\tdplotsetmaincoords{60}{110}
\foreach \X in {0,...,35}
{\pgfmathsetmacro{\Objymax}{{1.6*pi+0.5*sin(10*\X)*pi}}
\begin{tikzpicture}[tdplot_main_coords,>=stealth,declare function={%
pfft(\x)=2+0.3*sin(deg(\x));},/tikz/3D surface/.cd,
ymin/.initial=0,ymax/.initial=2.2*pi,xmin/.initial=1,xmax/.initial=4,
/tikz/3D object/.cd,
ymin/.initial=0.8*pi,ymax/.initial=\Objymax,xmin/.initial=1.8,xmax/.initial=3.2]
 \draw[->] (0,0,0) coordinate (O) -- (5,0,0) coordinate(X) node[pos=1.1]{$x$};
 \draw[->] (O) -- (0,5,0) node[pos=1.1]{$y$};
 \draw[->] (O) -- (0,0,5) node[pos=1.1]{$z$};
 \draw[thick] plot[variable=\x,domain=\pgfkeysvalueof{/tikz/3D object/ymin}:\pgfkeysvalueof{/tikz/3D object/ymax},smooth] 
 (\pgfkeysvalueof{/tikz/3D object/xmax},\x,{pfft(2*\x)}) 
 coordinate (T1)--
 plot[variable=\x,domain=\pgfkeysvalueof{/tikz/3D object/ymax}:\pgfkeysvalueof{/tikz/3D object/ymin},smooth] 
 (\pgfkeysvalueof{/tikz/3D object/xmin},\x,{pfft(2*\x)}) coordinate
 (T3)-- cycle;
 \draw (\pgfkeysvalueof{/tikz/3D object/xmax},\pgfkeysvalueof{/tikz/3D object/ymin},0) coordinate (B4)-- 
 (\pgfkeysvalueof{/tikz/3D object/xmax},\pgfkeysvalueof{/tikz/3D
 object/ymax},0) coordinate (B1)
 -- (\pgfkeysvalueof{/tikz/3D object/xmin},\pgfkeysvalueof{/tikz/3D object/ymax},0) coordinate (B2) -- (\pgfkeysvalueof{/tikz/3D object/xmin},\pgfkeysvalueof{/tikz/3D object/ymin},0) coordinate (B3) -- cycle;
 \path (\pgfkeysvalueof{/tikz/3D object/xmax},\pgfkeysvalueof{/tikz/3D object/ymin},{pfft(2*\pgfkeysvalueof{/tikz/3D object/ymin})}) coordinate (T4)
  (\pgfkeysvalueof{/tikz/3D object/xmin},\pgfkeysvalueof{/tikz/3D
  object/ymax},{pfft(2*\pgfkeysvalueof{/tikz/3D object/ymax})}) coordinate (T2);
 \foreach \X in {1,...,4}
 {\draw (B\X) -- (T\X);}
 \path[opacity=0.3,left color=blue,right color=blue,middle color=blue!20,shading
  angle=72]
   plot[variable=\x,domain=\pgfkeysvalueof{/tikz/3D surface/ymin}:{(\pgfkeysvalueof{/tikz/3D
   surface/ymax}+\pgfkeysvalueof{/tikz/3D surface/ymin})/2},smooth]
   (\pgfkeysvalueof{/tikz/3D surface/xmax},\x,{pfft(2*\x)}) --
   plot[variable=\x,domain={(\pgfkeysvalueof{/tikz/3D
   surface/ymax}+\pgfkeysvalueof{/tikz/3D surface/ymin})/2}:\pgfkeysvalueof{/tikz/3D surface/ymin},smooth] (\pgfkeysvalueof{/tikz/3D surface/xmin},\x,{pfft(2*\x)}) -- cycle;
 \path[opacity=0.3,left color=blue,right color=blue,middle color=blue!20,shading
  angle=72]
   plot[variable=\x,domain={(\pgfkeysvalueof{/tikz/3D
   surface/ymax}+\pgfkeysvalueof{/tikz/3D surface/ymin})/2}:\pgfkeysvalueof{/tikz/3D surface/ymax},smooth] 
   (\pgfkeysvalueof{/tikz/3D surface/xmax},\x,{pfft(2*\x)}) --
   plot[variable=\x,domain=\pgfkeysvalueof{/tikz/3D surface/ymax}:{(\pgfkeysvalueof{/tikz/3D
   surface/ymax}+\pgfkeysvalueof{/tikz/3D surface/ymin})/2},smooth]   (\pgfkeysvalueof{/tikz/3D surface/xmin},\x,{pfft(2*\x)}) -- cycle;
 \draw plot[variable=\x,domain=\pgfkeysvalueof{/tikz/3D surface/ymin}:\pgfkeysvalueof{/tikz/3D surface/ymax},smooth] 
 (\pgfkeysvalueof{/tikz/3D surface/xmax},\x,{pfft(2*\x)}) --
 plot[variable=\x,domain=\pgfkeysvalueof{/tikz/3D surface/ymax}:\pgfkeysvalueof{/tikz/3D surface/ymin},smooth] 
 (\pgfkeysvalueof{/tikz/3D surface/xmin},\x,{pfft(2*\x)}) -- cycle;
\end{tikzpicture}}