No. That is quite frankly not possible.
There are, however, Japanese names like Ai that only have vowels
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The words "I" and "a" each contain only one letter which is a vowel. a word that has only vowels could be aiea and it is a city name
The only one of the United States with three consecutive vowels in its name is Hawaii
Hawaii.
all words have vowels
Can it only consist of vowels? Many words have 5 vowels. Queueing has five in a row.