Free Sides Research Articles

Research on Cutting Characteristics of Rock Plate with Two Sides Fixed and Two Sides Free

Conical pick wear is an urgent problem in the roadway excavation caused by hard rock difficult to break. The traditional method of increasing cutting power to improve cutting performance of conical pick significantly increases pick wear. In the paper, a saw blade and conical pick combined cutting method is proposed based on increased free surface. To research the fracture morphology and cutting force of rock plate, theoretical, numerical, and experimental methods are used. By theoretical research, the bending mechanical model of rock plate bending is established. The cutting position and the junction between the free sides and fixed sides are preferentially broken. A numerical model combining the erosion and damage constitutive model is built, and the cutting process of rock plate was presented. According to rock plate experiment, the peak cutting force increases with the increasing uniaxial compressive strength, thickness of rock plate, and cutting depth of conical pick and decreases with the increasing width and height of rock plate. Exponential relationships exist between peak cutting force and thickness, width and height of rock plate, and cutting depth of conical pick. Linear relationship exists between peak cutting force and uniaxial compressive strength. The size of rock fragments increases with uniaxial compressive strength, width, and height of rock plate.

Mechanical Properties and Failure Behaviour of Architected Alumina Microlattices Fabricated by Stereolithography 3d Printing

The mechanical behaviour of Simple Cubic, Octet Truss and Kelvin Cell alumina microlattices with solid struts was systematically studied through experiments and simulations. Our results showed that the specific mechanical properties of the microlattices were the best for Simple Cubic, worst for Kelvin Cell, and followed Ashby’s power law well at small relative densities (≤ 0.3). At higher relative densities, the power law changed as joint deformation became increasingly important to overall lattice mechanics. The Simple Cubic lattices failed in a column-by-column manner from the sides inwards to the centre, while fracture in Octet Truss and Kelvin Cell lattices took place predominantly along the diagonal (110) plane. This was confirmed to be due to the interplay between the fixed top and bottom boundaries with the free sides of the lattices. At low relative densities, the microlattice struts were also observed to fail in a sequential, localized manner, in contrast to the simultaneous fracture observed at higher relative densities. Compared to current materials, the alumina microlattices exhibited outstanding specific moduli and specific strength, as well as limited ductility in the form of pseudoplastic strains (0.1% - 0.5%). Therefore, alumina microlattices are expected to be an invaluable addition to the material catalogue for engineering designers.

New analytical solutions for vibration problem of thick plates

Exact solutions for the vibrations and stability problems in the mechanics of solids are sufficiently rare. For rectangular thick plates, exact solutions in the form of trigonometric series were constructed only for the case when all or two opposite sides of the plate are simply-supported. The discussion about the possibility of constructing exact solutions continues to this day. As a rule, an approximate solution is constructed in the analytical form on the basis of a variational approach. It should be noted, that as frequency increases, the number of basic functions involved in the solution also has to be increased, consequently the solutions of such type are inefficient for describing a structural element within the framework of such methods as the Continuous Element method, the Spectral Element method and the Dynamic Stiffness method. In the present research, for the first time, the analytical solutions for the vibration problem of thick orthotropic plates are obtained. The modified trigonometric basis is used to construct the general solution for the free vibration problem of the plate in a series, permitting the derivation of an infinite system of linear algebraic equations. Cases of practically important boundary conditions of completely free sides and fully clamped sides are considered. It should be noted that the presented analytical solutions for FFFF and CCCC boundary allows to completely describe the structural element in the form of a plate by means of a dynamic stiffness matrix and their use for modeling more complex structures, also in the framework of methods such as Continuous Element method, Spectral Element method and Dynamic Stiffness method. The obtained results could also be applied in projecting constructions, in developing new devices and in the optimization of their parametersin projecting of constructions, in developing new devices and in the optimization of their parameters.

Free Vibrations of a Thin Elastic Orthotropic Cylindrical Panel with Free Еdges

Using a system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of a thin elastic orthotropic cylindrical panel with free edges is investigated. To calculate its natural frequencies and to identify the respective vibration modes, the generalized Kantorovich–Vlasov method of reduction to ordinary differential equations is employed. To find the natural frequencies of possible types of vibrations, dispersion equations are derived. An asymptotic relation between the dispersion equations of the problem in hand and of an analogous problem for a rectangular plate with free sides is established. Determined is also a relation between the dispersion equations of the problem and of the boundary-value problem for a semi-infinite orthotropic nonclosed circular cylindrical shell with three free edges. With the example of an orthotropic cylindrical panel, the values of dimensionless characteristics of its natural frequencies are derived.

Conceptual design and analysis of a dredger robot for irrigation canals

PurposeThis paper aims to present a solution to dredging the irrigation canals using a robotic system. Considering the importance of irrigating water, the waste within the water canals should be avoided. Irrigation canals are artificial linear structures in the landscape that are used for transporting the water. One important problem in water transferring is the waste materials flow inside the water, and in some areas, they block the main stream, reducing the effective capacity of the canal. Among the waste materials, aquatic plants are grown on the surface of the canal that needs to be removed from the canal. This removal operation is conducted using chemical, biological, ecological and physical methods with complex supply systems. In addition, robotic systems are used as such complex systems. So, a robotic system is proposed to dredging the irrigation canals. The assumed robot was manufactured in AGRINS laboratory of Tehran University.Design/methodology/approachDesign procedure, dynamic modelling and simulation of this robotic system are studied. To validate the system design before its construction, ADAMS software is used to perform simulations. Finally, performance evaluation of the dredger robot in the canal is studied based on the experimental data.FindingsResults show that the design procedure has been correctly fitted to the real condition. Therefore, the designed robot could be easily used to dredging irrigation canals.Practical implicationsThe assumed robot was manufactured in AGRINS laboratory of Tehran University.Originality/valuePerforming a dredging operation in the canals could be conducted by a new technique considering both free sides of the canal. Therefore, in this paper, a conceptual design of a 3-wheels stair dredger robot is numerically and experimentally studied.

Finite element study of tunable cantilever plate structure using position change

In this paper, a tunable cantilever plate structure is presented, in which a box is attached to each corner of its free sides and a ball is placed in each box. Change of the balls position makes natural frequency of the structure variable, which expands working bandwidth of the structure to accommodate the complex ambient vibration. The modal analysis of the tunable cantilever plate is carried out by the finite element software-ABAQUS. Changing the balls position, it is found that there are maximum and minimum values in the natural frequency of the self-tuning structure, which forms a resonance bandwidth. Moreover, there are multiple position combinations of two balls at the same natural frequency in the range of resonance band. The paper studies the influence of mass and geometrical dimensions of boxes and balls on the natural frequency and bandwidth. While ensuring strength and stiffness of the structure, optimal material and size parameters are selected to improve the resonant bandwidth. This provides a theoretical basis for applying the tunable structure to piezoelectric energy harvester.

Experimental study on the natural frequency of tunable piezoelectric cantilever plate

PEH (piezoelectric energy harvester) outputs a higher voltage when the natural frequency matches ambient vibration frequency. How to widen working frequency band is a hot issue in study of PEH. In this paper, an auto-tuning PEH is presented by attaching a box to each corner of its free sides and a ball is placed in each box. Change of the balls position makes natural frequency of PEH variable, which expands working bandwidth of the device to accommodate complex ambient vibration. Fixing the equipment on experimental platform by designing fixture, hammering experiments are carried out to measure natural frequency of the structure when balls are in different positions. It is found that the maximum and minimum natural frequencies exist in the auto-tuning PEH, which form a resonance bandwidth. Moreover, there are multiple position combinations of two balls at the same natural frequency in the range of resonance bandwidth. Fixed the apparatus on exciter by the fixture, and a constant excitation frequency is selected in the bandwidth to perform auto-tuning experiments on the instrument. It is observed that location of balls is automatically changed to make natural frequency of the system coincide with the excitation, and the law of variation in balls position is obtained. The converter is subjected to sweeping experiments through an exciter and an oscilloscope. Using voltage-frequency diagrams, it is shown that the auto-tuning PEH outputs a higher voltage and its frequency band is wider when the ball rolls freely compared to two cases where balls are fixed.

On Interface Conditions for Flows in Coupled Free-Porous Media

Many processes in nature (e.g., physical and biogeochemical processes in hyporheic zones, and arterial mass transport) occur near the interface of free-porous media. A firm understanding of these processes needs an accurate prescription of flow dynamics near the interface which (in turn) hinges on an appropriate description of interface conditions along the interface of free-porous media. Although the conditions for the flow dynamics at the interface of free-porous media have received considerable attention, many of these studies were empirical and lacked a firm theoretical underpinning. In this paper, we derive a complete and self-consistent set of conditions for flow dynamics at the interface of free-porous media. We first propose a principle of virtual power by incorporating the virtual power expended at the interface of free-porous media. Then by appealing to the calculus of variations, we obtain a complete set of interface conditions for flows in coupled free-porous media. A noteworthy feature of our approach is that the derived interface conditions apply to a wide variety of porous media models. We also show that the two most popular interface conditions—the Beavers–Joseph condition and the Beavers–Joseph–Saffman condition—are special cases of the approach presented in this paper. The proposed principle of virtual power also provides a minimum power theorem for a class of flows in coupled free-porous media, which has a similar mathematical structure as the ones enjoyed by flows in uncoupled free and porous media. The derived interface conditions are summarized along with a pictorial description of the problem, which pertains to the flow of an incompressible fluid in coupled free-porous media. $$\Psi $$ is the power expended density along the interface. $$\mathbf {v}_{\text {free}}$$ and $$\mathbf {v}_{\text {por}}$$ are the velocities in the free and porous regions, respectively. A superposed asterisk on a (vectorial) quantity denotes its tangential component along the interface. $$v_n$$ is the normal component of the velocity at the interface from the free region into the porous region. $$\mathbf {T}_{\text {free}}^{\text {extra}}$$ and $$\mathbf {T}_{\text {por}}^{\text {extra}}$$ , respectively, denote the extra Cauchy stresses in the free and porous regions. $$\mathbf {t}_{\text {free}}$$ and $$\mathbf {t}_{\text {por}}$$ , respectively, denote the tractions on the free and porous sides of the interface with outward normals $$\widehat{\mathbf {n}}_{\text {free}}$$ and $$\widehat{\mathbf {n}}_{\text {por}}$$ . A unit tangential vector along the interface is denoted by $$\widehat{\mathbf {s}}$$ .

NodeTrix Planarity Testing with Small Clusters

We study the NodeTrix planarity testing problem for flat clustered graphs when the maximum size of each cluster is bounded by a constant $k$. We consider both the case when the sides of the matrices to which the edges are incident are fixed and the case when they can be chosen arbitrarily. We show that NodeTrix planarity testing with fixed sides can be solved in $O(k^{3k+\frac{3}{2}} \cdot n)$ time for every flat clustered graph that can be reduced to a partial 2-tree by collapsing its clusters into single vertices. In the general case, NodeTrix planarity testing with fixed sides can be solved in $O(n)$ time for $k = 2$, but it is NP-complete for any $k > 2$. NodeTrix planarity testing remains NP-complete also in the free sides model when $k > 4$.

PLATING UNDER LATERAL LOADS WITH SINGULAR POINTS ON THE COUNTER

The article proposes special techniques for calculating plates with singular points on the counter that need no singular solution building. The analysis of circular plate with mixed support conditions is performed by means of overdetermined boundary collocation method using special Schwarz method. The analysis of the plate with three clamped and one free sides is performed through reducing two dimensional boundary value problems to those of one-dimensional type using special correcting function.

On the exact solutions of the biharmonic problem of the theory of elasticity in a half-strip

We have constructed the solution of the first basic odd-symmetric boundary value problem in the theory of elasticity in a half-strip with free longitudinal sides. The solution is represented as series in Papkovich–Fadle eigenfunctions whose coefficients are found in an explicit form by using functions biorthogonal to the Papkovich–Fadle eigenfunctions. It is shown that the obtained solution describes residual stresses in an infinite strip with zero boundary conditions on its sides and the displacements that arise when the residual stresses are released as a consequence of the formation of a discontinuity. The same formulas give the exact solution of a boundary value problem for the half-strip with stresses specified at its end in the traditional statement, and only the displacements should now be taken with the opposite sign. In the constructed solutions, the angular points have the properties of infinitesimal elements, where, for the uniqueness of the solution, the boundary functions must be specified together with all their derivatives. In this, they are different from an angular point in an infinite wedge. The final formulas are simple and can easily be used in engineering.

Free public transport as a way to minimize the negative effects of transport congestion in cities

The article presents the causes and effects of road congestion in cities and solutions that minimize the negative effects of transport congestion. One of the given ways is to introduce free public transport. This article presents the conditions for the implementation of free public transport, its positive and negative sides and examples of Polish cities that have decided to apply such a solution.

Structure and Magnetic Properties of Fe-Cu-Nb-Si-B with Various Niobium Concentration

The microrelief of the contact, free sides and cuts of three metal alloys with various niobium contents were studied. It is shown that samples with high niobium content are X-ray amorphous, the alloys FeCu1Si16B6, FeCu1Nb3Si16B6are characterized by an amorphous-crystalline structure. The change in the magnetic characteristics and electrical resistance of alloys in the course of thermomagnetic annealing is studied. It is shown that an increase in the Nb content in an alloy increases its temperature stability and the temperature of the onset of crystallization processes.

The asymptotics of natural oscillations of a long two-dimensional Kirchhoff plate with variable cross-section

After scaling, a long Kirchhoff plate with rigidly clamped ends and free lateral sides is described by a mixed boundary-value problem for the biharmonic operator in a thin domain with weakly curved boundary. Based on a general procedure for constructing asymptotic formulae for solutions of elliptic problems in thin domains, asymptotic expansions are derived for the eigenvalues and eigenfunctions of this problem with respect to a small parameter equal to the relative width of the plate and are also justified. In the low-frequency range of the spectrum the limiting problem is a Dirichlet problem for a fourth-order ordinary differential equation with variable coefficients, and in the mid-frequency range it is (quite unexpectedly) a Dirichlet problem for a second-order equation. The phenomenon of a boundary layer in a neighbourhood of the ends of the plate is investigated. This makes it possible to construct infinite formal asymptotic series for simple eigenvalues and the corresponding eigenfunctions, and to develop a model with enhanced precision. Asymptotic constructions for plates with periodic rapidly oscillating boundaries or for other sets of boundary conditions corresponding to mechanically reasonable ways to fix the ends of the plate are discussed. Bibliography: 46 titles.

Asymptotics of the Deflection of a Cruciform Junction of Two Narrow Kirchhoff Plates

Two two-dimensional plates with bending described by Sophie Germain’s equation with the biharmonic operator are joined in the form of a cross with clamped ends, but with free lateral sides outside the cross core. Asymptotics of the deflection of the junction with respect to the relative width of the plates regarded as a small parameter is constructed and justified. The variational-asymptotic model includes a system of two ordinary differential equations of the fourth and second orders with Dirichlet conditions at the endpoints of the one-dimensional cross and the Kirchhoff transmission conditions at its center. They are derived by analyzing the boundary layer near the crossing of the plates and mean that the deflection and the angles of rotation at the central point are continuous and that the total bending force and the principal torques vanish. Possible generalizations of the asymptotic analysis are discussed.

Limitations of the Fluorination of Graphene on a Substrate

The experimentally observed incomplete fluorination of graphene (CF x , x ≤ 0.2−0.3) on a smooth substrate has been explained. It has been shown that fluorine atoms are covalently attached primarily to scanty folds or to defects of graphene on one of its free sides.

Ground deformation source model at Kuchinoerabu-jima volcano during 2006\u20132014 as revealed by campaign GPS observation

We analyzed campaign Global Positioning System observation data in Kuchinoerabu-jima during 2006–2014. Most benchmarks located around Shin-dake crater showed crater-centered radial horizontal displacements. Horizontal displacements at western rim of the Shin-dake crater were tended to be larger compared to those at eastern rim. In addition, benchmark KUC14 which locates near the cliff at Furu-dake showed westward horizontal displacement rather than crater-centered radial (southward) one. Meanwhile, small displacements were detected at the benchmarks located at the foot of Kuchinoerabu-jima. We modeled the observed displacements applying a finite element method. We set entire FE domain as 100 × 100 × 50 km3. We set top of the domain as a free surface, and sides and bottom to be fixed boundaries. Topography was introduced in the area within Kuchinoerabu-jima using digital elevation model data provided by Kagoshima prefecture and elevation information from Google earth, and elevation of the outside area was assumed to be sea level. We assumed a stratified structure based on a one-dimensional P-wave velocity structure. We applied a vertical spheroid source model and searched optimal values of horizontal location, depth, equatorial and polar radiuses, and internal pressure change of the source using the forward modeling method. A spherical source with a radius of 50 m was obtained beneath the Shin-dake crater at a depth of 400 m above sea level. The internal pressure increase of 361 MPa yields its volume increase of 31,700 m3. Taking effects of topography and heterogeneity of ground into account allowed reproduction of overall deformation in Kuchinoerabu-jima. The location of deformation source coincides with hypocenters of shallow volcano-tectonic (VT) earthquakes and the aquifer estimated from a two-dimensional resistivity model by audio-frequency magnetotellurics method. The obtained deformation source may be corresponding to the pressurized aquifer, and shallow VT earthquakes and demagnetization may be caused by pressure and strain accumulation in the rocks around the aquifer. Applying the obtained spherical source to the tilt change before August 3, 2014 eruption, we found that 520 m3 of volcanic materials were supplied toward shallower in 1.5 h before the eruption. The depth and volume change of deformation source before May 2015 eruption detected by precise leveling surveys is deeper and two orders of magnitude greater compared to that before August 2014 eruption.

Basis properties of a problem for the Laplace operator on the square with spectral parameter in a boundary condition

We consider a classical spectral problem that arises when studying the natural vibrations of a loaded rectangular membrane fixed on two sides, the load being distributed along one of the free sides. We study the completeness, minimality, and basis property of the system of eigenfunctions and establish conditions guaranteeing the equiconvergence of spectral expansions in this system and in a given basis.

Surface quality analysis in ball end milling of Inconel 718 cantilevers by response surface methodology

The ball end milling process is commonly used for generating complex three-dimensional sculptured surfaces with definite curvature. In such cases, variation of surface properties along with the machined surface is not well understood. Therefore, this article investigates the effect of machining parameters on the quality of surface in ball end milling of thin-shaped cantilever of Inconel 718. A distinct variation is also observed in the measured values of deflection of workpiece: surface roughness and surface damage in different regions, that is, fixed end, mid portion and free end of machined surface. The experiments were conducted according to the central composite design with four factors, namely, cutting speed, feed, workpiece thickness and workpiece inclination with tool path orientation. It is observed that the process parameters have statistically significant effect on machined surface of Inconel 718. Horizontal tool path condition during milling is most favourable in all aspects of surface quality with high speed and lower feed. The surface roughness values at the fixed end of plate are less as compared with that of mid portion and free end sides. Scanning electron microscope images show various defects such as side flow, smeared layer, microparticle, grooves and feed marks.

Hygrothermal effects on mechanical behavior of scarf repaired carbon‐epoxy laminates subject to axial compression loads: Experiment and numerical simulation

Experimental and numerical study are carried out to investigate hygrothermal effects on the mechanical behavior and damage propagation of scarf repaired carbon fiber reinforced plastic (CFRP) laminates. Experimental tests were carried out under four environment conditions: room temperature/dry, room temperature/wet, elevated temperature (95°C)/dry and elevated temperature (95°C)/wet. Results showed no decrease in compression strength after moisture absorption, whereas the reduction under elevated temperature were 15.5% and 17.2% for dry and wet specimens, respectively. Furthermore, a finite element model was developed to simulate the failure process and predict structural strength, in which moisture diffusion, hygrothermal stress analysis and progressive damage model were considered. Good agreement was achieved between the predicted compression strength and experimental results. It is revealed that the damage in the adhesive initiates adjacent to 0° plies and propagates in circumferential direction. Water absorption causes initial damage in the edge of the adhesive layer, while it does not reduce the compression strength. And elevated temperature leads to earlier damage in adhesive. After large part of the adhesive layer damaged, damages in parent laminate occur and propagate transversely to the free edge sides until the final structural collapse, which is similar with the experimental phenomenon. POLYM. COMPOS., 39:904–914, 2018. © 2016 Society of Plastics Engineers