized respectively the wind energy collection, transmission, temporary and transformation. This device for wind power generation field provides a more efficient energy conversion mode. Among them, we creatively applied the ratchet, vertical pendulum mechanism so that the wind energy conversion rate has been increased greatly. At the same time, can also solve the highway electric equipment of the power supply problem. This device design makes the highway lighting lamps and other electric equipment of the power supply problem to obtain the very good solve, reduce power facilities installation cost. The effective use of natural wind, expand the scope of the use of wind energy, alleviate energy nervous, also reduce the pollution of the environment.

The response of quadrangular plates to buried charges

This paper presents experimental and numerical results of an investigation to determine the response of quadrangular steel plates subjected to explosive charges buried under dry construction sand. The buried charges were designed to simulate a landmine blast. Three parameters; depth of burial, stand-off distance and mass of explosive, were varied to provide a range of impulsive loads and plate responses. A vertical ballistic pendulum was used to measure the impulse imparted from the buried charges onto the deformable or rigid target plates. The results showed that as the depth of burial increases the impulse imparted onto the plate increases. The midpoint deflection of the plate reaches a maximum, after which the deflection decreases with a continual increase in depth of burial. The numerical model, developed in ANSYS AUTODYN R12.1a and validated against the experiments, provided insight into the transient response of both the plates and the sand. The numerical models indicated that for most of the tested stand-off distances the sand did not impact the plate as an ejecta but as a sand dome with complete containment of the detonation products. The sand serves to focus the high pressure and high temperature detonation products onto the plate. This focussing effect increases with the depth of burial. The plate deformation is dependent on the amount of energy the sand can absorb (via compaction) which is directly proportional to the depth of burial.