Discrétisation d'un barreau élastique et passage au continu

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SimulationProgramme Python

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# -*- coding: utf-8 -*-
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"""
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Chaine continue
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O. Thual, 21/08/2021
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"""
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#  clear all
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for iglob in list(globals().keys()):
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    if(iglob[0] != '_'):
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        exec('del {}'.format(iglob))
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# import libraries
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import numpy as np
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import matplotlib.pyplot as plt
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import os
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def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):
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    plt.figure(2)
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    plt.axvline(xaxe)
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    plt.axhline(yaxe)
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    plt.xticks(fontsize=12)
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    plt.yticks(fontsize=12)
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    plt.xlabel(xlab,fontsize=16 )
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    plt.ylabel(ylab,fontsize=16)
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def zfi(x,le=2):
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    miss=le-len(str(x))
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    a='0'*miss+str(x)
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    return a
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def animation(name):
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    a=np.linspace(0,L,N+1);
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    acont=np.linspace(0,L,501);
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    t=0; 
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    dt=T/Nt
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    for i in range(0,Nt+1):
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        title=name+" i="+zfi(i)
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        titlefig=name
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        print(title)
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        fig=plt.figure(N,figsize=(7,4))
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        plt.xlabel('a',fontsize=16 )
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        plt.ylabel(r'Déplacement $\xi$',fontsize=16)
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        plt.title(titlefig,fontsize=16)
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        # signal
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        t=dt*i;
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        xi=signal(a,t)
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        xicont=signal(acont,t)
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        for dup in duprange:
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            plt.scatter(a+sc*xi,dup+0*xi,marker='o',color='blue',s=40)
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            plt.scatter(a,dup+0*xi,marker='o',color='red',s=20)
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        plt.plot(acont,xicont,color='black',linewidth=3)
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        #plt.scatter(a,xi,marker='o',color='black',s=40)
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        plt.xlim(0,L)
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        plt.ylim(ymin,ymax)
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        namei=name+zfi(i)+'.png';
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        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
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        plt.savefig(namei)
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        #plt.show()
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        plt.close()
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    gifanim="Anim"+name+".gif"
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    os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    os.system('rm '+name+'*');   
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# Main 
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F=False; T=True
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def pulse(a,d):
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    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
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    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
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    f=np.concatenate((al,fc,ar))
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    return f
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def statio(a,d):
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    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
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    f=np.cos
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    return f
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# Pulse
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if T: 
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    N=20; L=10; d=4; c=1; 
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    T=(L+2*d)/c; Nt=20; sc=.9*L/N # scaling 
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    k=np.pi/d;
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    ymin=-.2; ymax=1;
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    duprange=np.linspace(-.2,1,7)
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    delay="80"
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    # signal 
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    def signal(a,t):
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        xi=pulse(a-c*t+d,d)
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        return xi
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    animation("Pulse") 
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 # Progressive-cos
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if F: 
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    N=20; L=10; c=1; 
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    Nt=20; sc=.9*L/N # scaling 
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    k=np.pi/L; omega=k*c;
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    ymin=-1; ymax=1;
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    duprange=np.linspace(-1,1,9)
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    delay="20"
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    # signal 
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    def signal(a,t):
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        xi=np.cos(n*k*(a-c*t))
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        return xi
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    for m in range(10,30,10):
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        n=m/10; T=2*L/(n*c); dt=T/Nt; T=T-dt;
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        print("Progressive-cos-10xn="+zfi(m))
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        animation("Progressive-cos-10xn="+zfi(m)) 
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 # Stationnaire-cos
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if F: 
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    N=20; L=10; c=1; 
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    T=2*L/c; Nt=20; sc=.9*L/N # scaling 
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    k=np.pi/L; omega=k*c;
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    ymin=-1; ymax=1;
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    duprange=np.linspace(-1,1,9)
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    delay="20"
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    # signal 
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    def signal(a,t):
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        xi=np.cos(n*k*a)*np.cos(omega*t+np.pi/2)
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        return xi
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    for m in range(5,55,5):
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        print("Stationaire-sin-10xn="+zfi(m))
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        n=m/10; animation("Stationaire-cos-10xn="+zfi(m)) 
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 # Stationnaire-sin
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if F: 
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    N=20; L=10; c=1; 
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    T=2*L/c; Nt=20; sc=.9*L/N # scaling 
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    k=np.pi/L; omega=k*c;
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    ymin=-1; ymax=1;
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    duprange=np.linspace(-1,1,9)
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    delay="20"
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    # signal 
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    def signal(a,t):
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        xi=np.sin(n*k*a)*np.cos(omega*t+np.pi/2)
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        return xi
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    #for m in np.linspace(5,50,11):
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    for m in range(5,55,5):
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        print("Stationaire-sin-10xn="+zfi(m))
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        n=m/10; animation("Stationaire-sin-10xn="+zfi(m)) 
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