PERIODIC STRING RESPONSE TO AN IMPACT AND A SUDDENLY APPLIED CONCENTRATED STATIONARY FORCE
✍ Scribed by P.M. BELOTSERKOVSKIY
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 242 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
An in"nite periodic structure unsteady response to a forced excitation is considered. Any forced excitation can be presented as a sequence or a distribution of impulses. The instantaneous impulse is an in"nite sum of harmonic forces of the same amplitude and phase, whose frequencies "ll the in"nite band as follows from the Fourier transformation of the Dirac delta function. The solution to the problem of a periodic structure steady state response to excitation by a harmonic concentrated stationary force is obtained by reducing the problem to a di!erence equation and used to calculate the unsteady response. The in"nite periodic structure consisting of an in"nite stretched string, supported by equidistantly spaced identical suspensions, is considered. Each suspension consists of a spring and a dashpot with viscous damping, in parallel. Small transverse oscillations of the string without bending sti!ness are considered. In order to exclude from the solution the string slope, which experience a sudden change at the point, where a concentrated force is applied, and so at every suspension point, the boundary problem is solved over the string unloaded span. The string transverse de#ection at an arbitrary point of the span as well as its slope are expressed via the de#ection values at the beginning and at the end of the span. Then, two neighbour spans are considered together. A suspension reaction that depends on the suspension point de#ection is connected with the string slopes to the right and to the left of the point. The connection involves the string transverse de#ection at three successive suspension points and represents the second order di!erence equations. The solution to this equation allows one to express the string de#ections at all suspension points via only two, which relate to ends of the span, where the excitation is applied. Consideration of this span leads to calculation of the string steady state oscillations and response to an impact. To give an example of application, the latter is used to calculate the string response to a suddenly applied force.