How to get ID's of Children div's of a class with a specific Parent div ID

How to get ID's of Children div's of a class with a specific Parent div ID

I'm building a volunteer translation site.  In order to constantly update only  paragraphs that multiple translators are working on, I need to pass an array to PHP of A: which paragraphs are open, and B: which translations have been submitted and are visible on the user's screen.  PHP will then compare this with what is in the database and tell jQuery to add new submitted translation paragraphs or remove deleted ones.

I've managed to make a string of all the open Div's and have it updated every second, like this:

function cycle(){
   
    var data = '';
    $('.paragraphtobetranslated:visible').each(function(){

        var mytransid = $(this).attr('id');
        var translationids = '';
            $('#'+mytransid).children().filter('.submittedtranslations').each(function(){
                translationids = translationids + ',' + $(this).attr('id');

                });
        var thisrow = mytransid + '{' + translationids+'}';

        data = data + thisrow;

    });


    $('#ajaxbox').load('/processDifferences',{ 'data': data });

    setTimeout('ping()',1000);
}


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This line specifically doesn't work:             $('#'+mytransid).children().filter('.submittedtranslations').each(function(){

I'm not able to pass the id of the parent Div as "#" + the variable ID mytransid.  Can anyone tell me how to get only the IDs of the Divs of the class "submittedtranslations" with a Parent Div with a variable ID?

Thanks a lot for any help.  If anyone has additional advice on how to pass this as a multi-dimensional array, that would be appreciated too, but not absolutely essential to the task here.  I have no experience with javascript arrays or JSON.