Jooyong Cho

Modal spectral element formulation for axially moving plates subjected to in-plane axial tension

The use of frequency-dependent spectral element matrix (or dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the modal spectral element is formulated for thin plates moving with constant speed under a uniform in-plane axial tension. The concept of the Kantorovich method is used to formulate the modal spectral element matrix in the frequency-domain. The present modal spectral element is then evaluated by comparing its solutions with exact analytical solutions as well as with FEM solutions. The effects of the moving speed and the in-plane tension on the dynamic characteristics of a moving plate are investigated numerically.

An FFT-based spectral analysis method for linear discrete dynamic systems with non-proportional damping

This paper proposes a fast Fourier transforms (FFT)-based spectral analysis method for the dynamic analysis of linear discrete dynamic systems which have non-proportional viscous damping and are subjected to non-zero initial conditions. To evaluate the proposed FFT-based spectral analysis method, the forced vibration of a three degree-of-freedom (DOF) system is considered as an illustrative problem. The accuracy of the proposed FFT-based spectral analysis method is evaluated by comparing the forced vibration responses obtained by the present FFT-based spectral analysis method with those obtained by using the well-known Runge-Kutta method and modal analysis method.

Spectral element analysis for an axially moving viscoelastic beam

In this paper, a spectral element model is derived for the axially moving viscoelastic beams subject to axial tension. The viscoelastic material is represented in a general form by using the one-dimensional constitutive equation of hereditary integral type. The high accuracy of the present spectral element model is verified first by comparing the eigenvalues obtained by the present spectral element model with those obtained by using the conventional finite element model as well as with the exact analytical solutions. The effects of viscoelasticity and moving speed on the dynamics of moving beams are then numerically investigated.

A Frequency Response Function-Based Damage Identification Method for Cylindrical Shell Structures

In this paper, a structural damage identification method (SDIM) is developed for cylindrical shells and the numerically simulated damage identification tests are conducted to study the feasibility of the proposed SDIM. The SDIM is derived from the frequency response function solved from the structural dynamic equations of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of the local damages within a cylindrical shell. In contrast with most existing modal parameters-based SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM requires only the FRF-data measured in the damaged state. By virtue of utilizing FRF-data, one is able to make the inverse problem of damage identification well-posed by choosing as many sets of excitation frequency and FRF measurement point as needed to obtain a sufficient number of equations.

Spectral Element Analysis of the Continuum Systems with Arbitrary Initial Conditions

In this paper, an FFT-based spectral element method (SEM) is introduced for the linear continuum dynamic systems subjected to arbitrary, non-zero initial conditions. In the FFTbased SEM, the original equations of motion subjected to arbitrary initial conditions are transformed into a new set of equations of motion subjected to completely null initial conditions by using the pseudo-forces method so that the conventional spectral element analysis can be applied to obtain desired dynamic responses. A simply supported beam and a cantilevered beam are considered as the illustrative problems to evaluate the FFT-based SEM. The dynamic responses obtained by using the FFT-based SEM are shown to be in a good agreement with the analytical solutions obtained by using the mode superposition method.

Vibration Analysis of the Pipeline with Internal Unsteady Fluid Flow by Using Spectral Element Method

In this paper, a spectral element model is developed for the uniform straight pipelines conveying internal unsteady fluid flow. The spectral element matrix is formulated by using the exact frequency-domain solutions of the pipe-dynamics equations. The spectral element dynamic analysis is then conducted to evaluate the accuracy of the present spectral element model and to investigate the vibration characteristics and internal fluid characteristics of an example pipeline system.

SPECTRAL ELEMENT DYNAMIC ANALYSIS OF THE PIPELINE CONVEYING INTERNAL UNSTEADY FLOW

In this paper, a spectral element model is developed for the uniform straight pipelines conveying internal unsteady fluid. Four coupled pipe-dynamics equa- tions are derived first by using the Hamiltons princi- ple and the mechanics of fluid, in which the fluid pressure and velocity of the internal flow as well as the transverse and axial displacements of the pipeline are all treated as the dependent variables. The spec- tral element matrix is then formulated by using the exact frequency-domain solutions of the pipe- dynamics equations. The spectral element dynamic analyses are conducted to evaluate the accuracy of the present spectral element model and to investigate the vibration characteristics and internal fluid tran- sients of an example pipeline system.

A Forced Vibration Response-Based Damage Identification Method for Cylindrical Shells

This paper presents a feasibility study on a structural damage identification method (SDIM) developed herein for cylindrical shells. The SDIM is derived directly from the governing differential equations of motion of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of local damages within a cylindrical shell. In contrast with most of existing modal parameters-based SDIMs, which requires only model parameters measured in both intact and damaged states, the present SDIM utilizes the FRF-data in the damaged state instead of the modal parameters in the damaged state. By virtue of utilizing FRF-data, a sufficient number of equations can be derived by choosing as many sets of excitation frequency and FRF measurement point as needed. The feasibility of the present SDIM is numerically tested through some illustrative examples, taking into account the random noises in FRF-data.Copyright

Dynamics of an Axially Moving Viscoelastic Beam Subject to Axial Tension

In this paper, a spectral element model is derived for the dynamics and stability analyses of the axially moving viscoelastic beams subject to axial tension. The viscoelastic material is represented in a general form by using the one-dimensional constitutive equation of hereditary integral type. The high accuracy of the present spectral element model is verified first by comparing the eigenvalues obtained by the present spectral element model with those obtained by using the conventional finite element model as well as with the exact analytical solutions. The effects of viscoelasticity and moving speed on the dynamics and stability of moving beams are numerically investigated. 2004 Elsevier Ltd. All rights reserved.