Line Springs Research Articles

Review on Non - Carbonated Beverages (Soft Drinks)

Non-Carbonated soft drinks are a significant segment of global beverage markets. They are made by adding glucose directly to the beverage or to the water used to dilute a concentrated syrup. Glucose can come from a variety of industrial sources, but it must meet appropriate standards. Glucose levels vary depending on the product. Typical ingredients and packaging styles are discussed. Most products are pasteurized during the filling and processing process to ensure microbiological safety and stability. Natural mineral water is briefly discussed as well. Life line springs pvt.ltd., processes non-carbonated beverages with pasteurization, water treatment, blending, and other processes using materials such as water, sugar syrup, glucose, flavors, and finished product package coding (date, batch no. etc).

Hydrogeology and origin of waters of the Panyam Volcanic Line springs, Jos Plateau, Nigeria

The PVL springs are used for both domestic and agricultural purposes. The seepage from the springs has resulted in producing a large expanse of wetlands and is therefore intensively use for dry season farming. The aim of this study was to determine the hydrogeological, hydrochemical characteristics, origin and their suitability for domestic and irrigation. The hydrogeology of the springs was determined by field mapping. The physico-chemical parameters were determined in the field and by laboratory methods. For the cation and anion analysis the ICP-MS and the wet methods were employed respectively. The stable isotope composition of oxygen (δ18O) and hydrogen (δ2H) were analyzed by Isotope Ratio Mass Spectrometer. The hydrochemical analysis revealed that the PVL springs waters are generally neutral with an average pH value of 7.3. The average TDS and EC values are 127.8mg/l and 246µs/cm respectively. These values fall within fresh water class. The average Mg2+,Ca2+, Na+ and K+ cation concentration values are 16.3mg/l, 15.8mg/l, 10.8mg/l and 5.58mg/l respectively. The average anions concentration of HCO3-, SO4 and Cl- are 140mg/l, 8.6mg/l and 3.4mg/l respectively. Piper trilinear diagram show that the spring waters is predominantly Mg-Ca-HCO3 water type with potable qualities based on WHO drinking water standards. The sodium Adsorption Ratio (SAR) and Sodium Soluble Percentage (SSP) values range between 0.44 to 0.84 and 26.4 to 54% respectively and falls within irrigation quality standards. Stable isotope compositions of δ18O and δ2H ranges from -3.60/00 to -4.90/00 and -200/00 to -280/00 respectively falls within the meteoric water composition. This is further affirmed by the δ2H versus δ18O plot on the correlation diagram with Standard Meteoric Water Line.

Hydrogeology and origin of waters of the Panyam Volcanic Line springs, Jos Plateau, Nigeria

The PVL springs are used for both domestic and agricultural purposes. The seepage from the springs has resulted in producing a large expanse of wetlands and is therefore intensively use for dry season farming. The aim of this study was to determine the hydrogeological, hydrochemical characteristics, origin and their suitability for domestic and irrigation. The hydrogeology of the springs was determined by field mapping. The physico-chemical parameters were determined in the field and by laboratory methods. For the cation and anion analysis the ICP-MS and the wet methods were employed respectively. The stable isotope composition of oxygen (δ18O) and hydrogen (δ2H) were analyzed by Isotope Ratio Mass Spectrometer. The hydrochemical analysis revealed that the PVL springs waters are generally neutral with an average pH value of 7.3. The average TDS and EC values are 127.8mg/l and 246µs/cm respectively. These values fall within fresh water class. The average Mg2+,Ca2+, Na+ and K+ cation concentration values are 16.3mg/l, 15.8mg/l, 10.8mg/l and 5.58mg/l respectively. The average anions concentration of HCO3-, SO4 and Cl- are 140mg/l, 8.6mg/l and 3.4mg/l respectively. Piper trilinear diagram show that the spring waters is predominantly Mg-Ca-HCO3 water type with potable qualities based on WHO drinking water standards. The sodium Adsorption Ratio (SAR) and Sodium Soluble Percentage (SSP) values range between 0.44 to 0.84 and 26.4 to 54% respectively and falls within irrigation quality standards. Stable isotope compositions of δ18O and δ2H ranges from -3.60/00 to -4.90/00 and -200/00 to -280/00 respectively falls within the meteoric water composition. This is further affirmed by the δ2H versus δ18O plot on the correlation diagram with Standard Meteoric Water Line.

Design of a Spatial Vibration System for Prescribed Ratio of Energy Peaks

The work ratio is a primary factor in the applications relevant to wide bandwidth requirements because a bandwidth depends on resonant peaks. Especially, since a single-body system can have up to six resonant peaks, a six degree-of-freedom spatial system is more desirable for a broad bandwidth design. This paper presents a novel design method of a spatial vibration system for any prescribed ratio of energy peaks. Firstly, we introduce an important and concise geometric nature of a spatial vibration system with a single rigid body when it has only rotational vibration modes. The vibration modes represent vibration axes and six lines of action can be obtained by transforming the vibration modes by the mass matrix. It is shown that the six axes of vibration and six lines of action form two orthocentric tetrahedra that share the orthocenter coincident with the mass center. It is also shown that the stiffness matrix determined from two tetrahedra can always be realized by means of parallel connection of line springs. Using the orthocentric tetrahedra, we acquire analytical expressions for the energy produced by external forces at resonant frequencies, which is used to determine vibration modes that satisfy the requirements for given mass properties and six target resonant frequencies. Finally, the stiffness matrix that satisfies requirements is found and realized. To illustrate the process of the presented method, we use four numerical examples with different work ratios and demonstrate that the method is useful for a wide bandwidth.

Design of serial linkage-type vibration energy harvester with three resonant frequencies

This paper presents a new design method of a planar 3 degrees-of-freedom(DOF) serial linkage-type vibration energy harvester with a single proof mass. The harvester is designed to generate electrical power at equally spaced three target resonant frequencies which can be chosen arbitrarily. For given target frequencies and a proof mass, the design method involves (1) the determination of the stiffness matrix, (2) the synthesis of the stiffness by means of a parallel connection of three line springs and (3) its conversion into a 3DOF device connected serially by torsional springs. The torsional springs are realized by the flexible hinge joints and the polyvinylidene fluoride(PVDF) films are attached on the joints. Upon determination of the desired stiffness matrix, the SQP algorithm is utilized to find the optimum locations and spring constants of the serial hinge joints for the minimum difference among three electrical power peaks. The FEM analysis and experiments are conducted to verify the proposed design method. Three measured resonant power peaks occur at 24.7, 30.4 and 33.6 Hz comparing to the target frequencies of 25, 30 and 35 Hz. The normalized maximum power of is generated at 24.7 Hz. The experimental results also demonstrate that the harvester can generate at least 18.6% of the peak power throughout the frequency range from 23.1 to 36.5 Hz, which ensures consistently acquirable power within the operating frequency range by virtue of the coupled effect of a serial linkage-type structure.

Transverse vibration and stability of a functionally graded rotating annular disk with a circumferential crack

Out of plane vibration of rotating disks limits their performances especially at certain critical speed. The critical speed of these disks may be affected by the presence of defects such as a circumferential crack. In this paper out of plane vibration of functionally graded (FG) rotating annular disks with a circumferential open crack is investigated. The cracked disk is modeled as two sub-disks, connected at the crack location by translational and rotational line springs, simulating the crack plate response to induced shear force and bending moment at the crack radius. These spring stiffness constants are obtained numerically using the finite element method (FEM) as a function of crack depth and radius. The rotational spring stiffness strongly depends on the disk rotation speed, while the stiffness of the translational spring is found to be independent of the disk speed. Both spring constants depend on the spatial distribution of the disk elastic modulus.The in-plane disk stresses are obtained using a semi-analytical approach. Those in plane stresses are used to obtain the governing equation of out of plane motion of the disk. A finite difference scheme is used to solve the partial differential equation of motion to obtain eigenvalues, critical speed and associated mode shapes. The lowest critical speed, which is one of the important parameters limiting the performance of the rotating disk, is obtained from the Campbell Diagram. It is found that irrespective of the distribution of the modulus of elasticity in the FG disk, increasing the crack depth or decreasing the crack radial distance from the disk center decreases the critical speed. The critical speed reduction is more pronounced for the case when the disk material modulus of elasticity is decreasing from the disk center.

Optimized multicomponent vs. classical geothermometry: Insights from modeling studies at the Dixie Valley geothermal area

A new geothermometry approach is explored, incorporating multicomponent geothermometry coupled with numerical optimization to provide more confident estimates of geothermal reservoir temperatures when results of classical geothermometers are inconsistent. This approach is applied to geothermal well and spring waters from the Dixie Valley geothermal area (Nevada), to evaluate the influence of salt brines mixing and dilution of geothermal fluids on calculated temperatures. The main advantage of the optimized multicomponent method over classical geothermometers is its ability to quantify the extent of dilution and gas loss experienced by a geothermal fluid, and to optimize other poorly constrained or unknown parameters (such as Al and Mg concentrations), allowing the reconstruction of the deep reservoir fluid composition and therefore gaining confidence in reservoir temperatures estimations. Because the chemical evolution of deep geothermal fluids is a combination of multiple time-dependent processes that take place when these fluids ascend to the surface, reactive transport modeling is used to assess constraints on the application of solute geothermometers. Simulation results reveal that Al and Mg concentrations of ascending fluids are sensitive to mineral precipitation–dissolution affecting reservoir temperatures inferred with multicomponent geothermometry. In contrast, simulations show that the concentrations of major elements such as Na, K, and SiO2 are less sensitive to re-equilibration. Geothermometers based on these elements give reasonable reservoir temperatures in many cases, except when dilution or mixing with saline waters has taken place. Optimized multicomponent geothermometry yields more representative temperatures for such cases. Taking into account differences in estimated temperatures, and chemical compositions of the Dixie Valley thermal waters, a conceptual model of two main geothermal reservoirs is proposed. The first reservoir is located along the Stillwater range normal fault system and has an estimated temperature of 240–260°C. It covers the area corresponding to the geothermal field but could extend towards the south-west where deep temperatures of 200–225°C are estimated. The second reservoir has an estimated temperature of 175–190°C and extends from well 62-21 to northeastern Hyder, Lower Ranch, Fault Line, and Jersey springs.

Design method of planar three-degrees-of-freedom serial compliance device with desired compliance characteristics

In this article, a novel method for the systematic design of a planar three-degrees-of-freedom compliance device with desired compliance characteristics is presented. For the realization of desired compliance, the synthesis method of stiffness of a planar mechanism is first derived. The compliance device may be directly realized by means of parallel connections of the synthesized springs. However, the use of several mechanical elements such as joints and guides for spring assemblies for the realization may cause significant complexity in manufacturing the compliance device with high precision and in compact size. In order to resolve the problem, the form of serial connections of three torsional springs which has the same compliance as the form of parallel connections of the synthesized line springs is proposed. The serial form of torsional springs can be physically realized by designing proper shape of the circular flexure hinge corresponding to each of the torsional springs. For the illustration of the proposed design method, a planar serial compliance device with high compliance to the normal contact force is designed and verified by finite element method analysis.

Realization of an Arbitrary Planar Stiffness With a Simple Symmetric Parallel Mechanism

This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure based on geometry is presented and mechanism compactness is discussed.

Vibration Analysis of a Rectangular Thin Plate with Two Parallel Cracks

The modeling of cracked plates is important to structural damage detection following the model-based approach. However, very little research has modeled plates with multiple cracks. In 2000, Khadem and Rezaee proposed a method for calculating the modal parameters of a plate with a single-crack parallel to one of the sides. The main purpose of this paper is to extend that work and develop a solution method for calculating the dynamic responses of a classically damped rectangular thin plate with two cracks. The basic idea is to treat the cracks as line springs with varying degrees of stiffness along their lines. When the plate is deflected or when it is vibrating, the slope of the plate is discontinuous at the two sides of the crack line. This change in slope varies along the crack as the crack depth is not uniform. In the governing equation, the cracks are considered as the continuity conditions along the crack line. It is assumed that each crack influences the stiffness only in its neighborhood, with that influence vanishing at a sufficient distance from the crack. By following this assumption, the natural frequencies of the cracked plate can be calculated using energy methods, and the time-domain response of the plate can then be calculated using the modal superposition method. The possibility of using the two-dimensional spatial wavelet transform in crack detection is also explored in this paper.

The conditions for mode decoupling of a linear vibration system with diagonalizable stiffness matrices via screw theory

In this article, a new geometric approach to the conditions for mode decoupling of an elastically suspended rigid body with a diagonalizable stiffness matrix is presented. The necessary and sufficient condition for diagonalization of a spatial stiffness matrix by a proper co-ordinate transformation is derived using the form of the stiffness matrix expressed by uniquely determined three orthogonal lines and three orthogonal torsional springs. Three orthogonal planes are defined by use of the axes of the line springs. Both the spatial displacements lying on or perpendicular to each of the planes and the spatial forces induced due to the displacements are decoupled into two linearly independent three-systems of screws. From this property and the geometric relations between those planes obtained from the stiffness and the principal planes of inertia, the conditions for mode decoupling of the vibration system are derived and the possible locations of the axes of the decoupled vibration modes are identified.

Screw System Approach to Physical Realization of Stiffness Matrix With Arbitrary Rank

It is possible to realize the desired compliance characteristics of a robot in a form of a passive compliance device, which demands the synthesis technique of a stiffness matrix by parallel connections of line and/or torsional springs. In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, thereby the synthesis equation is derived. Examination of the numbers of free design parameters involved in the synthesis suggests that a line or free vector for a spring can be freely selected from the induced wrench space depending on the rank of the stiffness matrix. The recursive synthesis method that allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix is proposed.

Geometrical design method of multi-degree-of-freedom dynamic vibration absorbers

This paper presents a new geometrical design method of multi-degree-of-freedom (mdof) dynamic vibration absorbers that reduce multiple modes of vibration. The design of an mdof vibration absorber involves, in general, the complexity of the equations and large numbers of design variables. For this reason, previous researches mainly focused on finding optimized stiffness and damping values that minimize the vibration responses. In this paper, we introduce a simple geometrical design method in which the sets of three mutually orthogonal line springs are used to first simplify the stiffness matrix. The dynamic equations of a main body and an absorber are then decoupled to obtain the geometric design rules for an mdof absorber. Numerical examples are used to illustrate the new design method.

Stiffness Modeling of the Soft-Finger Contact in Robotic Grasping

This paper investigates the soft-finger contact by presenting the contact with a set of line springs based on screw theory, reveals the rotational effects, and identifies the stiffness properties of the contact. An elastic model of a soft-finger contact is proposed and a generalized contact stiffness matrix is developed by applying the congruence transformation and by introducing stiffness mapping of the line springs in translational directions and rotational axes. The effective stiffnesses along these directions and axes are hence obtained and the rotational stiffnesses are revealed. This helps create a screw representation of a six-dimensional soft-finger contact and produce an approach of analyzing and synthesizing a robotic grasp without resorting to the point contact representation. The correlation between the rotational stiffness, the number of equivalent point contacts and the number of equivalent contours is given and the stiffness synthesis is presented with both modular and direct approaches. The grasp thus achieved from the stiffness analysis contributes to both translational and rotational restraint and the stiffness matrix so developed is proven to be symmetric and positive definite. Case studies are presented with a two-soft-finger grasp and a three-soft-finger grasp. The grasps are analyzed with a general stiffness matrix which is used to control the fine displacements of a grasped object by changing the preload on the contact.

Spatial stiffness realization with parallel springs using geometric parameters

This paper investigates the synthesis of a spatial stiffness matrix using simple line springs. A new algorithm is developed, which enables the selection of constituent springs based on their positions and directions. The constraining space of the line springs is then investigated. It is shown that an isotropic stiffness matrix, in general, can be split into the sum of two rank-3 stiffness matrices. The three line springs of the first matrix can be selected to pass through any arbitrary points in space, while the three line springs of the second stiffness matrix lie on a quadric surface, which is usually a hyperboloid of one sheet.

Finite element modelling of cracked inelastic shells with large deflections: two-dimensional and three-dimensional approaches

Higher utilization of structural materials leads to a need for accurate numerical tools for reliable predictions of structural response. In some instances, both material and geometrical non-linearities are allowed for, typically in assessments of structural collapse or residual strength in damaged conditions. The present study addresses the performance of surface-cracked inelastic shells with out-of-plane displacements not negligible compared to shell thickness. This situation leads to non-linear membrane force effects in the shell. Hence, a cracked part of the shell will be subjected to a non-proportional history of bending moment and membrane force. An important point in the discretization of the problem is whether a two-dimensional model describes the structural performance sufficiently, or a three-dimensional model is required. Herein, the two-dimensional modelling is performed by means of a Mindlin shell finite element. The cracked parts are accounted for by means of inelastic line spring elements. The three-dimensional models employ eight-noded solid elements. These models also account for ductile crack growth due to void coalescence by means of a modified Gurson–Tvergaard constitutive model, hence providing detailed solutions that the two-dimensional simulations can be tested against. Using this, the accuracy of the two-dimensional approach is checked thoroughly. The analyses show that the two-dimensional modelling is sufficient as long as the cracks do not grow. Hence, using fracture initiation as a capacity criterion, shell elements and line springs provide acceptable predictions. If significant ductile tearing occurs before final failure, the line spring ligaments have to be updated due to crack growth.

Crack bridging by through-thickness reinforcement in delaminating curved structures

The problem of how through-thickness reinforcement opposes the opening of delamination cracks in curved laminar structures is examined theoretically. Finite element calculations have been performed to show how the through-thickness reinforcement modifies the energy release rate of a delamination crack. Solutions are found for perfectly bonded and debonded cases. Energy conservation arguments are then used to define constitutive laws for equivalent continuous bridging springs acting on the delamination fracture surfaces. This step allows the immediate application of useful concepts from the literature on bridged cracks. Results are summarized for convenient use and trends are highlighted by relating the exact numerical results to analytical approximations for the perfectly bonded and debonded cases. Through-thickness reinforcement will be effective at modest volume fractions, provided the spacing of the discrete reinforcing elements is not much greater than the laminate thickness, in which case buckling between successive reinforcements facilitates delamination. With this provision, the present results confirm that simplistic linear constitutive laws used for bridging line springs in prior work are fairly accurate for most feasible values of geometrical and material parameters; and a minor amendment to the prior work, which is provided in analytic form, will lead to conservative design rules.

Numerical studies on crack growth in a steel tubular T-joint

The results of a numerical investigation on fatigue crack growth of an offshore tubular T-joint under the action of axial, in-plane and out-of-plane bending loads are presented in this paper. Extensive stress analysis has been carried out to determine the location of the hot spot stress along the brace—chord intersection for each load case. Semi-elliptical cracks with varying crack lengths and crack depths were introduced at the hot spot location by means of line spring elements for stress intensity factor evaluation. The line springs were properly constrained to prevent the problem of crack surface penetration. The stress intensity factors obtained are then used in a crack growth law for life estimation.

Applicability of J-Integral to Tension-Softening Materials

This brief paper addresses the application of the J-integral to fracture analysis and toughness characterization of quasi-brittle materials, with specific focus on the tension-softening behavior in the fracture process zone. Concern is often raised on the validity of the J-integral when unloading occurs in the material points along which the J-integral contour path traverses, particularly during process-zone growth. This paper clarifies that this concern is misplaced. Whereas the J-integral contour wraps around the tension-softening line springs of the bridging elements in the process zone, the material points on the J-integral contour undergoes elastic loading and unloading. Therefore application of the J-integral to quasi-brittle materials does not violate the basic tenet of the assumption of nonlinear elastic material behavior underlying the J-integral theoretical formulation.

A study of the perturbed stress state of a closed cylindrical shell with a system of part-through transverse cracks

We study the elastic equilibrium of a closed infinite circular cylindrical shell with a system of surface cracks of identical length and depth. We use the method of singular integral equations together with the modeling of solid matter in the plane of a part-through crack by irregularly distributed “line springs”. We conduct a numerical analysis of the variation of the relative stress intensity factor at the center of a crack as a function of the parameters of a crack and the number of cracks. We study cracks located on both the interior and exterior surface of the shell.