Abstract
The present work is concerned with dynamic characteristics of beam‐stiffened rectangular plate by an improved Fourier series method (IFSM), including mobility characteristics, structural intensity, and transient response. The artificial coupling spring technology is introduced to establish the clamped or elastic connections at the interface between the plate and beams. According to IFSM, the displacement field of the plate and the stiffening beams are expressed as a combination of the Fourier cosine series and its auxiliary functions. Then, the Rayleigh–Ritz method is applied to solve the unknown Fourier coefficients, which determines the dynamic characteristics of the coupled structure. The Newmark method is adopted to obtain the transient response of the coupled structure, where the Rayleigh damping is taken into consideration. The rapid convergence of the current method is shown, and good agreement between the predicted results and FEM results is also revealed. On this basis, the effects of the factors related to the stiffening beam (including the length, orientations, and arrangement spacing of beams) and elastic parameters, as well as damping coefficients on the dynamic characteristics of the stiffened plate are investigated.
Highlights
Academic Editor: Angelo Marcelo Tusset e present work is concerned with dynamic characteristics of beam-stiffened rectangular plate by an improved Fourier series method (IFSM), including mobility characteristics, structural intensity, and transient response. e artificial coupling spring technology is introduced to establish the clamped or elastic connections at the interface between the plate and beams
According to IFSM, the displacement field of the plate and the stiffening beams are expressed as a combination of the Fourier cosine series and its auxiliary functions. en, the Rayleigh–Ritz method is applied to solve the unknown Fourier coefficients, which determines the dynamic characteristics of the coupled structure. e Newmark method is adopted to obtain the transient response of the coupled structure, where the Rayleigh damping is taken into consideration. e rapid convergence of the current method is shown, and good agreement between the predicted results and FEM results is revealed
Based on the improved Fourier series method, Xu et al [10] examined the free vibration of the beam-stiffened rectangular plate, where beams of arbitrary lengths and placement angles were taken into consideration. ree different modelling approaches were reported by Bhar et al [11] to carry out the component-wise vibration analysis of the stiffened plate, and comparative studies between different models were given. e static, free vibration and buckling analysis of the stiffened plate were carried out by Nguyen- oi et al [12] using CS-FEM-DSG3
Summary
In terms of the coupling structure shown, the Lagrange function (L) can be expressed as follows: N. in which the number of stiffening beams is denoted by N, i 0 means unreinforced bare plate, and Wexc represents the work done by the external excitation force acting on the plate: Wexc B fuu + fvv + fwwdS. DTmi ETmi FTmi composed of the unknown Fourier coefficient, F. denotes the external force vector, and the mass matrix and stiffness matrix of the coupled systems are displayed by M and K, where their elements are only related to the material properties, geometric dimensions, and boundary constraints of the beamstiffened plate structure. Denotes the external force vector, and the mass matrix and stiffness matrix of the coupled systems are displayed by M and K, where their elements are only related to the material properties, geometric dimensions, and boundary constraints of the beamstiffened plate structure Their expressions are presented as follows: M. The force in the above equation (29) can be either point force or pressure
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