68
6 Herz’s Task
1
2R 1
+
1
2R 2
= π(k 1 + k 2 )
c
b
.
(6.50)
By designating the load per unit of generatrix length as P 1 , we will obtain
P 1 =
b
−b
p(y)dy = 2c
b
0
1 −
y 2
b 2 dy, ?. ?. c =
P 1
πb
.
Substituting this result into formula (6.51) gives
b =
2P 1 R 1 R 2 (k 1 + k 2 )
R 1 + R 2
,
(6.51)
c = p max =
1
π
P 1 (R 1 + R 2 )
2R 1 R 2 (k 1 + k 2 )
.
(6.52)
References
1. M. Leonov, M. Osnovy mekhaniki uprugogo tela (Fundamentals of elastic body mechanics).
(Izd-vo AS Kirg. SSR, Frunze, 1963)
2. I. Vorovich, V. Aleksandrov, Mekhanika kontaktnykh vzaimodeistvii. Pod redaktsiei Vorovicha
I.I., Aleksandrova V.M. (Mechanics of contact interactions. Ed. by Vorovich I.I., Alexandrov
V.M.). (Fizmatlit Publ., Moscow, 2001)
3. E. Yanke, F. Ehmde, F. Lesh, Spetsial’nye funktsii (Formuly, grafiki, tablitsy) (Special functions
(formulas, graphs, tables)). (Nauka Publ., Moscow, 1977)
6 Herz’s Task
1
2R 1
+
1
2R 2
= π(k 1 + k 2 )
c
b
.
(6.50)
By designating the load per unit of generatrix length as P 1 , we will obtain
P 1 =
b
−b
p(y)dy = 2c
b
0
1 −
y 2
b 2 dy, ?. ?. c =
P 1
πb
.
Substituting this result into formula (6.51) gives
b =
2P 1 R 1 R 2 (k 1 + k 2 )
R 1 + R 2
,
(6.51)
c = p max =
1
π
P 1 (R 1 + R 2 )
2R 1 R 2 (k 1 + k 2 )
.
(6.52)
References
1. M. Leonov, M. Osnovy mekhaniki uprugogo tela (Fundamentals of elastic body mechanics).
(Izd-vo AS Kirg. SSR, Frunze, 1963)
2. I. Vorovich, V. Aleksandrov, Mekhanika kontaktnykh vzaimodeistvii. Pod redaktsiei Vorovicha
I.I., Aleksandrova V.M. (Mechanics of contact interactions. Ed. by Vorovich I.I., Alexandrov
V.M.). (Fizmatlit Publ., Moscow, 2001)
3. E. Yanke, F. Ehmde, F. Lesh, Spetsial’nye funktsii (Formuly, grafiki, tablitsy) (Special functions
(formulas, graphs, tables)). (Nauka Publ., Moscow, 1977)