Author: Osman Kartav
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
Book Description
In this study, in-plane free vibration characteristics of rotating curved beams are investigated by Finite Difference Method and Finite Element Method since the mathematical model of the present problem is based on the differential eigenvalue problem with variable coefficients. A computer program regarding the titled problem is developed in Mathematica and this program is verified by using results available in the literature. The effects of taper parameters of the curved beam and rotation speed on natural frequencies are investigated.
Vibration Analysis of Rotating Curved Beams with Variable Cross-section
Author: Osman Kartav
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
Book Description
In this study, in-plane free vibration characteristics of rotating curved beams are investigated by Finite Difference Method and Finite Element Method since the mathematical model of the present problem is based on the differential eigenvalue problem with variable coefficients. A computer program regarding the titled problem is developed in Mathematica and this program is verified by using results available in the literature. The effects of taper parameters of the curved beam and rotation speed on natural frequencies are investigated.
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
Book Description
In this study, in-plane free vibration characteristics of rotating curved beams are investigated by Finite Difference Method and Finite Element Method since the mathematical model of the present problem is based on the differential eigenvalue problem with variable coefficients. A computer program regarding the titled problem is developed in Mathematica and this program is verified by using results available in the literature. The effects of taper parameters of the curved beam and rotation speed on natural frequencies are investigated.
Free Vibration Analysis of Curved Beams with Variable Cross-sections on Elastic Foundations
Author: Ümit Okan Yazıcı
Publisher:
ISBN:
Category : Elasticity
Languages : en
Pages : 52
Book Description
Free out of plane vibration characteristics of curved beams with variable cross-sections on elastic foundations are studied by TMM (Transfer Matrix Method) since the mathematical model of the present system based on the coupled differential eigenvalue problem with variable coefficients which can not be solved easily by exact methods. Vibrations of beams on different elastic foundations are reviewed. Out of plane vibration of curved beams on different elastic foundations are investigated. TMM is detailed with its applications to vibration problems. To solve the vibration problems, TMM is examined with several computer programs developed in Mathematica. The accuracy of the TMM results obtained from the developed program is evaluated by comparing with FEM results found from model created in ANSYS. Finally, the effects of the variation of cross-section of the curved beams and elastic foundation parameters on natural frequencies are investigated.
Publisher:
ISBN:
Category : Elasticity
Languages : en
Pages : 52
Book Description
Free out of plane vibration characteristics of curved beams with variable cross-sections on elastic foundations are studied by TMM (Transfer Matrix Method) since the mathematical model of the present system based on the coupled differential eigenvalue problem with variable coefficients which can not be solved easily by exact methods. Vibrations of beams on different elastic foundations are reviewed. Out of plane vibration of curved beams on different elastic foundations are investigated. TMM is detailed with its applications to vibration problems. To solve the vibration problems, TMM is examined with several computer programs developed in Mathematica. The accuracy of the TMM results obtained from the developed program is evaluated by comparing with FEM results found from model created in ANSYS. Finally, the effects of the variation of cross-section of the curved beams and elastic foundation parameters on natural frequencies are investigated.
Out-of-plane Vibrations of Planar Curved Beams Having Variable Curvature and Cross-section
Author: Kaan Kaygısız
Publisher:
ISBN:
Category : Girders
Languages : en
Pages : 68
Book Description
In this study, out of plane vibration characteristics of curved beams having variable curvatures and cross-sections are studied by FDM (Finite Difference Method). The effects of curvature and cross-section of the curved beam on natural frequencies are investigated for the curved beams having; variable curvature & constant cross-section and variable curvature & variable cross-section. Mathematical model of the present problem is based on the coupled differential eigenvalue problem with variable coefficients. Numerical solutions of the problem in this study are obtained by the computer program developed in Mathematica. The accuracy of the present results obtained from the developed program is evaluated by comparing with FEM (Finite Element Method) results found from solid model created in ANSYS. Good agreement is obtained in the comparisons of the present results with other results. All results are presented in tabular and graphical forms.
Publisher:
ISBN:
Category : Girders
Languages : en
Pages : 68
Book Description
In this study, out of plane vibration characteristics of curved beams having variable curvatures and cross-sections are studied by FDM (Finite Difference Method). The effects of curvature and cross-section of the curved beam on natural frequencies are investigated for the curved beams having; variable curvature & constant cross-section and variable curvature & variable cross-section. Mathematical model of the present problem is based on the coupled differential eigenvalue problem with variable coefficients. Numerical solutions of the problem in this study are obtained by the computer program developed in Mathematica. The accuracy of the present results obtained from the developed program is evaluated by comparing with FEM (Finite Element Method) results found from solid model created in ANSYS. Good agreement is obtained in the comparisons of the present results with other results. All results are presented in tabular and graphical forms.
Vibrations of Variable Cross-section Curved Beams
Vibration Analysis of Pre-twisted Rotating Beams
Author: Tolga Yıldırım
Publisher:
ISBN:
Category :
Languages : en
Pages : 94
Book Description
A new linearly pretwisted rotating Timoshenko beam element, which has two nodes and four degrees of freedom per node, is developed and subsequently used for vibration analysis of pretwisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pretwisted beams. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pretwisted rotating Timoshenko beams are obtained and compared with previously published both theoretical and experimental results to confirm the accuracy and efficiency of the present model. The new pretwisted Timoshenko beam element has good convergence characteristics and excellent agreement is found with the previous studies.
Publisher:
ISBN:
Category :
Languages : en
Pages : 94
Book Description
A new linearly pretwisted rotating Timoshenko beam element, which has two nodes and four degrees of freedom per node, is developed and subsequently used for vibration analysis of pretwisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pretwisted beams. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pretwisted rotating Timoshenko beams are obtained and compared with previously published both theoretical and experimental results to confirm the accuracy and efficiency of the present model. The new pretwisted Timoshenko beam element has good convergence characteristics and excellent agreement is found with the previous studies.
Out of Plane Vibration of Curved Beams
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
A very thin circular curved beam is analyzed for its natural frequency in this project. Only out of plane vibrations are considered in this project. The stiffness matrix and mass matrix are derived from the strain energy and kinetic energy. This is done with the help of natural shape functions. The derivations are done in local coordinate system or Global Cartesian coordinate system. The out of plane deformations considered are the rigid body displacement of the centre of curvature in the axial direction, the rigid body rotation about the centre of curvature in the radial direction, and the rigid body rotation about the centre of curvature in the circumferential direction at the mid cross section.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
A very thin circular curved beam is analyzed for its natural frequency in this project. Only out of plane vibrations are considered in this project. The stiffness matrix and mass matrix are derived from the strain energy and kinetic energy. This is done with the help of natural shape functions. The derivations are done in local coordinate system or Global Cartesian coordinate system. The out of plane deformations considered are the rigid body displacement of the centre of curvature in the axial direction, the rigid body rotation about the centre of curvature in the radial direction, and the rigid body rotation about the centre of curvature in the circumferential direction at the mid cross section.
Anisotropic Doubly-Curved Shells
Author: Francesco Tornabene
Publisher: Società Editrice Esculapio
ISBN: 8835328993
Category : Technology & Engineering
Languages : en
Pages : 1199
Book Description
This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.
Publisher: Società Editrice Esculapio
ISBN: 8835328993
Category : Technology & Engineering
Languages : en
Pages : 1199
Book Description
This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.
Non-classical Vibrations of Arches and Beams
Author: Igorʹ Alekseevich Karnovskiĭ
Publisher: McGraw-Hill Professional Publishing
ISBN:
Category : Science
Languages : en
Pages : 266
Book Description
The demand for complex, high technology structures has increased the required accuracy of structural calculations. This in-depth reference covers solutions to the crucial vibration problems of beam and arch design. It covers: vibration analysis, compressive loads, elastic foundations, and more; transverse vibration equations; dynamics of deformable systems; and optimal designed beams.
Publisher: McGraw-Hill Professional Publishing
ISBN:
Category : Science
Languages : en
Pages : 266
Book Description
The demand for complex, high technology structures has increased the required accuracy of structural calculations. This in-depth reference covers solutions to the crucial vibration problems of beam and arch design. It covers: vibration analysis, compressive loads, elastic foundations, and more; transverse vibration equations; dynamics of deformable systems; and optimal designed beams.
Vibration of Continuous Systems
Author: Singiresu S. Rao
Publisher: John Wiley & Sons
ISBN: 1119424143
Category : Technology & Engineering
Languages : en
Pages : 816
Book Description
A revised and up-to-date guide to advanced vibration analysis written by a noted expert The revised and updated second edition of Vibration of Continuous Systems offers a guide to all aspects of vibration of continuous systems including: derivation of equations of motion, exact and approximate solutions and computational aspects. The author—a noted expert in the field—reviews all possible types of continuous structural members and systems including strings, shafts, beams, membranes, plates, shells, three-dimensional bodies, and composite structural members. Designed to be a useful aid in the understanding of the vibration of continuous systems, the book contains exact analytical solutions, approximate analytical solutions, and numerical solutions. All the methods are presented in clear and simple terms and the second edition offers a more detailed explanation of the fundamentals and basic concepts. Vibration of Continuous Systems revised second edition: Contains new chapters on Vibration of three-dimensional solid bodies; Vibration of composite structures; and Numerical solution using the finite element method Reviews the fundamental concepts in clear and concise language Includes newly formatted content that is streamlined for effectiveness Offers many new illustrative examples and problems Presents answers to selected problems Written for professors, students of mechanics of vibration courses, and researchers, the revised second edition of Vibration of Continuous Systems offers an authoritative guide filled with illustrative examples of the theory, computational details, and applications of vibration of continuous systems.
Publisher: John Wiley & Sons
ISBN: 1119424143
Category : Technology & Engineering
Languages : en
Pages : 816
Book Description
A revised and up-to-date guide to advanced vibration analysis written by a noted expert The revised and updated second edition of Vibration of Continuous Systems offers a guide to all aspects of vibration of continuous systems including: derivation of equations of motion, exact and approximate solutions and computational aspects. The author—a noted expert in the field—reviews all possible types of continuous structural members and systems including strings, shafts, beams, membranes, plates, shells, three-dimensional bodies, and composite structural members. Designed to be a useful aid in the understanding of the vibration of continuous systems, the book contains exact analytical solutions, approximate analytical solutions, and numerical solutions. All the methods are presented in clear and simple terms and the second edition offers a more detailed explanation of the fundamentals and basic concepts. Vibration of Continuous Systems revised second edition: Contains new chapters on Vibration of three-dimensional solid bodies; Vibration of composite structures; and Numerical solution using the finite element method Reviews the fundamental concepts in clear and concise language Includes newly formatted content that is streamlined for effectiveness Offers many new illustrative examples and problems Presents answers to selected problems Written for professors, students of mechanics of vibration courses, and researchers, the revised second edition of Vibration of Continuous Systems offers an authoritative guide filled with illustrative examples of the theory, computational details, and applications of vibration of continuous systems.