phenomenon 30.65 Chladni figures

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:2315 · p. 1033

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depends_on proposition 30.66 Chladni scaling ¶
- depends_on definition 30.63 Flexural rigidity ¶
  - depends_on proposition 30.33 Conversion among the moduli ¶
    - depends_on definition 30.31 The engineering moduli ¶
      - depends_on definition 30.20 Pressure and deviatoric stress ¶
      - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
    - depends_on phenomenon 30.32 Poisson contraction ¶
      - depends_on phenomenon 30.28 Hooke's law ¶
      - depends_on proposition 30.30 Stability bounds ¶
      - proves proof ch:13-continuum-elasticity@proof-14 ¶
    - proves proof ch:13-continuum-elasticity@proof-15 ¶
  - depends_on proposition 30.51 Moment and curvature ¶
    - depends_on definition 30.31 The engineering moduli ¶ ↺
    - depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
    - proves proof ch:13-continuum-elasticity@proof-27 ¶
- depends_on theorem 30.64 The Kirchhoff plate equation ¶
  - depends_on definition 30.63 Flexural rigidity ¶ ↺
  - depends_on theorem 16.38 Euler–Poisson equation ¶
    - depends_on corollary 7.44 Substitution and integration by parts ¶
      - depends_on proposition 7.31 Chain rule ¶
      - depends_on proposition 7.30 Leibniz rule ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-26 ¶
    - depends_on equation 16.15 eq:calcvar-first-variation ¶
    - depends_on lemma 16.18 Fundamental lemma ¶
      - depends_on definition 16.15 Variation; the first variation ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶
      - proves proof ch:14-calculus-of-variations@proof-8 ¶
    - proves proof ch:14-calculus-of-variations@proof-21 ¶
  - proves proof ch:13-continuum-elasticity@prooflink-2 ¶
- proves proof ch:13-continuum-elasticity@proof-33 ¶
depends_on theorem 30.64 The Kirchhoff plate equation ¶ ↺
proves proof ch:13-continuum-elasticity@proof-32 ¶

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type	direction	node	provenance	where
`cites`	→	Entdeckungen über die Theorie des Klanges	derived	parts/03-classical-mechanics/13-continuum-elasticity.tex:2322
`cites`	→	Recherches sur la théorie des surfaces élastiques	derived	parts/03-classical-mechanics/13-continuum-elasticity.tex:2325
`cites`	→	Über das Gleichgewicht und die Bewegung einer elastischen Scheibe	derived	parts/03-classical-mechanics/13-continuum-elasticity.tex:2325
`depends_on`	→	Chladni scaling	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2326
`depends_on`	→	The Kirchhoff plate equation	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2326
`proves`	←	ch:13-continuum-elasticity@proof-32	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2329