The effects of compressive axial load on the forced vibrations of the Rayleigh and Timoshenko double-beam system are discussed for three cases of particular excitation loadings. Thus the beam-type dynamic absorber can be used to suppress the excessive vibrations of corresponding beam systems. Vibrations caused by the harmonic exciting forces are discussed, and conditions of resonance and dynamic vibration absorption are formulated. The dynamic responses of the system caused by arbitrarily distributed continuous loads are obtained. The analytical solution of forced vibration with associated amplitude ratios is determined. The general solutions of forced vibrations of beams subjected to arbitrarily distributed continuous loads are found. Based on the Timoshenko beam theory, deflections of the beams are shown. Keywords: Forced vibration Timoshenko double beam Rayleigh double beam Winkler elastic layer Critical buckling force a b s t r a c t Forced vibration and buckling of a Rayleigh and Timoshenko double-beam system continuously joined by a Winkler elastic layer under compressive axial loading are considered in this paper. #Axial loading cracked#Comparison of analytical and numerical results indicates good accuracy of derived formulation for natural frequencies of the cracked double-beam system. The problem one more time was solved using the differential transform method to approve the accuracy of the analytical formulation for the cracked double-beam system. Using the obtained admissible functions and Rayleigh method, an explicit formulation was achieved for natural frequencies. #Axial loading crack#The unknown coefficients of polynomial functions were calculated by using boundary conditions of the system and compatibility conditions at the crack section. In the case of crack occurrence, the mode shapes of intact beam were modified by adding cubic polynomial functions to represent crack effect. In this regard, Rayleigh method was applied to derive explicit formulation for natural frequencies. To obtain natural frequencies, Eigenvalue problem solving finally yields an algebraic equation which must be solved numerically and does not show effects of different damage parameters in the explicit form. Material properties and cross section geometry of beams could be arbitrary and different from each other. Euler–Bernoulli hypothesis was applied to beams, and Winkler model was used for inner layer. In the present study, an analytical formula to estimate natural frequencies of a simply supported double-beam system in the presence of open crack is derived.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |