scholarly journals Dynamic Finite Element Analysis of Bending-Torsion Coupled Beams Subjected to Combined Axial Load and End Moment

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Nonlinear Eigenvalue Problem ◽  
Analytical Data ◽  
Compressive Force ◽  
Weighted Residual Method ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Dynamic Finite Element ◽  
Coupled Beams

The dynamic analysis of prestressed, bending-torsion coupled beams is revisited. The axially loaded beam is assumed to be slender, isotropic, homogeneous, and linearly elastic, exhibiting coupled flexural-torsional displacement caused by the end moment. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the vibration and stability of such beams are explored. Using the closed-form solutions of the uncoupled portions of the governing equations as the basis functions of approximation space, the dynamic, frequency-dependent, interpolation functions are developed, which are then used in conjunction with the weighted residual method to develop the Dynamic Finite Element (DFE) of the system. Having implemented the DFE in a MATLAB-based code, the resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies of illustrative beam examples, subjected to various boundary and load conditions. The proposed method is validated against limited available experimental and analytical data, those obtained from an in-house conventional Finite Element Method (FEM) code and FEM-based commercial software (ANSYS). In comparison with FEM, the DFE exhibits higher convergence rates and in the absence of end moment it produces exact results. Buckling analysis is also carried out to determine the critical end moment and compressive force for various load combinations.

scholarly journals Dynamic finite element analysis of bending-torsion coupled beams subjected to combined axial load and end moment

2021 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Nonlinear Eigenvalue Problem ◽  
Analytical Data ◽  
Compressive Force ◽  
Weighted Residual Method ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Dynamic Finite Element ◽  
Coupled Beams

The dynamic analysis of prestressed, bending-torsion coupled beams is revisited. The axially loaded beam is assumed to be slender, isotropic, homogeneous, and linearly elastic, exhibiting coupled flexural-torsional displacement caused by the end moment. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the vibration and stability of such beams are explored. Using the closed-form solutions of the uncoupled portions of the governing equations as the basis functions of approximation space, the dynamic, frequency-dependent, interpolation functions are developed, which are then used in conjunction with the weighted residual method to develop the Dynamic Finite Element (DFE) of the system. Having implemented the DFE in a MATLAB based code, the resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies of illustrative beam examples, subjected to various boundary and load conditions. The proposed method is validated against limited available experimental and analytical data, those obtained from an in-house conventional Finite Element Method (FEM) code and FEMbased commercial software (ANSYS). In comparison with FEM, the DFE exhibits higher convergence rates and in the absence of end moment it produces exact results. Buckling analysis is also carried out to determine the critical end moment and compressive force for various load combinations.

scholarly journals Dynamic finite element analysis of bending-torsion coupled beams subjected to combined axial load and end moment

2021 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Nonlinear Eigenvalue Problem ◽  
Analytical Data ◽  
Compressive Force ◽  
Weighted Residual Method ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Dynamic Finite Element ◽  
Coupled Beams

The dynamic analysis of prestressed, bending-torsion coupled beams is revisited. The axially loaded beam is assumed to be slender, isotropic, homogeneous, and linearly elastic, exhibiting coupled flexural-torsional displacement caused by the end moment. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the vibration and stability of such beams are explored. Using the closed-form solutions of the uncoupled portions of the governing equations as the basis functions of approximation space, the dynamic, frequency-dependent, interpolation functions are developed, which are then used in conjunction with the weighted residual method to develop the Dynamic Finite Element (DFE) of the system. Having implemented the DFE in a MATLAB based code, the resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies of illustrative beam examples, subjected to various boundary and load conditions. The proposed method is validated against limited available experimental and analytical data, those obtained from an in-house conventional Finite Element Method (FEM) code and FEMbased commercial software (ANSYS). In comparison with FEM, the DFE exhibits higher convergence rates and in the absence of end moment it produces exact results. Buckling analysis is also carried out to determine the critical end moment and compressive force for various load combinations.

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

scholarly journals Triply Coupled Bending-Bending-Torsion Vibrational Analysis of Rotating Beams Using Fem and Dynamic Finite Element Formulation

2021 ◽  
Author(s):  
Mohammad Shavezipur
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Convergence Rates ◽  
Equations Of Motion ◽  
Vibrational Analysis ◽  
Element Formulation ◽  
Shape Functions ◽  
Weighted Residual Method ◽  
Torsion Beam ◽  
Dynamic Finite Element

This research presents the numerical analysis of the triply coupled flap-wise, cord-wise and torsional vibrations of flexible rotating blades. Euler-Bernoulli bending and St. Venant torsion beam theories are considered to derive the governing differential equations of motion. Based on Finite Element Methodology (FEM), the cubic "Hermite" shape functions are implemented where the solution of the equations results in a linear engine problem. Then, the Dynamic (frequency dependent) Trigonometric Shape Functions (DISF's) for beam's uncoupled displacements are derived. The application of the Dynamic Finite Element (DFE) approach to the solution of the governing equations is then presented. The DFE formulation, based on the weighted residual method and the DTSF's results in a nonlinear engine problem representing eigenvalues and engine modes of the system. The applicability of the DFE method is then demonstrated by illustrative examples, where a Wittrick-Williams root counting technique is used to find the system's natural frequencies. The DFE approach, an intermediate method between FEM and "Exact" formulation, is characterized by higher convergence rates, and can be advantageously used when multiple natural frequencies and/or higher modes of beam-like structures are to be evaluated.

scholarly journals Triply Coupled Bending-Bending-Torsion Vibrational Analysis of Rotating Beams Using Fem and Dynamic Finite Element Formulation

2021 ◽  
Author(s):  
Mohammad Shavezipur
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Convergence Rates ◽  
Equations Of Motion ◽  
Vibrational Analysis ◽  
Element Formulation ◽  
Shape Functions ◽  
Weighted Residual Method ◽  
Torsion Beam ◽  
Dynamic Finite Element

This research presents the numerical analysis of the triply coupled flap-wise, cord-wise and torsional vibrations of flexible rotating blades. Euler-Bernoulli bending and St. Venant torsion beam theories are considered to derive the governing differential equations of motion. Based on Finite Element Methodology (FEM), the cubic "Hermite" shape functions are implemented where the solution of the equations results in a linear engine problem. Then, the Dynamic (frequency dependent) Trigonometric Shape Functions (DISF's) for beam's uncoupled displacements are derived. The application of the Dynamic Finite Element (DFE) approach to the solution of the governing equations is then presented. The DFE formulation, based on the weighted residual method and the DTSF's results in a nonlinear engine problem representing eigenvalues and engine modes of the system. The applicability of the DFE method is then demonstrated by illustrative examples, where a Wittrick-Williams root counting technique is used to find the system's natural frequencies. The DFE approach, an intermediate method between FEM and "Exact" formulation, is characterized by higher convergence rates, and can be advantageously used when multiple natural frequencies and/or higher modes of beam-like structures are to be evaluated.

Nonlinear Dynamic Response of Buoys under the Collision Load with Ships

2012 ◽  
Vol 204-208 ◽  
pp. 4455-4459 ◽  
Author(s):  
Liu Hong Chang ◽  
Chang Bo Jiang ◽  
Man Jun Liao ◽  
Xiong Xiao
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Analysis Software ◽  
Element Analysis ◽  
Nonlinear Dynamic Response ◽  
Dynamic Finite Element ◽  
Simulation Results ◽  
Collision Force ◽  
Explicit Dynamic ◽  
Element Theory

The explicit dynamic finite element theory is applied on the collision of ships with buoys for computer simulation. Using ANSYS/LS-DYNA finite element analysis software, the numerical simulation of the collision between the ton ship and the buoy with different structures and impact points. The collision force, deformation, displacement parameters and the weak impact points of a buoy are obtained. Based on the numerical simulation results, analysis of buoys and structural collision damages in anti-collision features are discussed, and several theoretical sugestions in anti-collision for the design of buoy are provided.

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