Sri RanganAyakai Nama:

SLOKAM 56

dhugdhArNavam Janana bhuvana preethyA BahumanyasE
  Janani dayitha prEmNA pushNAsi tathparamam padham
udhathi parama vyOmnOr-vismruthya mAdhrusa-rakshaNa-
  kshamamithi dhiyA bhUya:SrIranga dhAmani mOdhasE

Meaning according to Dr.V.N.Vedantha Desikan:

 This shrine is called SREERANGAM in the sense that it is the court-hall for Your sport and dance , where in SHREE sabdham refers to You. Because You have chosen this dais for Your purpose of ensuring the well being of all creatures , which are but Your children , all like me , knowing nothing about Your unmatched vaibhavam and yet deserving Your Motherly grace, You enjoy this location; evidently You have spurned Your birth-place ( the milky ocean) and Your husband's perrenial abode(Sree Vaikuntam) in favour of Sreerangam to be near us.

Special Notes:

Oh Sarva Loka MaathA! Your birth home (PiRantha aham) is the Milky Ocean and naturally You are very much attached to it. Your husband's home (Puhuntha aham) is the famous location praised by the Vedams as "Tadh VishNO: Paramam Padham". As the bride joining Your husband's home , You are very fond of this home too , since You adore Your husband .

Your Janana Bhavana preethi (Fondness for Your birth place ) makes You consider the Milky Ocean with great affection ; because of Your love for Your husband (Dayitha PrEmai), You adore Your Pukkaham (Your husband's abode) celebrated in the Vedams as "Tadh VishNO: Paramam padham". You have set aside those special and meaningful abodes and chosen however SREERANGAM as Your most preferred place of residence to save us helpless ones (akinchana janams). Since You chose residence in SrIrangam over the other two sites dear to You as the most auspicious place (Sree) for Your sport (Rangam) of protecting us. This is Your Ranga BhUmi and Sriya: Rangam and is not Sriyutham Rangam ( auspicious place, a term used for UpachAram purposes).Maadhrusa RakshaNam (protection of helpless ones like us) is Your motivation to minimize the importance of Your birth place and SrI Vaikuntam as Pukkaham and choose Sreerangam for the express purpose of protecting us. SrIranga dhAmani mOdhasE (You revel at this abode of SrIrangam) now. This is the wonder (adhisayathvam ) of the archAvathAram of SrI RanganAyaki at Sreerangam according to Swamy ParAsara Bhattar.

Sri RanganAyaki ThAyAr ThiruvadigaLE SaraNam,
Daasan, Oppiliappan Koil VaradAchAri SaThakOpan /Sadagopan