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P.v. Joshi - One of the best experts on this subject based on the ideXlab platform.
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Effect of crack location on vibration analysis of partially cracked isotropic and FGM micro-plate with non-Uniform Thickness: An analytical approach
International Journal of Mechanical Sciences, 2018Co-Authors: Ankur Gupta, N.k. Jain, R. Salhotra, P.v. JoshiAbstract:Abstract An analytical model is presented for nonlinear vibration analysis of variable Thickness, thin isotropic and functionally graded rectangular micro-plate containing a partial crack located within the centre line of the plate. Linear and parabolic Thickness variation is considered in one or both the in-plane directions of the plate. The Thickness variation is such that the volume of the plate is equal to that of the Uniform Thickness plate. The continuous line crack is parallel to one of the edges of the plate. The equations of motion are derived using the equilibrium principle based on Classical Plate Theory while the size effect is incorporated using the modified couple stress theory. The partial crack is represented by bending moment and in-plane force according to the simplified line spring model. The effect of in-plane forces is considered by employing the Berger's formulation. The derived governing equation is converted into a cubic nonlinear Duffing equation by employing Galerkin's method. The effect of nonlinearity is established by deriving the frequency response equation for the cracked variable Thickness plate using the method of multiple scales. The nonlinear frequency response curves show the phenomenon of bending hardening or softening. The influence of crack length, crack location, internal material length scale parameter, boundary conditions, gradient index, unidirectional and bidirectional taper constant on the fundamental frequency of square plate is demonstrated. Similar to Uniform Thickness plate, it is found that the presence of crack affects the vibration characteristics of variable Thickness plate. When compared to Uniform Thickness plate, the effect of crack can be reduced by varying the Thickness of the plate. Thus, it is concluded that in a given volume, it is better to employ variable Thickness plate as far as the vibration characteristics are considered.
Douglas J. Lafountain - One of the best experts on this subject based on the ideXlab platform.
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Studying Uniform Thickness II: Transversely non-simple iterated torus knots
Algebraic & Geometric Topology, 2011Co-Authors: Douglas J. LafountainAbstract:We prove that an iterated torus knot type fails the Uniform Thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot types that are transversely non-simple.
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Studying Uniform Thickness I: Legendrian simple iterated torus knots
Algebraic & Geometric Topology, 2010Co-Authors: Douglas J. LafountainAbstract:We prove that the class of topological knot types that are both Legendrian simple and satisfy the Uniform Thickness property (UTP) is closed under cabling. An immediate application is that all iterated cabling knot types that begin with negative torus knots are Legendrian simple. We also examine, for arbitrary numbers of iterations, iterated cablings that begin with positive torus knots, and establish the Legendrian simplicity of large classes of these knot types, many of which also satisfy the UTP. In so doing we obtain new necessary conditions for both the failure of the UTP and Legendrian nonsimplicity in the class of iterated torus knots, including specific conditions on knot types.
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STUDYING Uniform Thickness II: TRANSVERSALLY NON-SIMPLE ITERATED TORUS KNOTS
2009Co-Authors: Douglas J. LafountainAbstract:We prove that an iterated torus knot type fails the Uniform Thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot types that are transversally non-simple. In this paper, we continue our general study of the Uniform Thickness property (UTP) in the context of iterated torus knots that are embedded in S 3 with the standard tight contact structure. As stated in a previous paper, Studying Uniform Thickness I (L), our goal in this study is to determine the extent to which iterated torus knot types fail to satisfy the UTP, and the extent to which this failure leads to cablings that are Legendrian or transversally non-simple. Motivation for this study is due to the work of Etnyre and Honda (EH1), who showed that the failure of the UTP is a necessary condition for transversal non-simplicity in the class of iterated torus knots. They also established that the (2,3) torus knot fails the UTP and supports a transversally non-simple cabling. In (L) we extended this study of the UTP by establishing new necessary conditions for both the failure of the UTP and transversal non-simplicity in the class of iterated torus knots; in so doing we obtained new families of Legendrian simple iterated torus knots. The specific goal of this note is to fully answer the first motivating question of our study by providing a complete UTP classification of iterated torus knots, that is, determining which iterated torus knot types satisfy the UTP, and which fail the UTP. We will also address the second motivating question of our study by proving that failure of the UTP for an iterated torus knot type is a sufficient condition for the existence of transversally non-simple cablings of that knot. Specifically, we have the following two theorems and corollary:
M. H. Zarandi - One of the best experts on this subject based on the ideXlab platform.
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Deformations and Stresses of an Exponentially Graded Magneto-Electro-Elastic Non-Uniform Thickness Annular Plate Which Rotates with Variable Angular Speed
International Journal of Applied Mechanics, 2020Co-Authors: M. Saadatfar, M. H. ZarandiAbstract:In this paper, mechanical behavior of an exponentially graded magneto-electro-elastic (EGMEE) rotating annular plate with non-Uniform Thickness placed in a magnetic field is investigated. Owing to ...
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Deformations and Stresses of an Exponentially Graded Magneto-Electro-Elastic Non-Uniform Thickness Annular Plate Which Rotates with Variable Angular Speed
International Journal of Applied Mechanics, 2020Co-Authors: M. Saadatfar, M. H. ZarandiAbstract:In this paper, mechanical behavior of an exponentially graded magneto-electro-elastic (EGMEE) rotating annular plate with non-Uniform Thickness placed in a magnetic field is investigated. Owing to variable angular speed, the Lorentz force exists in both radial and circumferential directions. The Thickness of the annular plate as well as material properties are assumed to alter through the radius as an exponential function. Employing the separation of variable method, three coupled governing partial differential equations are converted to ordinary differential equations. Next, the equations are solved employing Runge–Kutta and shooting methods. Finally, the effects of angular speed variation, Thickness variation, inhomogeneity index and magnetic field are disclosed. The results demonstrate that considering angular acceleration for the annular plate has a considerable effect on the Lorentz force resulting from the magnetic field.
Hamid Nayeb-hashemi - One of the best experts on this subject based on the ideXlab platform.
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Stress analysis in functionally graded rotating disks with non-Uniform Thickness and variable angular velocity
International Journal of Mechanical Sciences, 2016Co-Authors: Yue Zheng, Hassan Bahaloo, Davood Mousanezhad, Elsadig Mahdi, Ashkan Vaziri, Hamid Nayeb-hashemiAbstract:Abstract Stress field in functionally graded (FG) rotating disks with non-Uniform Thickness and variable angular velocity is studied numerically. The elastic modulus and mass density of the disks are assumed to be varying along the radius as a power-law function of the radial coordinate, while the Poisson's ratio is kept constant. The governing equations for the stress field is derived and numerically solved using the finite difference method for the case of fixed-free boundary conditions. Additionally, the effect of material gradient index (i.e., the level of material gradation) on the stress field is evaluated. Our results show that the optimum stress field is achieved by having a Thickness profile in the form of a rational function of the radial coordinate. Moreover, a smaller stress field can be developed by having greater mass density and elastic modulus at the outer radius of the disk (i.e., ceramic-rich composites at the outer radius). The numerical results additionally reveal that deceleration results in shear-stress development within the disks where a greater deceleration leads to greater shear stress; however this has almost no effect on the radial and circumferential stresses. Furthermore, the shear stress can cause a shift in the location of the maximum Von Mises stress, where for small deceleration, maximum Von Mises stress is located somewhere between the inner and outer radii, while for large deceleration it is located at the inner radius.
Ankur Gupta - One of the best experts on this subject based on the ideXlab platform.
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Effect of crack location on vibration analysis of partially cracked isotropic and FGM micro-plate with non-Uniform Thickness: An analytical approach
International Journal of Mechanical Sciences, 2018Co-Authors: Ankur Gupta, N.k. Jain, R. Salhotra, P.v. JoshiAbstract:Abstract An analytical model is presented for nonlinear vibration analysis of variable Thickness, thin isotropic and functionally graded rectangular micro-plate containing a partial crack located within the centre line of the plate. Linear and parabolic Thickness variation is considered in one or both the in-plane directions of the plate. The Thickness variation is such that the volume of the plate is equal to that of the Uniform Thickness plate. The continuous line crack is parallel to one of the edges of the plate. The equations of motion are derived using the equilibrium principle based on Classical Plate Theory while the size effect is incorporated using the modified couple stress theory. The partial crack is represented by bending moment and in-plane force according to the simplified line spring model. The effect of in-plane forces is considered by employing the Berger's formulation. The derived governing equation is converted into a cubic nonlinear Duffing equation by employing Galerkin's method. The effect of nonlinearity is established by deriving the frequency response equation for the cracked variable Thickness plate using the method of multiple scales. The nonlinear frequency response curves show the phenomenon of bending hardening or softening. The influence of crack length, crack location, internal material length scale parameter, boundary conditions, gradient index, unidirectional and bidirectional taper constant on the fundamental frequency of square plate is demonstrated. Similar to Uniform Thickness plate, it is found that the presence of crack affects the vibration characteristics of variable Thickness plate. When compared to Uniform Thickness plate, the effect of crack can be reduced by varying the Thickness of the plate. Thus, it is concluded that in a given volume, it is better to employ variable Thickness plate as far as the vibration characteristics are considered.
