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In this paper, we consider the bifurcation of limit cycles for generic L-Vsystem ($\dot{x}=y+x^2-y^2\pm\frac{4}{\sqrt{3}}xy,~\dot{y}=-x+2xy$) and B-Tsystem ($\dot{x}=y,~\dot{y}=-x+x^2$) under perturbations of piecewise smoothpolynomials with degree $n$. Here the switching line is $y=0$. By usingPicard-Fuchs equations, we bound the number of zeros of first order Melnikovfunction which controls the number of limit cycles bifurcating from the center.It is proved that the upper bounds of the number of limit cycles for genericL-V system and B-T system are respectively$36n-65~(n\geq4),~37,57,93~(n=1,2,3)$ and $12n+6$.

On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials