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By means of Man(a)sevich-Mawhin（M-M) continuation theorem，we will continue to investigate a thin plate system {D▽4ω+pha2ω/at2-a2ωa2φ/ax2ay2-a2ωa2φ/ax2ay2+2a2ω/axaya2φ/axay+μaw/at+0,▽4φ=Eh[(a2ω/axay)2-a2ωa2ω/ax2ay2],which can be derived from von Karman-type equation. Without loss of generality，we establish a criterion to guarantee the existence and uniqueness of periodic solutions for a second-order dimensional equation，which is the generalized form of that derived from the above system. The feasibility of the criterion will be verified by numerical simulation at the last section of this paper. Moreover，it is significant that the growth degree is allowed to be greater than 1 with respect to the variable of the nonlinear term，which generalize and improve on the corresponding results in the known literature.