tex的计算能力有限，使用 l3fp 帮助计算

讨论见此 tikz用plot画图象报错dimension too large

另外需要加上 xmax=1e4 选项才能显示完整.

\documentclass[1pt]{standalone}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{euler}
%\usepackage{MnSymbol}
%\usepackage{stmaryrd}
\usepackage{xcolor}
%use xfp package
\usepackage{xfp}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepgfplotslibrary{colormaps}
\usetikzlibrary{pgfplots.groupplots,matrix}
\pgfplotsset{height=8cm,width=8cm}
\begin{document}
\begin{tikzpicture}
    \begin{loglogaxis}[
        enlargelimits=false,
        grid=both,
        ymin=5e-6,ymax=1,
        xmax=1e4,
        ymode=normal,
        xlabel= undulations per revolution(UPR),
        ylabel=amplitude transmission,
        log basis y=10,
        log basis x=10,
        domain=1e0:1e4,samples=60,smooth,
        ]
        % use \fpeval with xfp, x --> \x 
        \addplot+[no marks,ultra thick,black]{\fpeval{exp(((0.4697*1/15*\x)^2)*(-3.1415))}}; 
        \addplot+[no marks,ultra thick,black]{\fpeval{exp(((0.4697*1.25/50*\x)^2)*(-3.1415))}};
        \addplot+[no marks,ultra thick,black]{\fpeval{exp(((0.4697*1.5/150*\x)^2)*(-3.1415))}};
        \addplot+[no marks,ultra thick,black]{\fpeval{exp(((0.4697*1.75/500*\x)^2)*(-3.1415))}};
        \addplot+[no marks,ultra thick,red,opacity=0.8]{exp(((0.4697*2/1500*x)^2)*(-3.1415))};
    \end{loglogaxis}
\end{tikzpicture}
\end{document}