Propagation des ondes mécaniques : micro-contenus

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

"""

Corde 

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=Time/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(r'$x$',fontsize=16 )

        plt.ylabel(r'Déplacement $y$',fontsize=16)

        plt.title(titlefig,fontsize=16)

        # signal

        t=dt*i;

        xi=signal(a,t)

        afin=a[N]; xifin=xi[N]

        xicont=signal(acont,t)

        plt.scatter(a,xi,marker='o',color='blue',s=40)

        if Redpoint: plt.scatter(afin,xifin,marker='o',color='red',s=160)

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

def anistatio(name):

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

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

    t=0; 

    dt=Time/Nt

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

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

    plt.ylabel(r'Déplacement $y$',fontsize=16)

    plt.xlim(0,L)

    plt.ylim(ymin,ymax)

    titlefig=name

    plt.title(titlefig,fontsize=16)

    title=name

    print(title)

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

        # signal

        t=dt*i;

        xi=signal(a,t)

        afin=a[N]; xifin=xi[N]

        xicont=signal(acont,t)

        plt.scatter(a,xi,marker='o',color='black',s=10)

        if Redpoint: plt.scatter(afin,xifin,marker='o',color='red',s=160)

        plt.plot(acont,xicont,color='black',linewidth=1)

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

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

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

    # big one

    t=3*Time/4

    xi=signal(a,t)

    xicont=signal(acont,t)

    plt.scatter(a,xi,marker='o',color='red',s=40)

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

    plt.savefig(namei)

    plt.show()

# Main 

F=False; T=True

Flagrm=T; Redpoint=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 statio(a,d):

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

    f=np.cos

    return f

 # Fonction reponse Corde de Melde

if F: 

    chimax=5; dchi=.01

    chi=np.linspace(dchi,chimax-dchi,200)

    Y=np.abs(1/np.sin(np.pi*chi))

    fig=plt.figure(1,figsize=(7,4))

    plt.xlabel(r'$X=\omega/\omega_1$',fontsize=16 )

    plt.ylabel(r'$|Y|=|A|/A_e$',fontsize=16)

    plt.title("Amplitude de la corde de Melde",fontsize=16)

    plt.plot(chi,Y,color='black',linewidth=3)

    plt.xlim(0,chimax)

    plt.ylim(0,4)

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

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

    plt.savefig("Melde")

    plt.show()

    plt.close()

 # Stationnaire-sin Melde

if F: 

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

    Nt=20; Redpoint=T

    dchi=.1; chimin=1.51;

    for m in range(0,10,1):

        chi=round(chimin+m*dchi,2)

        print("m=",m,"chi=",chi)

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

        Y=np.abs(1/np.sin(np.pi*chi))

        ymin=-4; ymax=4;

        de=20*chimin/chi

        print("de=",de)

        delay=str(de)

        # signal 

        def signal(a,t):

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

            return xi

        print("Melde-chi="+zfi(chi))

        animation("Melde-X="+zfi(chi)) 

 # Stationnaire-sin Melde remanant

if F: 

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

    Nt=20; Redpoint=T

    dchi=.1; chimin=1.51;

    for m in range(0,10,1):

        chi=round(chimin+m*dchi,2)

        print("m=",m,"chi=",chi)

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

        Y=np.abs(1/np.sin(np.pi*chi))

        ymin=-4; ymax=4;

        de=20*chimin/chi

        print("de=",de)

        delay=str(de)

        # signal 

        def signal(a,t):

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

            return xi

        print("Melde-chi="+zfi(chi))

        anistatio("Melde-X="+zfi(chi)) 

 # Stationnaire-sin entier

if F: 

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

    Time=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)

    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 range(10,100,10):

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

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

 # Stationnaire-sin entier remanant

if F: 

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

    Time=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)

    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 range(10,50,10):

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

        n=m/10; anistatio("Stationaire-fixe-fixe-10xn="+zfi(m)) 

 # Stationnaire-cos entier remanant

if T: 

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

    Time=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)

    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(10,50,10):

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

        n=m/10; anistatio("Stationaire-libre-libre-10xn="+zfi(m)) 

 # Stationnaire-sin demi entier

if F: 

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

    Time=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)

    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 range(5,105,10):

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

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

 # Stationnaire-sin demi entier remanat

if F: 

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

    Time=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)

    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 range(5,45,10):

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

        n=m/10; anistatio("Stationaire-fixe-libre-10xn="+zfi(m)) 

# -*- coding: utf-8 -*-
"""
Corde 
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=Time/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(r'$x$',fontsize=16 )
        plt.ylabel(r'Déplacement $y$',fontsize=16)
        plt.title(titlefig,fontsize=16)
        # signal
        t=dt*i;
        xi=signal(a,t)
        afin=a[N]; xifin=xi[N]
        xicont=signal(acont,t)
        plt.scatter(a,xi,marker='o',color='blue',s=40)
        if Redpoint: plt.scatter(afin,xifin,marker='o',color='red',s=160)
        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 Flagrm: os.system('rm '+name+'*');   

def anistatio(name):
    a=np.linspace(0,L,N+1);
    acont=np.linspace(0,L,501);
    t=0; 
    dt=Time/Nt
    fig=plt.figure(N,figsize=(7,4))
    plt.xlabel(r'$x$',fontsize=16 )
    plt.ylabel(r'Déplacement $y$',fontsize=16)
    plt.xlim(0,L)
    plt.ylim(ymin,ymax)
    titlefig=name
    plt.title(titlefig,fontsize=16)
    title=name
    print(title)
    for i in range(0,Nt+1):
        # signal
        t=dt*i;
        xi=signal(a,t)
        afin=a[N]; xifin=xi[N]
        xicont=signal(acont,t)
        plt.scatter(a,xi,marker='o',color='black',s=10)
        if Redpoint: plt.scatter(afin,xifin,marker='o',color='red',s=160)
        plt.plot(acont,xicont,color='black',linewidth=1)
        namei=name+zfi(i)+'.png';
        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
    # big one
    t=3*Time/4
    xi=signal(a,t)
    xicont=signal(acont,t)
    plt.scatter(a,xi,marker='o',color='red',s=40)
    plt.plot(acont,xicont,color='red',linewidth=3)
    plt.savefig(namei)
    plt.show()


# Main 
F=False; T=True
Flagrm=T; Redpoint=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 statio(a,d):
    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
    f=np.cos
    return f

 
 # Fonction reponse Corde de Melde
if F: 
    chimax=5; dchi=.01
    chi=np.linspace(dchi,chimax-dchi,200)
    Y=np.abs(1/np.sin(np.pi*chi))
    fig=plt.figure(1,figsize=(7,4))
    plt.xlabel(r'$X=\omega/\omega_1$',fontsize=16 )
    plt.ylabel(r'$|Y|=|A|/A_e$',fontsize=16)
    plt.title("Amplitude de la corde de Melde",fontsize=16)
    plt.plot(chi,Y,color='black',linewidth=3)
    plt.xlim(0,chimax)
    plt.ylim(0,4)
    plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
    plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
    plt.savefig("Melde")
    plt.show()
    plt.close()
 

 # Stationnaire-sin Melde
if F: 
    N=20; L=10; c=1; 
    Nt=20; Redpoint=T
    dchi=.1; chimin=1.51;
    for m in range(0,10,1):
        chi=round(chimin+m*dchi,2)
        print("m=",m,"chi=",chi)
        k=chi*np.pi/L; omega=k*c; Time=2*np.pi/omega
        Y=np.abs(1/np.sin(np.pi*chi))
        ymin=-4; ymax=4;
        de=20*chimin/chi
        print("de=",de)
        delay=str(de)
        # signal 
        def signal(a,t):
            xi=Y*np.sin(k*a)*np.cos(omega*t+np.pi/2)
            return xi
        print("Melde-chi="+zfi(chi))
        animation("Melde-X="+zfi(chi)) 
 
 # Stationnaire-sin Melde remanant
if F: 
    N=20; L=10; c=1; 
    Nt=20; Redpoint=T
    dchi=.1; chimin=1.51;
    for m in range(0,10,1):
        chi=round(chimin+m*dchi,2)
        print("m=",m,"chi=",chi)
        k=chi*np.pi/L; omega=k*c; Time=2*np.pi/omega
        Y=np.abs(1/np.sin(np.pi*chi))
        ymin=-4; ymax=4;
        de=20*chimin/chi
        print("de=",de)
        delay=str(de)
        # signal 
        def signal(a,t):
            xi=Y*np.sin(k*a)*np.cos(omega*t+np.pi/2)
            return xi
        print("Melde-chi="+zfi(chi))
        anistatio("Melde-X="+zfi(chi)) 
 
 
 
    
 # Stationnaire-sin entier
if F: 
    N=20; L=10; c=1; 
    Time=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)
    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 range(10,100,10):
        print("Stationaire-sin-10xn="+zfi(m))
        n=m/10; animation("Stationaire-fixe-fixe-10xn="+zfi(m)) 

  
 # Stationnaire-sin entier remanant
if F: 
    N=20; L=10; c=1; 
    Time=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)
    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 range(10,50,10):
        print("Stationaire-sin-10xn="+zfi(m))
        n=m/10; anistatio("Stationaire-fixe-fixe-10xn="+zfi(m)) 


  
 # Stationnaire-cos entier remanant
if T: 
    N=20; L=10; c=1; 
    Time=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)
    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(10,50,10):
        print("Stationaire-sin-10xn="+zfi(m))
        n=m/10; anistatio("Stationaire-libre-libre-10xn="+zfi(m)) 

 
 
    
    
    
 # Stationnaire-sin demi entier
if F: 
    N=20; L=10; c=1; 
    Time=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)
    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 range(5,105,10):
        print("Stationaire-fixe-libre-10xn="+zfi(m))
        n=m/10; animation("Stationaire-fixe-libre-10xn="+zfi(m)) 

    
 # Stationnaire-sin demi entier remanat
if F: 
    N=20; L=10; c=1; 
    Time=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)
    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 range(5,45,10):
        print("Stationaire-fixe-libre-10xn="+zfi(m))
        n=m/10; anistatio("Stationaire-fixe-libre-10xn="+zfi(m))