Dynamic behaviour of beams and rectangular plates under moving loads

This study concerns the dynamic characteristics of a prestressed isotropic, rectangular plate continuously supported by an elastic foundation and carrying accelerating mass M. Closed form solutions of the governing fourth order partial differential equations with variable and singular coefficients are presented. For the twodimensional plate problem, the solution techniques is based on the double Fourier Finite Sine integral transformation, the expansion of the Dirac Delta function in series form, a modification of Struble's asymptotic method and the use of Fresnel sine and Fresnel cosine integrals. Numerical analyses in plotted curves are presented. The analyses reveal interesting results on the effect of structural parameters such as foundation moduli, rotatory inertia correction factor and prestressing forces on the dynamic behaviour of isotropic rectangular plate under the actions of concentrated masses moving at variable velocity. In particular it is found that the critical velocity of the travelling load which brings about the occurrence of a resonance state increases as the values of these structural parameters increase.

Section: Analytical Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Omolofe

Oni

2015

“…These they commonly termed moving mass problems. These researchers include Stanisic et al [22], Milornir et al [11], Clastornic et al [3], Sadiku and Leipholz [19] and Gbadeyan and Oni [8]. Douglas et al [5] solved the problem of plate strip of varying thickness and the center of shear.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviour under moving concentrated masses of simply supported rectangular plates resting on variable Winkler elastic foundation

Oni

Awodola

2011

The response of simply supported rectangular plates carrying moving masses and resting on variable Winkler elastic foundations is investigated in this work. The governing equation of the problem is a fourth order partial differential equation. In order to solve this problem, a technique based on separation of variables is used to reduce the governing fourth order partial differential equations with variable and singular coefficients to a sequence of second order ordinary differential equations. For the solutions of these equations, a modification of the Struble's technique and method of integral transformations are employed. Numerical results in plotted curves are then presented. The results show that response amplitudes of the plate decrease as the value of the rotatory inertia correction factor R0 increases. Furthermore, for fixed value of R0, the displacements of the simply supported rectangular plates resting on variable elastic foundations decrease as the foundation modulus F0 increases. The results further show that, for fixed R0 and F0, the transverse deflections of the rectangular plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Therefore, the moving force solution is not a safe approximation to the moving mass problem. Hence, safety is not guaranteed for a design based on the moving force solution. Also, the analyses show that the response amplitudes of both moving force and moving mass problems decrease both with increasing Foundation modulus and with increasing rotatory inertia correction factor. The results again show that the critical speed for the moving mass problem is reached prior to that of the moving force for the simply supported rectangular plates on variable Winkler elastic foundation.

“…According to the local x, y, z coordinates of the plate element seen in Figure 2 Gbadeyan and Oni (1995), respectively: …”

Section: Finite Element Formulation Of a Mass That Moves Along An Arbmentioning

confidence: 99%

“…One of the important studies in this area, Nikkhoo et al (2012), examined the dynamic behavior of a thin plate excited by a moving mass using the Eigen function expansion method, whereas some researchers investigated the dynamic behavior of a Mindlin plate (Gbadeyan and Oni, 1995;Faria and Oguamanam, 2004;Gbadeyan and Dada, 2006;Amiri et al, 2013). Among the important FEM studies, Wu (2007) presented a moving load element taking into consideration the effects of the load for the dynamic analysis of inclined plates under moving loads.…”

Section: Introductionmentioning

confidence: 99%

A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory

Esen

2015

A combined plate element is presented for the analysis of transverse and longitudinal vibrations of a thin plate which carries a load moving along an arbitrary trajectory with variable velocity. Depending on the acceleration of the point load on its trajectory on the plate surface, the combined element, which is a combination of the 24 DOF plate element and an equivalent mass element, represents transverse (z) inertia, Coriolis and centripetal and longitudinal (x, y) inertia effects of the moving load. In order to obtain the combined element, mass, damping and stiffness matrices of the equivalent mass element representing the mass are first derived by using the relations between nodal forces, nodal deflections and deflection-shape functions of the plate element and the inertia and other forces of the moving mass according to the global coordinates on the plate and local coordinates on the plate element. Then, the obtained property matrices of the equivalent mass element and property matrices of the plate element were added together in order to obtain the combined plate element. For verification, the suggested technique was applied on a simply supported beam-plate under a moving load, and agreements were obtained with existing literature. In addition, intensive analysis and simulations were conducted at different dimensionless mass rates (mass of the load/mass of the plate) and angular velocities for a circular motion on a CCCC plate, and the results are provided. Furthermore, analysis results are provided for moving force condition which neglects the inertia, Coriolis and centripetal effects of the load, and it was shown that the moving mass assumption generated very different results with moving load assumption especially at high mass ratio and velocity values. Analysis results made it clear that the dynamic behaviour of the plate was differently affected by an orbiting mass depending on its mass ratio, orbiting radius and angular velocity