| 1. |
|
|
| 2. |
- Hägglund, Anders, 1972, et al.
(författare)
-
Dynamic cylindrical shell equations by power series expansions
- 2008
-
Ingår i: Proceedings of the 6th International Conference on Computation of Shell & Spatial Structures. ; , s. 14-17
-
Konferensbidrag (refereegranskat)abstract
- Dynamics of an infinite circular cylindrical shell is considered. The derivation process is based on power seriesexpansions of the displacement components in the radial direction. Using the three dimensional equations ofmotions, a set of recursion relations is identified expressing higher displacement coefficients in terms of lowerorder ones. The new approximate shell equations are hereby obtained from the boundary conditions, resultingin a set of six partial differential equations. These equations are believed to be asymptotically correct and itis, in principle, possible to go to any order. Dispersion curves, together with the eigenfrequencies for a 2Dcase, are calculated using exact, classical and expansion theories. It is shown that the approximate equationscontaining order h2 are in general as good as or better than the established theory of the same order.
|
|
| 3. |
- Hägglund, Anders, 1972, et al.
(författare)
-
Dynamic cylindrical shell equations by power series expansions
- 2008
-
Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 45:16, s. 4509-22
-
Tidskriftsartikel (refereegranskat)abstract
- The dynamics of an infinite circular cylindrical shell is considered. The derivation process is based on power series expansions of the displacement components in the radial direction. By using these expansions in the three-dimensional equations of motions, a set of recursion relations is identified expressing higher displacement coefficients in terms of lower order ones. The new approximate shell equations are hereby obtained from the boundary conditions, resulting in a set of six partial differential equations. These equations are believed to be asymptotically correct and it is, in principle, possible to go to any order. Equations of order up to and including the square of the thickness h2 are presented explicitly. This set of six equations are reduced to five as well as three equations and compared to classical theories. Dispersion curves, together with the eigenfrequencies for a 2D case, are calculated using exact, classical and expansion theories. It is shown that the approximate equations containing order h2 are in general as good as or better than the established theory of the same order.
|
|
| 4. |
- Hägglund, Anders, 1972
(författare)
-
Dynamic Plate and Shell Equations Using Power Series Expansions - Applications Including Elasticity, Poroelasticity and Fluid Loading
- 2007
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Thin structures are used in a wide range of engineering applications. The subject of this thesis is the derivation of approximate equations for the dynamics of thin plates and shells using series expansion methods.Approximate boundary conditions that simulate the behaviour of fluid-loaded elastic or poroelastic plates by eliminating the internal field variables are developed, using series expansions of the fields in the thickness coordinate. The resulting boundary conditions contain the sums and differences of the pressure fields and their partial derivatives in the thickness direction. The equations have been validated using transmission coefficients and dispersion curves for different combinations of fluids and elastic or poroelastic solids by comparison with the exact three-dimensional solutions as well as with classical plate models. Another approach studied in this thesis uses power series expansions of the displacement field in the thickness coordinate to obtain approximate dynamic equations for a cylindrical shell. The expansions are inserted into the equations of motion, creating a set of recursion relations expressing higher order displacement coefficients in terms of lower order ones. Using the recursion relations, equations with only the two lowest order coefficients are derived from the boundary conditions. By truncating the resulting shell equations to include terms up to a certain power of the thickness, a hierarchy of approximate shell equations is formed. The shell equations are presented explicitly with terms including up to the square of the thickness. The natural frequencies in the two-dimensional case (the ring) and the dispersion curves for propagating modes in the three-dimensional case are presented for different truncation orders, and compared with exact three-dimensional theory as well as with classical theories.The two seemingly different approaches used for plates and shells are in fact equivalent. One important factor of the approaches is that they are believed to yield asymptotically correct equations to any order, as the thickness tends to zero. Due to the complexity of higher order equations, only those of low order seem to be useful in an engineering context.
|
|
| 5. |
- Johansson, Martin, 1973, et al.
(författare)
-
Approximate boundary conditions for a fluid-loaded elastic plate
- 2005
-
Ingår i: Journal of the Acoustical Society of America. - : Acoustical Society of America (ASA). - 1520-8524 .- 0001-4966. ; 118:6, s. 3436-3446
-
Tidskriftsartikel (refereegranskat)abstract
- Approximate boundary conditions for an infinite elastic layer immersed in a fluid are derived. By using series expansions in the thickness coordinate of the plate fields, the displacements fields are eliminated, adopting the three-dimensional equations of motion. The sums and differences of the boundary pressure fields and their normal derivatives are related through a set of approximate boundary conditions, one symmetric and one antisymmetric. These equations involve powers in the layer thickness together with partial derivatives with respect to time as well as the spatial variables in the plate plane. The approximate boundary conditions can be truncated to an arbitrary order, and explicit relations are presented including terms of order five. Comparisons are made with effective boundary conditions using classical plate theories. The numerical examples involve reflection and transmission of plane waves incident on the plate at different angles, as well as the pressure fields due to a line force. Three fluid-loading cases are studied: modest, heavy, and light loadings. The results using truncated approximate boundary conditions are compared to exact and classical plate solutions. The examples show that the accuracies of the power series approximations of order three and higher are very good in the frequency interval considered.
|
|
