This paper details the creation of a device capable of generating a powerful and consistent static magnetic field. This apparatus serves the purpose of quantifying the magnetostrictive strain found in materials like a...This paper details the creation of a device capable of generating a powerful and consistent static magnetic field. This apparatus serves the purpose of quantifying the magnetostrictive strain found in materials like annealed cobalt ferrite and Terfenol-D, specifically those shaped as cylindrical rods. In our investigation, the use of static magnetic fields proves most advantageous. This choice is made to mitigate the generation of eddy currents, which would inevitably occur if the magnetic field intensity were varied. The fundamental idea behind this design involves employing a C-shaped iron core constructed from low-carbon mild steel. On this core, three coils are mounted, each capable of producing one-third of the required 9000 Oersted (Oe) magnetic field strength. The test specimen is situated within the “jaws” of the C-shaped core, thus completing the magnetic circuit. To manage the heat generated by each coil, a cooling system consisting of copper tubes is employed. These tubes facilitate the flow of air to dissipate the heat. To model and predict the magnetic field strength produced by the coils, finite element analysis (FEMM) software is utilized, and the results align closely with the anticipated outcomes. This design effectively generates a robust and unchanging magnetic field measuring a stable 9000 Oe in total. Consequently, this equipment finds utility in characterizing the magnetic properties of specific materials.展开更多
This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation the...This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.展开更多
文摘This paper details the creation of a device capable of generating a powerful and consistent static magnetic field. This apparatus serves the purpose of quantifying the magnetostrictive strain found in materials like annealed cobalt ferrite and Terfenol-D, specifically those shaped as cylindrical rods. In our investigation, the use of static magnetic fields proves most advantageous. This choice is made to mitigate the generation of eddy currents, which would inevitably occur if the magnetic field intensity were varied. The fundamental idea behind this design involves employing a C-shaped iron core constructed from low-carbon mild steel. On this core, three coils are mounted, each capable of producing one-third of the required 9000 Oersted (Oe) magnetic field strength. The test specimen is situated within the “jaws” of the C-shaped core, thus completing the magnetic circuit. To manage the heat generated by each coil, a cooling system consisting of copper tubes is employed. These tubes facilitate the flow of air to dissipate the heat. To model and predict the magnetic field strength produced by the coils, finite element analysis (FEMM) software is utilized, and the results align closely with the anticipated outcomes. This design effectively generates a robust and unchanging magnetic field measuring a stable 9000 Oe in total. Consequently, this equipment finds utility in characterizing the magnetic properties of specific materials.
文摘This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.
