I think you either need to install a ssh key
onto each server or use expect
and type your password once.
The ssh key solution:
Read this link, but do not set up a password for your RSA key.
The expect solution:
#!/bin/bash
# This function is sent to the server. I've used it for testing
function dosomething {
ls
}
# The script expects a file with servers separated with newlines.
FILE=$1
# If the file does not exist, it exits.
[ -f "${FILE}" ] || exit 1
# I didn't know your password and username. If you would like me to add it,
# please sent me a DM or paste it as comment ;-)
read -sp "username: " USERNAME
echo
read -sp "password: " PASSWORD
echo
# While the content of ${FILE} isn't empty...
while IFS= read -r SERVER; do
# .. use expect to spawn ssh, login with ${PASSWORD}, send the dosomething to
# the server, execute dosomething and exit.
expect <<-EOF
spawn ssh ${USERNAME}@${SERVER}
expect "*: " { send "${PASSWORD}\r" }
expect "*$ " { send "$(typeset -f dosomething)\r" }
expect "*$ " { send "dosomething\r" }
expect "*$ " { send "exit\r" }
EOF
done < ${FILE}
# You're up ;-)
exit $?