THE RATIONALLY SYMMETRIC MOTION OF A SMALL ANGLE TRUNCATED CONICAL SHELL DUE TO A CONSTANT VELOCITY PRESSURE FRONT. PART I. - ANALYSIS,
Abstract
A thin truncated conical shell is analyzed for the initial transient response due to the passage of a pressure front of constant velocity and amplitude. The principle of virtual work is applied to a segment of the shell, between two adjacent generatrices, treated as a beam on an elastic foundation. The ends of the shell are considered to be simply supported. First, the natural or free modes of vibration are approximated using an eight-term series of functions each satisfying the boundary condition. Then the resulting modes are used in conjunction with time dependent coefficients to formulate the forced response. Since an analytic solution of the differential equation was not readily possible, a numerical or iterative procedure was employed using a digital computer. Part I, the present report, consists of the analysis and derivations pertinent to the problem. Part II, to be issued separately, contains the numerical results and plotted data. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1963
- Accession Number
- AD0425702
Entities
People
- Joseph I. Bluhm
Organizations
- United States Army Research Laboratory