Logarithmic Function

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R C Batra - One of the best experts on this subject based on the ideXlab platform.

  • free vibration of bi directional Functionally graded material circular beams using shear deformation theory employing Logarithmic Function of radius
    Composite Structures, 2019
    Co-Authors: Jamshid Fariborz, R C Batra
    Abstract:

    Abstract Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering , e.g., stiffened floors, fuselage , railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their applications and possibly make them lighter without sacrificing strength is to comprise them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. Here, we study free vibrations of FGM circular beams by using a shear deformation theory that incorporates through-the-thickness Logarithmic variation of the circumferential displacement , does not require a shear correction factor , and has a parabolic through-the-thickness distribution of the shear strain. The radial displacement of a point is assumed to depend only upon its angular position. Thus the beam theory generalizes the Timoshenko beam theory. Equations governing transient deformations of the beam are derived by using Hamilton’s principle. Assuming a time harmonic variation of displacements, and by utilizing a generalized differential quadrature method (GDQM), the free vibration problem is reduced to solving an algebraic eigenvalue problem whose solution provides frequencies and corresponding mode shapes. Results are presented for different spatial variations of the material properties, boundary conditions, and the beam aspect ratio. It is found that frequencies of the FGM beam are bounded by those of two geometrically identical homogeneous beams composed of the two constituents of the beam. Keeping other variables fixed, the change in the beam opening angle results in very close frequencies of the first two modes of vibration at a critical value of the opening angle, a phenomenon usually called mode transition. The critical opening angle is essentially the same for radially graded, bidirectionally graded and monolithic beams. It equals about 80° (60°) for clamped-clamped (hinged-hinged) beams.

  • shear deformation theory using Logarithmic Function for thick circular beams and analytical solution for bi directional Functionally graded circular beams
    Composite Structures, 2017
    Co-Authors: Anup Pydah, R C Batra
    Abstract:

    A shear deformation theory including a Logarithmic Function in the postulated expression for the circumferential displacement is developed for thick circular beams and is used to analytically solve static deformations of bi-directional Functionally graded circular beams. The consideration of a Logarithmic term is motivated by the displacement field in the analytical solution of the plane strain elasticity problem of a hollow circular cylindrical shell. The non-zero shear traction boundary conditions at the two major surfaces of the beam are a priori satisfied by the assumed displacement field. The material properties are assumed to vary according to exponential and power laws, respectively, in the tangential and the thickness directions. Parametric studies conducted for the variation of stresses and displacements indicate that material properties can be tailored to satisfy several structural constraints. For the bending of a sandwich beam with a bi-directionally graded core and homogeneous isotropic facesheets, it is found that the maximum interfacial bending stress, the peak interfacial shear stress and the maximum interfacial peeling stress can be reduced, respectively, by 20%, 44% and 42%.

Yuanping Li - One of the best experts on this subject based on the ideXlab platform.

  • modular design and implementation of fpga based tap selective maximum likelihood channel estimator
    WSEAS Transactions on Signal Processing archive, 2008
    Co-Authors: Jengkuang Hwang, Yuanping Li
    Abstract:

    The modular design of the optimal tap-selective maximum-likelihood (TSML) channel estimator based on field-programmable gate array (FPGA) technology is studied. A novel range reduction algorithm is included in the natural Logarithmic Function (NLF) emulator based on the coordinate rotation digital computer (CORDIC) methodology and is integrated into the TSML channel estimator system. The low-complexity TSML algorithm, which is employed for sparse multipath channel estimation, is proposed for long-range broadband block transmission systems. Furthermore, the proposed range reduction algorithm aims to solve the limited interval problem in the CORDIC algorithm base on Xilinx's SG platforms. The modular approach facilitates the reuse of modules.

  • modular design and implementation of fpga based tap selective maximum likelihood channel estimator
    IEEE International Conference on Circuits and Systems for Communications, 2008
    Co-Authors: Jengkuang Hwang, Yuanping Li
    Abstract:

    The modular design of the optimal tap-selective maximum-likelihood (TS-ML) channel estimator based on field- programmable gate array (FPGA) technology is studied. A novel range reduction algorithm is included in the natural Logarithmic Function (NLF) emulator based on the coordinate rotation digital computer (CORDIC) methodology and is integrated into the TS- L channel estimator system. The low-complexity TSML algorithm, which is employed for sparse multipath channel estimation, is proposed for long-range broadband block transmission systems. Furthermore, the proposed range reduction algorithm aims to solve the limited interval problem in the CORDIC algorithm. The modular approach facilitates the reuse of modules.

Jengkuang Hwang - One of the best experts on this subject based on the ideXlab platform.

  • modular design and implementation of fpga based tap selective maximum likelihood channel estimator
    WSEAS Transactions on Signal Processing archive, 2008
    Co-Authors: Jengkuang Hwang, Yuanping Li
    Abstract:

    The modular design of the optimal tap-selective maximum-likelihood (TSML) channel estimator based on field-programmable gate array (FPGA) technology is studied. A novel range reduction algorithm is included in the natural Logarithmic Function (NLF) emulator based on the coordinate rotation digital computer (CORDIC) methodology and is integrated into the TSML channel estimator system. The low-complexity TSML algorithm, which is employed for sparse multipath channel estimation, is proposed for long-range broadband block transmission systems. Furthermore, the proposed range reduction algorithm aims to solve the limited interval problem in the CORDIC algorithm base on Xilinx's SG platforms. The modular approach facilitates the reuse of modules.

  • modular design and implementation of fpga based tap selective maximum likelihood channel estimator
    IEEE International Conference on Circuits and Systems for Communications, 2008
    Co-Authors: Jengkuang Hwang, Yuanping Li
    Abstract:

    The modular design of the optimal tap-selective maximum-likelihood (TS-ML) channel estimator based on field- programmable gate array (FPGA) technology is studied. A novel range reduction algorithm is included in the natural Logarithmic Function (NLF) emulator based on the coordinate rotation digital computer (CORDIC) methodology and is integrated into the TS- L channel estimator system. The low-complexity TSML algorithm, which is employed for sparse multipath channel estimation, is proposed for long-range broadband block transmission systems. Furthermore, the proposed range reduction algorithm aims to solve the limited interval problem in the CORDIC algorithm. The modular approach facilitates the reuse of modules.

Anup Pydah - One of the best experts on this subject based on the ideXlab platform.

  • shear deformation theory using Logarithmic Function for thick circular beams and analytical solution for bi directional Functionally graded circular beams
    Composite Structures, 2017
    Co-Authors: Anup Pydah, R C Batra
    Abstract:

    A shear deformation theory including a Logarithmic Function in the postulated expression for the circumferential displacement is developed for thick circular beams and is used to analytically solve static deformations of bi-directional Functionally graded circular beams. The consideration of a Logarithmic term is motivated by the displacement field in the analytical solution of the plane strain elasticity problem of a hollow circular cylindrical shell. The non-zero shear traction boundary conditions at the two major surfaces of the beam are a priori satisfied by the assumed displacement field. The material properties are assumed to vary according to exponential and power laws, respectively, in the tangential and the thickness directions. Parametric studies conducted for the variation of stresses and displacements indicate that material properties can be tailored to satisfy several structural constraints. For the bending of a sandwich beam with a bi-directionally graded core and homogeneous isotropic facesheets, it is found that the maximum interfacial bending stress, the peak interfacial shear stress and the maximum interfacial peeling stress can be reduced, respectively, by 20%, 44% and 42%.

Jamshid Fariborz - One of the best experts on this subject based on the ideXlab platform.

  • free vibration of bi directional Functionally graded material circular beams using shear deformation theory employing Logarithmic Function of radius
    Composite Structures, 2019
    Co-Authors: Jamshid Fariborz, R C Batra
    Abstract:

    Abstract Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering , e.g., stiffened floors, fuselage , railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their applications and possibly make them lighter without sacrificing strength is to comprise them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. Here, we study free vibrations of FGM circular beams by using a shear deformation theory that incorporates through-the-thickness Logarithmic variation of the circumferential displacement , does not require a shear correction factor , and has a parabolic through-the-thickness distribution of the shear strain. The radial displacement of a point is assumed to depend only upon its angular position. Thus the beam theory generalizes the Timoshenko beam theory. Equations governing transient deformations of the beam are derived by using Hamilton’s principle. Assuming a time harmonic variation of displacements, and by utilizing a generalized differential quadrature method (GDQM), the free vibration problem is reduced to solving an algebraic eigenvalue problem whose solution provides frequencies and corresponding mode shapes. Results are presented for different spatial variations of the material properties, boundary conditions, and the beam aspect ratio. It is found that frequencies of the FGM beam are bounded by those of two geometrically identical homogeneous beams composed of the two constituents of the beam. Keeping other variables fixed, the change in the beam opening angle results in very close frequencies of the first two modes of vibration at a critical value of the opening angle, a phenomenon usually called mode transition. The critical opening angle is essentially the same for radially graded, bidirectionally graded and monolithic beams. It equals about 80° (60°) for clamped-clamped (hinged-hinged) beams.