FREE VIBRATIONS OF DOUBLY CURVED IN-PLANE NON-HOMOGENEOUS SHELLS

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

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 610 KB
• Volume: 225
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2268

✦ Synopsis

A method for investigating free vibrations rectangular non-homogeneous shells is proposed. By non-homogeneity, we de"ne a chage of sti!ness of shell bending caused by an introduction of another material or change of a shell thickness is de"ned. It is assumed that a shell possesses an arbitrary value of rectangular parts with di!erent bending sti!ness.

From equation ( 10) we get the equations of motion

and the deformation continuity relation

obtained: (a) one equilibrium equation

When in equations ( 13) and ( 14) we take E"const, "const and using integration by parts we "nally obtain the equations

where N denotes the number of sti!ness parts; I , I are coe$cients of bending sti!ness and density of the k sti!ness parts [see equation ( 18)], showing a relative * GH *x * TX *x # * GH *y * TX *y #2(1! ) * GH *x*y * TX *x*y # * GH *x * TX *y # *w GH *y * TX *x dx dy, * GH *x * TX *y # \ * GH *x ! * GH *y * TX *x #2(1# ) * GH *x*y * TX *x*y dx dy J TXGH " ! k V * GH *y #k W * GH *x TX dx dy. (23)