Influence of external load on forced vibration of rectangular plate

. Rectangular plate is one typical structure with wild application in engineering, and the force vibration is the basis for analysis of sound radiation of plate. In this work, numerical simulation is conducted for force vibration of rectangular plate, and the influence of external load is also studied. Numerical results show that, the rectangular plate will resonate under external load at certain driven frequency, and it’s strictly related to structural modal frequencies. Structural vibration response will change obvious with the change of location of external load. When the location is fixed, with the increase of action region of external load, the acceleration of plate will decrease and some new resonance frequencies will be observed. Conclusions here will lay foundation for further work on sound radiation of plate.


Introduction
Rectangular plate is one typical structure which has wildly application in aero-space, ship structure, marine structures, and so on. Vibration characteristic of rectangular plate receives great attentions from researchers, since it's the foundation for sound radiation of plate. Bardell et.al. [1] applied the Ritz method to analyze the inplane vibration of rectangular plate with different boundary conditions. Gorman [2][3][4][5][6] put forward a new superposition method for solving the vibration of rectangular plate with free, simply-supported and clamped boundary conditions. Based on the differential quadrature method (DQM), Xing et.al. [7] put forward a new method with high accuracy for in-plane vibration of rectangular plate. Du et.al. [8][9] use the Fourier series to analyze the vibration of rectangular plate with elastic boundary conditions. But, it should also be important to get clear the influence of external load on structural vibration. In this work, numerical analysis for forced vibration of rectangular plate is carried out, and the influence of external load (i.e., location and action region) on structural vibration is also conducted.

Numerical simulation of forced vibration 2.1 Structural model
The finite element model for rectangular plate is shown in Fig.1, the plate is of length 2640mm, width 800mm, thickness 10mm. Both long edges are clamped. Material for the plate is 316L steel.

Forced vibration
Harmonic vibration of plate is conducted here by applying an external point unit force at the center of plate in normal direction. The frequency range for numerical analysis is 10Hz-3000Hz. Mean acceleration of plate is plotted in Fig.2.
It's note that the plate will resonate at certain excitation frequency, i.e., 80Hz, 430Hz, 1120Hz, and so on. Due to the setting of step length of 10mm in numerical simulation, little difference is note between structural modal frequency and resonance frequency.

Location of point excitation
To analyze the influence of load location on structural vibration response, three cases of location at the center, L/4 and short edge are calculated, and the mean acceleration of plate is plotted in Fig.3.
It's noted that, the change of load location will affect the amplitude of vibration acceleration, resonance frequency remains the same, and new resonance frequency will be observed. Since the structural modal frequencies do not change. But the change of load location will lead to different contribution of structural mode to vibration response, and finally result in different structural responses.

Action region of external load
Point load is ideal, and action region should be considered in engineering. Therefore, the effect of action region on structural vibration response is studied in this section. Three cases of action region, 120 mm×70 mm, 120 mm× 100 mm, 340 mm × 180mm, ware calculated and compared. Numerical results are shown in Fig.4. The total acceleration level in 10Hz-3000Hz are listed in table 1.
It's noted that: 1) general distributions of acceleration versus driven frequency from three cases are similar, main resonant frequencies are the same since structural modal frequency do not change. 2) With the increase of action region, few new resonance frequencies will be noted, since the change of action region will change the contribution of structural modes to vibrational response, and few modal contribution will increase and be the main part; 3) With the increase of action region, structural acceleration level will decrease.

Conclusion
In this work, numerical simulation is conducted for force vibration of rectangular plate, and the influence of external load is also studied. Numerical results show that, the rectangular plate will resonate under external load at certain driven frequency, and it's strictly related to structural modal frequencies. Structural vibration response will change obvious with the change of location of external load. When the location is fixed, with the increase of action region of external load, the acceleration of plate will decrease and some new resonance frequencies will be observed. Conclusions here will help to give a better understanding of the sound radiation of rectangular plate.