Abstract
A frequency-domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time-domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM-based vibration analysis technique is first presented for single-span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM-based vibration analysis technique are verified by comparison with other well-known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.
Highlights
In the structural engineering field, moving load problems, which deal with vibrations of structures under moving forces or masses, have been important research subjects over the last few decades
Us, the frequency-domain spectral element method (SEM) based on the fast Fourier transform (FFT) theory [26, 27] has been suggested as an alternative to the finite element method (FEM). e spectral element matrix used in the SEM is formulated from the frequency-dependent dynamic shape functions derived from free-wave solutions that satisfy the governing equations of motion in the frequency domain. us, the SEM can provide highly accurate solutions by representing a uniform structure member as a single finite element, regardless of its size, and significantly reduce the computational cost compared to the FEM
A frequency-domain vibration analysis method was proposed for thin rectangular plates subjected to a moving point force, and it was applied to several single-span and multispan rectangular plates. e moving point force was transformed into the frequency domain as a series of stationary point forces distributed along the trajectory of the moving point force
Summary
In the structural engineering field, moving load problems, which deal with vibrations of structures under moving forces or masses, have been important research subjects over the last few decades. For the SEM analysis, they used the spectral finite strip element model developed for a Levytype plate, and, in the frequency domain, they transformed the moving point force into the modal form by using the separation of variable method. To the authors’ best knowledge, there are no reports in the literature on the application of the generic type of spectral plate element model to the vibration analysis of a thin plate structure with arbitrary boundary conditions, subjected to a moving point force with arbitrary trajectory. Us, we propose a new SEM-based vibration analysis method for isotropic single-span or multispan thin plate structures with arbitrary boundary conditions, subjected to a moving point force by using the generic type of spectral plate element model developed by Park et al [29]. The effects of the boundary conditions, moving speed, and the trajectory of a moving force on the vibration responses of the single-span square plates and three-span rectangular plates are numerically investigated
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