Frank Behnke is the brother of my GGrandmother, Anna Behnke. I don't have his birth/death dates but in researching Anna I found their mother to be Louise b.1853,and d.27Nov1936. Louise was daughter of John Krinebrink(best spelling of last name I can make out from her death cert.)Frank and Anna's father was Carl Behnke,b.10 Oct1849 in Mecklenburg-Strelitz,Germany. He died 13 July 1923 in ChurchHill village,Liberty township, Trumbull county,Ohio. Other than "Behnke" for his fathers name,neither his mother or father are listed on his death certificate. His obit says "he had been highly esteemed and respected by all who knew him".
It appears that Louise, Frank and Anna traveled to America on the SS Rhenania, arriving New York on Nov 7, 1881. They are listed as BEHNKE,Carl Female wife age 26; BEHNKE,Franz Male child age 6; and BEHNKE,Anna Female child,age 11months. Also listed with them in the manifest is KREIENBRING,Johanna F woman age 64, and KREIENBRING,Minna F daughter, age 26. All are listed as from Mecklenburg (Charlottenhof) and all are listed as destination Youngston (sic),Ohio. Also going to 'Youngston' is BUNNING, Aug, male farmer age 22 from Mecklenburg. I don't know what relation, if any, this person is. This information was found on the Immigrant Ships Transcribers Guild website.
Hope some of this is of interest to you. If your research leads you to identify what I assume would have been Carl Behnke's earlier arrival in America, or any of Franks line beyond Louise and Carl, or to info on his siblings I would love to know what you find.