Propagation des ondes mécaniques : micro-contenus

# -*- coding: utf-8 -*-

"""

D'Alembert

O. Thual, 21/08/2021

"""

#  clear all

for iglob in list(globals().keys()):

    if(iglob[0] != '_'):

        exec('del {}'.format(iglob))

# import libraries

import numpy as np

import matplotlib.pyplot as plt

import os

def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):

    plt.figure(2)

    plt.axvline(xaxe)

    plt.axhline(yaxe)

    plt.xticks(fontsize=12)

    plt.yticks(fontsize=12)

    plt.xlabel(xlab,fontsize=16 )

    plt.ylabel(ylab,fontsize=16)

def zfi(x,le=2):

    miss=le-len(str(x))

    a='0'*miss+str(x)

    return a

def animation(name):

    a=np.linspace(0,L,N+1);

    acont=np.linspace(0,L,501);

    t=0; 

    dt=T/Nt

    for i in range(0,Nt+1):

        title=name+" i="+zfi(i)

        titlefig=name

        print(title)

        fig=plt.figure(N,figsize=(7,4))

        plt.xlabel('x',fontsize=16 )

        plt.ylabel(r'$\psi$',fontsize=16)

        plt.title(titlefig,fontsize=16)

        # signal

        t=dt*i;

        xi=signal(a,t)

        xicont=signal(acont,t)

        plt.plot(acont,xicont,color='black',linewidth=3)

        plt.xlim(0,L)

        plt.ylim(ymin,ymax)

        namei=name+zfi(i)+'.png';

        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        

        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        

        plt.savefig(namei)

        plt.show()

        plt.close()

    gifanim="Anim"+name+".gif"

    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);

    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);    

    if flagp: os.system('rm '+name+'*');   

def animationboth(name):

    a=np.linspace(0,L,N+1);

    acont=np.linspace(0,L,501);

    t=0; 

    dt=T/Nt

    for i in range(0,Nt+1):

        title=name+" i="+zfi(i)

        titlefig=name

        print(title)

        fig=plt.figure(N,figsize=(7,4))

        plt.xlabel('x',fontsize=16 )

        plt.ylabel(r'$\psi$',fontsize=16)

        plt.title(titlefig,fontsize=16)

        # signal

        t=dt*i;

        xicont=signal(acont,t)

        xileft=signalleft(acont,t)

        xiright=signalright(acont,t)

        plt.plot(acont,xicont,color='black',linewidth=3)

        plt.plot(acont,xileft,color='green',linewidth=3)

        plt.plot(acont,xiright,color='red',linewidth=3)

        plt.xlim(0,L)

        plt.ylim(ymin,ymax)

        namei=name+zfi(i)+'.png';

        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        

        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        

        plt.savefig(namei)

        plt.show()

        plt.close()

    gifanim="Anim"+name+".gif"

    os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);

    #os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);

    if flagp: os.system('rm '+name+'*');  

def animationbothwith(name):

    a=np.linspace(0,L,N+1);

    acont=np.linspace(0,L,501);

    t=0; 

    dt=T/Nt

    for i in range(0,Nt+1):

        title=name+" i="+zfi(i)

        titlefig=name

        print(title)

        fig=plt.figure(N,figsize=(7,4))

        plt.xlabel('x',fontsize=16 )

        plt.ylabel(r'$\psi$',fontsize=16)

        plt.title(titlefig,fontsize=16)

        # signal

        t=dt*i;

        xicont=signal(acont,t)

        xileft=signalleft(acont,t)

        xiright=signalright(acont,t)

        xinit=signalinit(acont)

        plt.plot(acont,xinit,color='grey',linewidth=3)

        plt.plot(acont,xicont,color='black',linewidth=3)

        plt.plot(acont,xileft,color='green',linewidth=3)

        plt.plot(acont,xiright,color='red',linewidth=3)

        plt.xlim(0,L)

        plt.ylim(ymin,ymax)

        namei=name+zfi(i)+'.png';

        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        

        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        

        plt.savefig(namei)

        plt.show()

        plt.close()

    gifanim="Anim"+name+".gif"

    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);

    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);

    if flagp: os.system('rm '+name+'*');  

# Main 

F=False; T=True

flagp=F; flagall=F;

def pulse(a,d):

    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];

    k=np.pi/d; fc=.5*(1+np.cos(k*ac));

    f=np.concatenate((al,fc,ar))

    return f

def leftsin(a,k):

    al=a[a<=0]; ar=0*a[a>0];

    fl=-np.sin(k*al);

    f=np.concatenate((fl,ar))

    return f

def rightsin(a,k):

    al=0*a[a<=0]; ar=a[a>0];

    fr=np.sin(k*ar);

    f=np.concatenate((al,fr))

    return f

def statio(a,d):

    k=np.pi/d; fc=.5*(1+np.cos(k*ac));

    f=np.cos

    return f

# Condition initiale

if F or flagall: 

    N=20; L=10; d=2; c=1; 

    T=.7*L/c; Nt=20; sc=.9*L/N # scaling 

    k=4*np.pi/L; omega=k*c;

    ymin=-.2; ymax=1.1;

    delay="80"

    # signal 

    def signalinit(a):

        xi=pulse(-L/2+a,d)

        return xi

    def signal(a,t):

        xi=.5*pulse(-L/2+a-c*t,d)+.5*pulse(-L/2+a+c*t,d)

        return xi

    def signalleft(a,t):

        xi=.5*pulse(-L/2+a+c*t,d)

        return xi

    def signalright(a,t):

        xi=.5*pulse(-L/2+a-c*t,d)

        return xi

    animationbothwith("Condition-initiale") 

# Deux pulses

if T or flagall: 

    N=20; L=10; d=2; c=1; 

    T=(L+2*d)/c; Nt=20; sc=.9*L/N # scaling 

    k=np.pi/d;

    ymin=-.2; ymax=1;

    duprange=np.linspace(-.2,1,7)

    delay="80"

    # signal 

    def signal(a,t):

        xi=.5*pulse(a+d-c*t,d)+.5*pulse(a-L-d+c*t,d)

        return xi

    def signalleft(a,t):

        xi=.5*pulse(a-L-d+c*t,d)

        return xi

    def signalright(a,t):

        xi=.5*pulse(a+d-c*t,d)

        return xi

    animationboth("Deux-pulses") 

# Deux pulses inegaux

if F or flagall: 

    N=20; L=10; d=2; c=1; 

    T=(L+2*d)/c; Nt=20; sc=.9*L/N # scaling 

    k=np.pi/d;

    ymin=-.2; ymax=1;

    duprange=np.linspace(-.2,1,7)

    delay="80"

    # signal 

    def signal(a,t):

        xi=.7*pulse(a+d-c*t,d)+.3*pulse(a-L-d+c*t,d)

        return xi

    def signalleft(a,t):

        xi=.3*pulse(a-L-d+c*t,d)

        return xi

    def signalright(a,t):

        xi=.7*pulse(a+d-c*t,d)

        return xi

    animationboth("Deux-pulses-inegaux") 

 # Progessive-cos

if T or flagall: 

    N=20; L=10; c=1; 

    T=2*L/c; Nt=20; sc=.9*L/N # scaling 

    k=2*np.pi/L; omega=k*c;

    ymin=-1; ymax=1;

    duprange=np.linspace(-1,1,9)

    delay="20"

    # signal 

    def signal(a,t):

        xi=np.cos(n*k*a-omega*t)

        return xi

    m=20;n=m/10; 

    animation("Progressive-cos-10xn="+zfi(m)) 

 # Onde stationnaire

if T or flagall: 

    N=20; L=10; c=1; 

    T=2*L/c; Nt=82; sc=.9*L/N # scaling 

    k=4*np.pi/L; omega=k*c;

    ymin=-1; ymax=1;

    delay="20"

    # signal 

    def signal(a,t):

        xi=.5*rightsin(-L+a+c*t,k)+.5*leftsin(a-c*t,k)

        return xi

    def signalleft(a,t):

        xi=.5*rightsin(-L+a+c*t,k)

        return xi

    def signalright(a,t):

        xi=.5*leftsin(a-c*t,k)

        return xi

    animationboth("Onde-stationnaire") 

 # Stationnaire-cos

if F or flagall: 

    N=20; L=10; c=1; 

    T=2*L/c; Nt=20; sc=.9*L/N # scaling 

    k=np.pi/L; omega=k*c;

    ymin=-1; ymax=1;

    #duprange=np.linspace(-1,1,9)

    duprange=np.linspace(-2,-1,1)

    delay="20"

    # signal 

    def signal(a,t):

        xi=np.cos(n*k*a)*np.cos(omega*t+np.pi/2)

        return xi

    for m in range(5,55,5):

        print("Stationaire-sin-10xn="+zfi(m))

        n=m/10; animation("Stationaire-cos-10xn="+zfi(m)) 

 # Stationnaire-sin

if F or flagall: 

    N=20; L=10; c=1; 

    T=2*L/c; Nt=20; sc=.9*L/N # scaling 

    k=np.pi/L; omega=k*c;

    ymin=-1; ymax=1;

    #duprange=np.linspace(-1,1,9)

    duprange=np.linspace(-2,-1,1)

    delay="20"

    # signal 

    def signal(a,t):

        xi=np.sin(n*k*a)*np.cos(omega*t+np.pi/2)

        return xi

    #for m in np.linspace(5,50,11):

    for m in range(5,55,5):

        print("Stationaire-sin-10xn="+zfi(m))

        n=m/10; animation("Stationaire-sin-10xn="+zfi(m)) 

# -*- coding: utf-8 -*-
"""
D'Alembert
O. Thual, 21/08/2021
"""

#  clear all
for iglob in list(globals().keys()):
    if(iglob[0] != '_'):
        exec('del {}'.format(iglob))
# import libraries
import numpy as np
import matplotlib.pyplot as plt
import os


def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):
    plt.figure(2)
    plt.axvline(xaxe)
    plt.axhline(yaxe)
    plt.xticks(fontsize=12)
    plt.yticks(fontsize=12)
    plt.xlabel(xlab,fontsize=16 )
    plt.ylabel(ylab,fontsize=16)
    
def zfi(x,le=2):
    miss=le-len(str(x))
    a='0'*miss+str(x)
    return a

def animation(name):
    a=np.linspace(0,L,N+1);
    acont=np.linspace(0,L,501);
    t=0; 
    dt=T/Nt
    for i in range(0,Nt+1):
        title=name+" i="+zfi(i)
        titlefig=name
        print(title)
        fig=plt.figure(N,figsize=(7,4))
        plt.xlabel('x',fontsize=16 )
        plt.ylabel(r'$\psi$',fontsize=16)
        plt.title(titlefig,fontsize=16)
        # signal
        t=dt*i;
        xi=signal(a,t)
        xicont=signal(acont,t)
        plt.plot(acont,xicont,color='black',linewidth=3)
        plt.xlim(0,L)
        plt.ylim(ymin,ymax)
        namei=name+zfi(i)+'.png';
        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
        plt.savefig(namei)
        plt.show()
        plt.close()
    gifanim="Anim"+name+".gif"
    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);    
    if flagp: os.system('rm '+name+'*');   

def animationboth(name):
    a=np.linspace(0,L,N+1);
    acont=np.linspace(0,L,501);
    t=0; 
    dt=T/Nt
    for i in range(0,Nt+1):
        title=name+" i="+zfi(i)
        titlefig=name
        print(title)
        fig=plt.figure(N,figsize=(7,4))
        plt.xlabel('x',fontsize=16 )
        plt.ylabel(r'$\psi$',fontsize=16)
        plt.title(titlefig,fontsize=16)
        # signal
        t=dt*i;
        xicont=signal(acont,t)
        xileft=signalleft(acont,t)
        xiright=signalright(acont,t)
        plt.plot(acont,xicont,color='black',linewidth=3)
        plt.plot(acont,xileft,color='green',linewidth=3)
        plt.plot(acont,xiright,color='red',linewidth=3)
        plt.xlim(0,L)
        plt.ylim(ymin,ymax)
        namei=name+zfi(i)+'.png';
        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
        plt.savefig(namei)
        plt.show()
        plt.close()
    gifanim="Anim"+name+".gif"
    os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
    #os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
    if flagp: os.system('rm '+name+'*');  

def animationbothwith(name):
    a=np.linspace(0,L,N+1);
    acont=np.linspace(0,L,501);
    t=0; 
    dt=T/Nt
    for i in range(0,Nt+1):
        title=name+" i="+zfi(i)
        titlefig=name
        print(title)
        fig=plt.figure(N,figsize=(7,4))
        plt.xlabel('x',fontsize=16 )
        plt.ylabel(r'$\psi$',fontsize=16)
        plt.title(titlefig,fontsize=16)
        # signal
        t=dt*i;
        xicont=signal(acont,t)
        xileft=signalleft(acont,t)
        xiright=signalright(acont,t)
        xinit=signalinit(acont)
        plt.plot(acont,xinit,color='grey',linewidth=3)
        plt.plot(acont,xicont,color='black',linewidth=3)
        plt.plot(acont,xileft,color='green',linewidth=3)
        plt.plot(acont,xiright,color='red',linewidth=3)
        plt.xlim(0,L)
        plt.ylim(ymin,ymax)
        namei=name+zfi(i)+'.png';
        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
        plt.savefig(namei)
        plt.show()
        plt.close()
    gifanim="Anim"+name+".gif"
    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
    if flagp: os.system('rm '+name+'*');  


# Main 
F=False; T=True
flagp=F; flagall=F;

def pulse(a,d):
    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
    f=np.concatenate((al,fc,ar))
    return f

def leftsin(a,k):
    al=a[a<=0]; ar=0*a[a>0];
    fl=-np.sin(k*al);
    f=np.concatenate((fl,ar))
    return f

def rightsin(a,k):
    al=0*a[a<=0]; ar=a[a>0];
    fr=np.sin(k*ar);
    f=np.concatenate((al,fr))
    return f

def statio(a,d):
    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
    f=np.cos
    return f


# Condition initiale
if F or flagall: 
    N=20; L=10; d=2; c=1; 
    T=.7*L/c; Nt=20; sc=.9*L/N # scaling 
    k=4*np.pi/L; omega=k*c;
    ymin=-.2; ymax=1.1;
    delay="80"
    # signal 
    def signalinit(a):
        xi=pulse(-L/2+a,d)
        return xi
    def signal(a,t):
        xi=.5*pulse(-L/2+a-c*t,d)+.5*pulse(-L/2+a+c*t,d)
        return xi
    def signalleft(a,t):
        xi=.5*pulse(-L/2+a+c*t,d)
        return xi
    def signalright(a,t):
        xi=.5*pulse(-L/2+a-c*t,d)
        return xi
    animationbothwith("Condition-initiale") 


# Deux pulses
if T or flagall: 
    N=20; L=10; d=2; c=1; 
    T=(L+2*d)/c; Nt=20; sc=.9*L/N # scaling 
    k=np.pi/d;
    ymin=-.2; ymax=1;
    duprange=np.linspace(-.2,1,7)
    delay="80"
    # signal 
    def signal(a,t):
        xi=.5*pulse(a+d-c*t,d)+.5*pulse(a-L-d+c*t,d)
        return xi
    def signalleft(a,t):
        xi=.5*pulse(a-L-d+c*t,d)
        return xi
    def signalright(a,t):
        xi=.5*pulse(a+d-c*t,d)
        return xi
    animationboth("Deux-pulses") 


# Deux pulses inegaux
if F or flagall: 
    N=20; L=10; d=2; c=1; 
    T=(L+2*d)/c; Nt=20; sc=.9*L/N # scaling 
    k=np.pi/d;
    ymin=-.2; ymax=1;
    duprange=np.linspace(-.2,1,7)
    delay="80"
    # signal 
    def signal(a,t):
        xi=.7*pulse(a+d-c*t,d)+.3*pulse(a-L-d+c*t,d)
        return xi
    def signalleft(a,t):
        xi=.3*pulse(a-L-d+c*t,d)
        return xi
    def signalright(a,t):
        xi=.7*pulse(a+d-c*t,d)
        return xi
    animationboth("Deux-pulses-inegaux") 


 # Progessive-cos
if T or flagall: 
    N=20; L=10; c=1; 
    T=2*L/c; Nt=20; sc=.9*L/N # scaling 
    k=2*np.pi/L; omega=k*c;
    ymin=-1; ymax=1;
    duprange=np.linspace(-1,1,9)
    delay="20"
    # signal 
    def signal(a,t):
        xi=np.cos(n*k*a-omega*t)
        return xi
    m=20;n=m/10; 
    animation("Progressive-cos-10xn="+zfi(m)) 


 # Onde stationnaire
if T or flagall: 
    N=20; L=10; c=1; 
    T=2*L/c; Nt=82; sc=.9*L/N # scaling 
    k=4*np.pi/L; omega=k*c;
    ymin=-1; ymax=1;
    delay="20"
    # signal 
    def signal(a,t):
        xi=.5*rightsin(-L+a+c*t,k)+.5*leftsin(a-c*t,k)
        return xi
    def signalleft(a,t):
        xi=.5*rightsin(-L+a+c*t,k)
        return xi
    def signalright(a,t):
        xi=.5*leftsin(a-c*t,k)
        return xi
    animationboth("Onde-stationnaire") 

 
 # Stationnaire-cos
if F or flagall: 
    N=20; L=10; c=1; 
    T=2*L/c; Nt=20; sc=.9*L/N # scaling 
    k=np.pi/L; omega=k*c;
    ymin=-1; ymax=1;
    #duprange=np.linspace(-1,1,9)
    duprange=np.linspace(-2,-1,1)
    delay="20"
    # signal 
    def signal(a,t):
        xi=np.cos(n*k*a)*np.cos(omega*t+np.pi/2)
        return xi
    for m in range(5,55,5):
        print("Stationaire-sin-10xn="+zfi(m))
        n=m/10; animation("Stationaire-cos-10xn="+zfi(m)) 

 
 # Stationnaire-sin
if F or flagall: 
    N=20; L=10; c=1; 
    T=2*L/c; Nt=20; sc=.9*L/N # scaling 
    k=np.pi/L; omega=k*c;
    ymin=-1; ymax=1;
    #duprange=np.linspace(-1,1,9)
    duprange=np.linspace(-2,-1,1)
    delay="20"
    # signal 
    def signal(a,t):
        xi=np.sin(n*k*a)*np.cos(omega*t+np.pi/2)
        return xi
    #for m in np.linspace(5,50,11):
    for m in range(5,55,5):
        print("Stationaire-sin-10xn="+zfi(m))
        n=m/10; animation("Stationaire-sin-10xn="+zfi(m))