Abstract
A theoretical solution method for the in-plane vibration characteristics of the plate with cutouts is proposed in this paper. The energy principle in conjunction with the Rayleigh–Ritz solution technique is adopted for the theoretical modeling of the in-plane vibration of the structure. The energy functions for the plate with cutouts are established by subtracting the energies of the cutout domains from the total energies of the whole plate. To ensure continuity over the entire solution domain, the in-plane displacements are composed of two-dimensional standard Fourier series and supplementary functions. The in-plane eigenmodes of the plates with different square cutouts are compared with the results obtained from the finite element method (FEM), with good agreements. The influences of the cutouts on the in-plane vibration characteristics of the plates with cutouts are investigated by varying the number, size, and position of the cutouts.
Highlights
In studying the effects of cutouts within the structure, the cutouts are mostly located in the center of the structure, and the number of cutouts is less than two
To behave the physical characteristics of the cutouts within the structure, the influence of cutouts on the vibration characteristic of the structure is considered in terms of energy [21]. e energy principle combined with the Rayleigh–Ritz solution is adopted to determine the vibration characteristics of the structures with cutouts. e effect of the cutouts is taken into account by subtracting the energies of the cutout domains from the total energies of the whole plate. e modal characteristics of square plates with different cutouts are predicted by the present method and verified by finite element method (FEM)
Description of the Numerical Model. e geometric sketch of the plate with cutouts investigated in this paper is given in Figure 1. e boundary conditions of the rectangular plate with cutouts shown in Figure 1 can be represented by two kinds of springs with determined stiffness constants. e linear springs are attached to the edges in the normal or tangential direction. e dimensions in x and y directions for the rectangular plate with cutouts are represented as a and b, respectively. e rectangular cutouts positions are unrestricted in Figure 1. e length and width of the ith cutout are, respectively, (Xdi-Xci) and (Ydi-Yci), in which the size of the rectangular cutout is variable
Summary
In studying the effects of cutouts within the structure, the cutouts are mostly located in the center of the structure, and the number of cutouts is less than two. In the Results and Discussion, the influences of the number, size, and position of the cutouts on the natural frequencies and mode shapes of the plate with cutouts are investigated.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call