Two-dimensional elasticity solution for transient response of simply supported beams under moving loads

• Published in: Acta mechanica Vol. 217; no. 3-4; pp. 205 - 218
• Main Authors: Hasheminejad, Seyyed M., Rafsanjani, Ahmad
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.03.2011; Springer; Springer Nature B.V
• Subjects: Applied sciences; Beams (radiation); Beams (structural); Building structure; Buildings. Public works; Classical and Continuum Physics; Concrete structure; Construction (buildings and works); Control; Dynamical Systems; Elasticity; Engineering; Engineering Thermodynamics; Exact sciences and technology; Fourier series; Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Inversions; Laplace transforms; Load; Mathematical models; Oscillations; Physics; Solid Mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Theoretical and Applied Mechanics; Vibration; Vibration analysis; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Free Vibration; Composite Beam; Timoshenko Beam; Elastic Foundation; Differential Quadrature; Thick beam; Transient response; Vibration; Timoshenko beam; Simple support; Bernoulli Euler model; State space method; Elastic wave; Transverse load; Aspect ratio; Fourier series; Modeling; Concentrated load; Inverse problem; Finite element method; Linear elasticity; Moving load; Series expansion; Laplace transformation; Elastodynamics; Sinusoidal excitation; Dynamic load
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-010-0393-7

A semi-analytical analysis for the transient elastodynamic response of an arbitrarily thick simply supported beam due to the action of an arbitrary moving transverse load is presented, based on the linear theory of elasticity. The solution of the problem is derived by means of the powerful state space technique in conjunction with the Laplace transformation with respect to the time coordinate. The inversion of Laplace transform has been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations and obtain uniformly convergent solutions. Detailed numerical results for the transient vibratory responses of concrete beams of selected thickness parameters are obtained and compared for three types of harmonic moving concentrated loads: accelerated, decelerated and uniform. The effects of the load velocity, pulsation frequency and beam aspect ratio on the dynamic response are examined. Also, comparisons are made against solutions based on Euler–Bernoulli and Timoshenko beam models. Limiting cases are considered, and the validity of the model is established by comparison with the solutions available in the existing literature as well as with the aid of a commercial finite element package.