Ilwook Park

Dynamics and guided waves in a smart Timoshenko beam with lateral contraction

Surface-bonded wafer-type piezoelectric transducers (PZTs) have been widely used to excite or measure ultrasonic guided waves for the structural health monitoring of thin-walled structures. For successful prediction of the dynamics and ultrasonic guided waves, it is essential to use very reliable computational models for the PZT-bonded multi-layer smart structures. In this paper, the spectral element model is developed for two-layer smart beams which consist of a metallic base beam layer and a PZT layer. Axial-bending-shear-contraction coupled equations of motion and boundary conditions are derived by using Hamiltons principle with Lagrange multipliers based on the Timoshenko beam theory and Mindlin–Herrmann rod theory. The high accuracy of this spectral element model is verified in due course and the effects of a lateral contraction on the dynamics and guided wave characteristics of the example smart beams are investigated by using this spectral element model. In addition, the constraint forces at the interface between the base beam and the PZT layer are also investigated via Lagrange multipliers.

Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: () the boundary splitting and () the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

Transverse Vibration and Waves in a Membrane: Frequency Domain Spectral Element Modeling and Analysis

Although the spectral element method (SEM) has been well recognized as an exact continuum element method, its application has been limited mostly to one-dimensional (1D) structures, or plates that can be transformed into 1D-like problems by assuming the displacements in one direction of the plate in terms of known functions. We propose a spectral element model for the transverse vibration of a finite membrane subjected to arbitrary boundary conditions. The proposed model is developed by using the boundary splitting method and the waveguide FEM-based spectral super element method in combination. The performance of the proposed spectral element model is numerically validated by comparison with exact solutions and solutions using the standard finite element method (FEM).

Static and Dynamic Interfacial Stresses Analysis for Three-Layer Beam Structures Using Spectral Element Method

As the structural integrity at the interfaces of a three-layer structure certainly depends on the shear and normal (peeling) stress concentrations near the free ends of the cover plate, it is very important to predict the static and dynamic interfacial stresses in an accurate and efficient way for successful designs of three-layer beam-type structures subject to various loading conditions. Thus, this paper presents a frequency-domain spectral element method by which both static and dynamic interfacial stresses can be accurately predicted. To that end, the governing equations of motion for three-layer beam-type structures are derived by using Hamiltons principle and then the spectral element model is formulated in the frequency domain by using the variational method. The high accuracy of the present spectral element model is verified in due course. Numerical studies are then conducted to investigate static and dynamic interfacial stresses for an example three-layer beam subjected to various loadings.

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

A Method of Lamb-Wave Modes Decomposition for Structural Health Monitoring

Lamb waves have received a great attention in the structural health monitoring (SHM) societies because they can propagate over relatively large distances in wave guides such as thin plates and shells. The time-of-flights of Lamb waves can be used to detect damages in a wave guide. However, due to the inherent dispersive and multi-mode characteristics of Lamb waves, one must decompose the Lamb wave modes into the symmetric and anti-symmetric modes for SHM applications. Thus, this paper proposes a decomposition method for the two-mode Lamb waves based on two rules: the group velocity ratio rule and the mode amplitude ratio rule. The group velocity ratio rule means that the ratio of the group velocities of fundamental symmetric and anti-symmetric modes is constant, while the mode amplitude ratio rule means that the magnitude of the fundamental symmetric modes of all measured response signals should be always larger than those of the anti-symmetric mode once the input signal is applied so that the magnitude of fundamental symmetric mode of excited Lamb-wave is larger than that of anti-symmetric mode, and vice versa. The proposed method is verified through the experiments ducted for an aluminum plate specimen.

An approximate spectral element model for the dynamic analysis of an FGM bar in axial vibration

As FGM (functionally graded material) bars which vibrate in axial or longitudinal direction have great potential for applications in diverse engineering fields, developing a reliable mathematical model that provides very reliable vibration and wave characteristics of a FGM axial bar, especially at high frequencies, has been an important research issue during last decades. Thus, as an extension of the previous works (Hong et al. 2014, Hong and Lee 2015) on three-layered FGM axial bars (hereafter called FGM bars), an enhanced spectral element model is proposed for a FGM bar model in which axial and radial displacements in the radial direction are treated more realistic by representing the inner FGM layer by multiple sub-layers. The accuracy and performance of the proposed enhanced spectral element model is evaluated by comparison with the solutions obtained by using the commercial finite element package ANSYS. The proposed enhanced spectral element model is also evaluated by comparison with the author