In this article, based on combinatorial methods, the structure of RFPrLrR circulant matrices and the identities of matrix norms, we give three lower bounds and upper bounds for spectral norms of RFPrLrR circulant matrices involving exponential forms and trigonometric functions by using a different method. Moreover, we introduce new geometric RFPrLrR circulant matrix, and then we obtain three lower bounds for spectral norms and its upper bound.