Analytical solutions for free and forced vibrations of a multiple cracked Timoshenko beam subject to a concentrated moving load

• Published in: Acta mechanica Vol. 221; no. 1-2; pp. 79 - 97
• Main Authors: Shafiei, M., Khaji, N.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.09.2011; Springer; Springer Nature B.V
• Subjects: Beams (structural); Classical and Continuum Physics; Control; Crack propagation; Dynamical Systems; Engineering; Engineering Thermodynamics; Exact sciences and technology; Forced vibration; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Mathematical analysis; Mathematical models; Mechanical engineering; Moving loads; Physics; Solid Mechanics; Springs (elastic); Static elasticity (thermoelasticity...); Structural and continuum mechanics; Theoretical and Applied Mechanics; Timoshenko beams; Velocity; Vibration; Vibration analysis; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Crack Depth; Forced Vibration; Bernoulli Beam; Timoshenko Beam; Cantilever Beam; Crack array; Modal analysis; Forced vibration; Free vibration; Eigenfunction; Timoshenko beam; Rupture; Modeling; Concentrated load; Edge crack; Crack propagation; Boundary value problem; Moving load; Superposition method; Cracked beam
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-011-0495-x

An analytical approach for evaluating the forced vibration response of uniform beams with an arbitrary number of open edge cracks excited by a concentrated moving load is developed in this research. For this purpose, the cracked beam is modeled using beam segments connected by rotational massless linear elastic springs with sectional flexibility, and each segment of the continuous beam is assumed to satisfy Timoshenko beam theory. In this method, the equivalent spring stiffness does not depend on the frequency of vibration and is obtained from fracture mechanics. Considering suitable compatibility requirements at cracked sections and corresponding boundary conditions, characteristic equations of free vibration response are derived. Then, forced vibration response is treated under a moving load with a constant velocity. Using the determined eigenfunctions, the forced vibration response may be obtained by the modal superposition method. Finally, some parametric studies are presented to show the effects of crack parameters and moving load velocity.