Dynamic Response Of Infinite Beams On Viscoelastic Foundations To Moving Load

With the continuous development of national economy and highwaytransportation industry, the high speed and heavy duty phenomenon has becomeextraordinary common. The dynamic load of heavy duty vehicle is the complicatevibration problem.Dynamic response of Euler beams and Timoshenko beams on viscoelasticfoundation to a moving load is proposed by integral transformation in the secondchapter. The Green’s function of the beams is obtained by means of two-dimensionalFourier transform. The deflection of beam is represented using inverse Fouriertransform. The theorem of residue is then applied to represent the generalizedintegral in the form of contour integral in the complex plane. The research in theinfluence of parameters of beam and subgrade are provided with illustrations. It’sclear that viscosity and shear modulus of subgrade have significant effect on thedeflection of the beam. Then the numerical solution of the integral expression isresearched by spline interpolation. It proved that the closed-form solution we solvedis right.The chapter three investigates the dynamic response of infinite Euler beamssupported by nonlinear viscoelastic foundations subjected to a moving concentratedforce and a harmonic moving load. Nonlinear foundation is assumed to be cubic. Thenonlinear governing equations of motion are developed by considering the effects ofthe shear modulus of foundations. The differential equation is solved usingmulti-scale perturbation method in conjunction with complex Fourier transform. Anapproximate closed form solution is derived in an integral form based on thepresented Green’s function and the theorem of residues, which is used for thecalculation of the integral. The dynamic response distribution along the length of thebeam is obtained from the closed form solution. The derivation process demonstrates that two moving loads for the dynamic response of infinite beams on nonlinearfoundations give the consistent result. The numerical results investigate theinfluences of the shear modulus of foundations on dynamic responses. Moreover, theinfluences on the dynamic response are numerically studied for nonlinearity,viscoelasticity and other system parameters.The chapter four investigates the dynamic response of infinite Timoshenkobeams supported by nonlinear viscoelastic foundations subjected to a movingconcentrated force and a harmonic moving load. Nonlinear foundation is assumed tobe cubic. The nonlinear governing equations of motion are developed by consideringthe effects of the shear deformable beams and the shear modulus of foundations atthe same time. The differential equations are solved using multi-scale perturbationmethod and Adomian decomposition method in conjunction with complex Fouriertransformation. An approximate closed form solution is derived in an integral formbased on the presented Green’s function and the theorem of residues, which is usedfor the calculation of the integral. The dynamic response distribution along thelength of the beam is obtained from the closed form solution. The derivation processdemonstrates that two moving loads for the dynamic response of infinite beams onnonlinear foundations give the consistent result. The numerical results investigate theinfluences of the shear deformable beam and the shear modulus of foundations ondynamic responses. Moreover, the influences on the dynamic response arenumerically studied for nonlinearity, viscoelasticity and other system parameters.Using two methods, Chapter five presents an investigation into the steady stateresponse of an infinite Timoshenko beam on nonlinear viscoelastic Pasternakfoundation subjected to a harmonic moving load. Nonlinear foundation is assumed tobe cubic. By employing the standard Adomian decomposition method (ADM) andthe modified decomposition method, the nonlinear term is decomposed respectively.The approximate closed form solution has been determined via complex Fouriertransformation. Numerical results indicate that the two kinds of ADM predict qualitatively the same tendencies of the dynamic response with the changingparameters, but the deflection of beam predicted by the modified ADM is smallerthan that by the standard ADM. The parametric study is performed and the influenceof the shear modulus of Timoshenko beams and foundation, nonlinearity and loadfrequency is investigated.Finally, the results of the thesis are summarized and the further work issuggested.