Question

Write a computer code to do the mode summation for a string with a length of 20, wave velocity of 3. The string was plucked at time 0 by a source at position 8. The source function is ?=exp[−(?+?)./4].

1a. Show the mode summation at time 1,2, 3 for the first 40 modes.

1b. Show the mode summation at time 1, 2, 3 for the first 80 modes.

You need to have sufficient comments in your scripts. It is not required, but is preferred to use Matlab to make a movie of the wave propagation.

Answer 1

program synt_seis_strings
    implicit none
    real, parameter :: pi = 4*atan(1.0)
    real :: stln,vel,xsrc,xrcvr,tseis,dt,tau,npiL,srctm,rcvrtm,wn,Fwn,spctm,coswt
    integer :: i,n,j
    integer, parameter :: nmode=200    !number of modes (nmode)
    integer, parameter :: nt=100    !number of time steps(nt)
    real(kind=16), dimension(1:nmode) :: Uxt
    real(kind=16), dimension(1:nt) :: Umode
    character*12 :: filename

    
    print *, 'Enter the string length (ex: 1.0):'
    read *, stln

    print *, 'Enter the wave speed: (ex: 1.0):'
    read *, vel
    

    print *, 'Enter the position of the source (in m) (ex: 0.2) :'
    read *, xsrc
    
    print *, 'Enter the position of the receiver (in m) (ex: 0.7) :'
    read *, xrcvr

    print *, 'Enter the duration of the seismogram (in sec) (ex: 1.25) :'
    read *, tseis

    dt=tseis/nt    !time step in sec
    tau=0.02    !source shape term

    
    do 5 i=1,nt
        Uxt(i)=0.0
    5 continue
    do 10 n=1,nmode
        npiL=n*pi/stln
        srctm=sin(npiL*xsrc)    !source term
        rcvrtm=sin(npiL*xrcvr)    !Receiver term
        wn=n*pi*vel/stln    !mode frequency
        Fwn=exp(-((tau*wn)**2)/4)    !weighting factor of different frequencies

        spctm=srctm*rcvrtm*Fwn        !space term
        
        do 15 j=1,nt
            coswt=cos(wn*dt*(j-1))    !time term
            Uxt(j)=Uxt(j) + coswt*spctm    !displacement
        15 continue
    
    10 continue
        open(unit=1,file='seism.dat')
        write(1,'(f6.2,f12.6)') (dt*(j-1),Uxt(j), j=1,nt)    !writing the displacement
        close(1)
        
        
    stop
end program synt_seis_strings