Vibration of beams with general boundary conditions due to a moving random load M. Abu-Hilal Summary The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed, and fixed– free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation. Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force on the dynamic response of beams are studied in detail. Keywords Vibration, Beam, Moving load, Random load 1 Introduction The general problem of transverse vibrations of beams due to moving loads is an important research topic in mechanical, industrial and civil engineering. Vibrations of this kind occur in bridges, runways, railways, beams subjected to pressure waves and piping systems subjected to two-phase flow. Several studies have been performed to explore the various aspects of the moving load problem. The dynamic response of a simply supported beam subjected to a moving single and continuous random load, which moves with constant velocity was studied in [1, 2]. Also, the effects of damping on the response of beams were studied there. In [3, 4], was studied the response of simply supported beams at general boundary conditions subjected to a stream of random moving loading systems of Poissonian pulse-type, i.e. with mutually independent, identically distributed force amplitudes arriving at the beam at independent random times. The stream of loading systems was assumed to move with different types of motion: accel- erating, decelerating and at constant velocity. The random vibration of a simply supported elastic beam subjected to random loads moving with constant and time-varying velocity and axial forces was considered in [5]. Paper [6] studied the dynamic response of simply sup- ported rotating Euler–Bernoulli, Rayleigh and Timoshenko beams due to random moving loads. In [7], the vibration problem was treated for a simply supported beam subjected to randomly spaced moving loads with a constant velocity. Assuming that the load sequence is a Poisson process and the inertial effect of moving loads can be neglected, the authors ex- amined the time history, the power spectral density, and the various moments of the re- sponse. The dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes was studied in [8]. Based on the introduction of two influence functions, one of which satisfies the nonhomogeneous, the other the homogeneous differential equa- tions for beam response, the authors obtained explicit expressions for expected value and variance of the beam deflection. In [9], a linear dynamic analysis for determining the coupled flexural and torsional vibration of multispan suspension bridges was presented. The dynamic analysis duly considers the nonlinear bridge-vehicle interactive force, eccentricity of the vehicle path, surface irregularity of the bridge pavement, cable-tower connection and end Archive of Applied Mechanics 72 (2003) 637 – 650 Ó Springer-Verlag 2003 DOI 10.1007/s00419-002-0228-7 637 Received 3 December 2001; accepted for publication 30 April 2002 M. Abu-Hilal Department of Mechanical and Industrial Engineering, Applied Sciences University, Amman 11931, Jordan