3-D THEORY VERSUS 2-D APPROXIMATE THEORY OF FREE ORTHOTROPIC (ISOTROPIC) PLATE AND SHELL VIBRATIONS, PART 2: NUMERICAL ALGORITHMS AND ANALYSIS

✍ Scribed by J. AWREJCEWICZ; V.A. KRYSKO

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 289 KB
• Volume: 226
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2320

✦ Synopsis

The three-dimensional theory of orthotropic and isotropic plates (with and without concentrated masses) vibrations is used to estimate a validity of the two-dimensional theories application range. First, a general analytical approach is presented, and then the algorithms for numerical calculations are developed. Many examples obtained in the form of tables and drawings support the considerations and also some practically valid conclusions applied to isotropic and transversal-isotropic plates are derived.

Equations ( 1) can be replaced by an equivalent system. First one can disconnect the tension components. Then a vibration problem of a conical orthotropic shell with added elements is reduced to determination of the displacements components u, v, w satisfying the following equations:

After introducing the dimensionless parameters

x"xN a, y"yN b, z"2hzN , u"2huN , v"2hvN , w"2hw N , "a/2h, "b/2h,

1 *u *x*y # 1 *v *z*y # *w *z #w "0. (26) A 1 *; *x #A 1 *< *y #A *= *z * *y *= *y (y!y G ) (x!x G )