Injoon Jang

Spectral element analysis of the axial-bending-shear coupled vibrations of composite Timoshenko beams

This article presents a spectral element model for the axially loaded axial-bending-shear coupled vibrations of composite laminated beams, which are represented by the Timoshenko beam models based on the first-order shear deformation theory. The variation approach is used to formulate the frequency-dependent spectral element matrix (often called exact dynamic stiffness matrix) for the present spectral element model. As the spectral element matrix is formulated from exact wave solutions satisfying the frequency domain governing equations of motion transformed by the use of discrete Fourier transform theory, the present spectral element model cannot only provide extremely accurate solutions with using only a minimum number of degrees of freedom but also contribute to improving the computation efficiency. The high accuracy of the present spectral element model is numerically verified by comparing its solutions with exact analytical solutions available from references as well as with the solutions obtained by conventional finite element method. The effects of the axial loading and damping are also numerically investigated. For the numerical verification, the finite element model is also provided for the axially loaded axial-bending-shear coupled composite laminated Timoshenko beams.

Nonlinear Spectral Element Model for the Blood Flow in Human Arteries

It has been well‐known that the cardiovascular diseases are closely related to the blood flow characteristics such as blood pressure and blood flow rate in a blood vessel. Thus it is very important to predict such blood flow characteristics in an accurate and efficient way. To that end, this paper develops a nonlinear one‐dimensional (1D) viscoelastic spectral element model for the blood flow in an artery with slowly varying cross‐section by using the variational approach. In this study, the mechanical behavior of the artery wall is represented by the standard solid viscoelastic model and the nonlinear spectral element model is formulated by using the frequency‐dependent dynamic shape functions which are derived from the free wave solutions to the governing differential equations in frequency‐domain. A direct iterative method is used in conjunction with the alternating frequency‐time method to obtain either frequency‐domain or time‐domain solutions from the nonlinear spectral element model.

Spectral Element Model for the Transverse Vibrations of Thin Plates

The frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) has been known to provide very accurate solutions in structural dynamics by using only a minimum number of degrees of freedom which may resolve the computation and cost problems. Thus, this paper presents a spectral element model for thin plates by using the concept of plane-waves superposition.Copyright

Spectral element modeling and analysis of the blood flows in viscoelastic vessels

Abstract As the cardiovascular diseases are closely related to the blood flow characteristics such as blood flow rates and pressures in vessels, accurate prediction of the blood flow characteristics in an efficient way has been an important research issue. In this paper, one-dimensional (1D) nonlinear spectral element model is developed by using the variational approach for the blood flows in the vessels with slowly varying cross-sections. The mechanical behavior of the vessel walls is represented by the Kelvin viscoelastic model. The nonlinear spectral element model is formulated by using the frequency-dependent dynamic shape functions which are derived from the free wave solutions to the frequency-domain governing differential equations. The direct iterative method based on an alternating frequency–time method is used to obtain frequency-domain or time-domain solutions from the nonlinear spectral element model. The nonlinear spectral element model is applied to an example artery and its high accuracy is validated by comparing with the solutions obtained by the conventional finite element method. In addition, the effects of the viscoelasticity of artery wall and the nonlinear fluid terms on the blood flow characteristics in the example artery are investigated.

Spectral Element Model for the Vibration of a Bending-Shear-Torsion Coupled Composite Timoshenko Beam

In this paper, a spectral element model is developed for axially loaded bending-shear-torsion coupled composite laminated beams. The composite laminated beams are represented by the Timoshenko beam model based on the first-order shear deformation theory. The spectral element model is formulated by using the variational method from frequency-dependent dynamic shape functions. The dynamic shape functions are derived from exact wave solutions to the governing differential equations of motion which are transformed into the frequency-domain by using the DFT theory. The numerical results show that the present spectral model provides extremely accurate natural frequencies for an example problem when compared to the results obtained by using the conventional finite element model which is also presented in this paper.Copyright