Abstract
The steady-state free and forced response and stability for large amplitude motion of a beam with clamped ends is investigated. Elastic restraint of the ends is included in order to relate theory with experiment. A multimode analytical and numerical technique is used to obtain theoretical solutions for both response and stability. Experimental results largely confirm the results of the analysis. It is concluded that, while single mode analyses are adequate in some cases, there are circumstances where a multimode analysis is essential to predict the observed results. Nomenclature Am = amplitude of the rath mode E = Young's modulus F = transverse force FQ = generalized force h = beam thickness I = second moment of area of the cross section Ks = axial spring factor k = axial spring constant ki = rotational spring constant L = beam length PO = initial axial tension Pom = nondimensional amplitude of the generalized harmonic force t = time w = transverse displacement x = axial coordinate Mmkin,Fim, = modal constants GmrsjGmgrs
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