# Modal Shapes Circular Plate

I am trying to produce the next figures:

I try with this code:

\begin{tikzpicture}
\begin{axis}[view={60}{20}]
domain=1:0, y domain=0:2*pi,
z buffer=sort]
({((1-(x^2))^2)*cos(y)},
{((1-(x^2))^2)*sin(y)},x);
\end{axis}
\end{tikzpicture}


But I do not understand why it does not produce what I need.

Here is a proposal for the mesh only. The blue curve can be done, too, but is more involved.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{math}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[view={60}{20},unit vector ratio=1 1 0.5]