The Short-Time Impulse Response of Euler-Bernoulli Beams

@article{citeulike:877800, abstract = {We study an undamped, simply supported, Euler-Bernoulli beam given an instantaneous impulse at a point G, far from its ends. The standard modal solution obscures interesting mathematical features of the initial response, which are studied here using dimensional analysis, an averaging procedure of Zener, a similarity solution for an infinite beam, asymptotics, heuristics, and numerics. Results obtained include short-time asymptotic estimates for various dynamic quantities, as well as a numerical demonstration of fractal behavior in the response. The leading order displacement of G is proportional to . The first correction involves small amplitudes and fast oscillations: something like t3/2 cos(t\&\#150;1). The initial displacement of points away from G is something like t cos(t\&\#150;1). For small t, the deformed shape at points x far from G is oscillatory with decreasing amplitude, something like x\&\#150;2 cos(x2). The impulse at G does not cause impulsive support reactions, but support forces immediately afterwards have large amplitudes and fast oscillations that depend on inner details of the impulse: for an impulse applied over a time period , the ensuing support forces are of (\&\#150;1/2). Finally, the displacement of G as a function of time shows structure at all scales, and is nondifferentiable at infinitely many points. \©2004 ASME}, author = {Chatterjee, Anindya }, citeulike-article-id = {877800}, doi = {10.1115/1.1667531}, journal = {Journal of Applied Mechanics}, keywords = {elasticity, plates}, number = {2}, pages = {208--218}, posted-at = {2006-09-29 16:15:23}, priority = {2}, publisher = {ASME}, title = {The Short-Time Impulse Response of Euler-Bernoulli Beams}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=JAMCAV000071000002000208000001\&idtype=cvips\&gifs=yes}, volume = {71}, year = {2004} }

TY - JOUR ID - citeulike:877800 L3 - citeulike-article-id:877800 TI - The Short-Time Impulse Response of Euler-Bernoulli Beams JF - Journal of Applied Mechanics VL - 71 IS - 2 SP - 208 EP - 218 PB - ASME N2 - We study an undamped, simply supported, Euler-Bernoulli beam given an instantaneous impulse at a point G, far from its ends. The standard modal solution obscures interesting mathematical features of the initial response, which are studied here using dimensional analysis, an averaging procedure of Zener, a similarity solution for an infinite beam, asymptotics, heuristics, and numerics. Results obtained include short-time asymptotic estimates for various dynamic quantities, as well as a numerical demonstration of fractal behavior in the response. The leading order displacement of G is proportional to . The first correction involves small amplitudes and fast oscillations: something like t3/2 cos(t–1). The initial displacement of points away from G is something like t cos(t–1). For small t, the deformed shape at points x far from G is oscillatory with decreasing amplitude, something like x–2 cos(x2). The impulse at G does not cause impulsive support reactions, but support forces immediately afterwards have large amplitudes and fast oscillations that depend on inner details of the impulse: for an impulse applied over a time period , the ensuing support forces are of (–1/2). Finally, the displacement of G as a function of time shows structure at all scales, and is nondifferentiable at infinitely many points. ©2004 ASME KW - elasticity KW - plates AU - Chatterjee, Anindya PY - 2004/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAMCAV000071000002000208000001&idtype=cvips&gifs=yes ER -