The rational mechanics of flexible or elastic bodies 1638-1788

Cover......Page 1
Title page......Page 3
CONTENTS......Page 7
Foreword......Page 11
Prefatory Note concerning the presumed technological origin of the science of elasticity......Page 13
1. Remarks of the ancients on vibration and elasticity......Page 15
2. Western researches before 1600......Page 18
3. BEECKMAN on the suspension bridge (1614-1615), on vibration (1614-1618), and on elasticity (1620-1630)......Page 24
4. MERSENNX on vibration and rupture (1623-1636)......Page 28
5. The vibrating string, the breaking of a beam, and the catenary in GALILEO\'S Discorsi (1638)......Page 34
6. The unpublished work of HUYGENS on the suspension bridge (I646), the breaking of a beam (1662), the vibrating string (1673), and the vibrating rod (1688)......Page 44
7. PARDIES\' essays on the catenary and on elastic beams (1673)......Page 50
8. HOOKE\'S law of spring (1675, 1678) and researches on the arch (1675), on ropes (1669), and on sound (1675-1681)......Page 53
9. MARIOTTE and LEIBNIZ on elastic beams (1684)......Page 59
10. The contest to find the catenary (1690)......Page 64
11. JAMES BERNOULLI\'S researches on the general theory of flexible lines (I691-1704), and later work to 1717......Page 75
12. JAMES BERNOULLI\'S first researches on the elastica (1691-1694)......Page 88
13. JAMES BERNOULLI\'S attempts toward a theory of the neutral fibre (1695-1705)......Page 96
14. PARENT\'S researches on the neutral fibre (1704-1713)......Page 109
15. Researches on theoretical and experimental elasticity by JAMES RICCATI (1720-1723) and others......Page 114
16. Experiments on the nodes of vibrating bodies by NOBLE and PIGOT (c. 1674), SAUVEUR (1696-1701), DE LA HIRE (1709), and ZENDRINI (1715-1716)......Page 118
17. TAYLOR\'S analysis of the continuous vibrating string (1713)......Page 129
18. JOHN BERNOULLI\'S analysis of the loaded vibrating string (1727)......Page 132
19. Summary: EULER\'S heritage......Page 136
20. EULER\'S derivation of JAMES BERNOULLI\'S law of bending from HOOKE\'S law of extension; introduction of the modulus of extension (1727)......Page 142
21. EULER\'S unification of the catenary and the elastica (1728)......Page 146
22. MUSSCHENBROEK\'S experimental discovery of the law of buckling in compression (1729)......Page 150
23. DANIEL BERNOULLI\'S discovery of the simple modes and proper frequencies of vibrating systems (1733), and related work of EULER......Page 154
24. DANIEL BERNOULLI\'S and EULER\'S first calculations of simple modes and proper frequencies for the transverse oscillations of bars (1734-1735)......Page 165
25. Further researches on the elastica; EULER\'S general solution for linear vibration problems (1735-1739)......Page 170
26. The first differential equations of motion: JOHN BERNOULLI\'S and D\'ALEMBERT\'S treatments of the hanging cord (1742-1743)......Page 179
27. DANIEL BERNOULLI\'S definitive work on the transverse vibrations of bars (1740-1742)......Page 192
28. EULER\'S treatise on elastic curves (1743). 1. Static deflection......Page 199
29. EULER\'S treatise on elastic curves (1743). II. Vibrations......Page 219
30. EULER\'S equations of finite motion for linked systems and for the continuous string (1744)......Page 222
31. EULER\'S general solution for longitudinal vibration of the loaded elastic cord ( 1748)......Page 229
32. Summary to 1748......Page 234
33. D\'ALEMBERT\'S first memoir (1746): The partial differential equation and its solution by an \"equation\"......Page 237
34. EULER\'S first memoir (1748): The solution by arbitrary functions......Page 244
35. EULER\'S \"first principles of mechanics\" (1750)......Page 250
36. DANIEL BERNOTILLI\'S memoirs on the composition of simple modes (1753)......Page 254
37. EULER\'S second memoir (1754): The central importance of the partial differential equation......Page 259
38. LAGRANGE\'S first memoir (1759): The explicit solution for the loaded string, and a faulty passage to the limit......Page 263
39. Miscellaneous polemics (1760-1767)......Page 273
40. EULER\'S researches on the propagation and reflection of waves (1764-1765)......Page 281
41. Miscellaneous polemics to 1788......Page 286
42. Summary of the theory of the vibrating string to 1788......Page 295
43. The earliest researches on non-uniform strings: Simple modes for special cases, and EULER\'S general inverse method (1752-1765)......Page 301
44. Polemics, errors, and further special cases (1770-1788)......Page 311
45. Plane vibrations of a heavy cord hung from one end......Page 316
46. EULER\'S faulty theories of curved rods (1760, 1774)......Page 320
47. EULER\'S definitive work on the ix kinds of transverse vibration of straight rods (1772-1774), and its experimental verification by JORDAN RICCATI (1782) and by CHLADNI (1787)......Page 322
48. EULER\'S theory of the vibrating membrane (1759)......Page 330
49. CHLADNI\'S experiments on the vibrations of free plates (1787)......Page 335
50. Discrete models......Page 341
51. EULER\'S calculation of buckling loads for columns of non-uniform cross-section (1757)......Page 345
52. The distinction of different kinds of buckling by DANIEL & JOHN III BERNOULLI (1766)......Page 347
53. LAGRANGE\'S two memoirs (1770, 1773)......Page 349
54. EULER\'S determination of the height at which a heavy vertical column buckles (1776, 1778)......Page 356
55. LAGRANGE\'S variational equations of motion for flexible lines (1761)......Page 371
56. EULER\'S theory of the skew elastica (1774-1775)......Page 374
57. Miscellaneous researches (1754-1768)......Page 383
58. EULER\'S introduction of shear force and derivation of the general equations of equilibrium for a deformable line (1771, 1774)......Page 390
59. COULOMB\'S introduction of interior shearing stress (1773)......Page 396
60. EULER\'S formal definition of the modulus of extension and final scaling laws for the frequencies and buckling loads of straight rods (1774, 1776)......Page 401
61. COULOMB\'S experiments on torsion (1777, 1784)......Page 405
62. An evaluation from the eighteenth century: LAGRANGE\'S Mechanique Analitique (1788)......Page 409
63. Some later evaluations: CHLADNI (1802), T. YOUNG (1807), LOVE (1892)......Page 412
64. A modern evaluation......Page 416
INDEX OF NAMES......Page 429