On a theory concerning the dynamical behavior of structures carrying moving masses

2015

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: Introductionmentioning

confidence: 99%

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

Omolofe

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

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.

“…Again, an approximate analytical method due to Struble is resorted to. It is remarked at this juncture that neglecting the terms representing the inertia term of the moving mass, we obtain equation (17). The homogeneous part of this equation can be replaced by a free system operator defined by the modified frequency γ mf due to the presence of the effect of rotatory inertia.…”

Section: Solution Of the Transformed Governing Equationmentioning

confidence: 99%

“…An equivalent free system operator defined by the modified frequency then replaces equation (17). Thus, we set the right-hand-side of (17) to zero and consider a parameter η 0 < 1 for any arbitrary ratio ε 0 , defined as…”

Section: Solution Of the Transformed Governing Equationmentioning

confidence: 99%

“…It is observed that when η 0 = 0, we recover the frequency of the moving force problem when the rotatory inertia effect of the beam is neglected. Thus, to solve the non-homogeneous equation (17), the differential operator which acts on V (m, t) and V (k, t) is replaced by the equivalent free System operator defined by the modified frequency γ mf , thus using equation (30) the homogeneous part of equation (17) can be written as…”

Section: Solution Of the Transformed Governing Equationmentioning

confidence: 99%

See 1 more Smart Citation

Flexural motions under accelerating loads of structurally prestressed beams with general boundary conditions

Omolofe

2010

The transverse vibration of a prismatic Rayleigh beam resting on elastic foundation and continuously acted upon by concentrated masses moving with arbitrarily prescribed velocity is studied. A procedure involving generalized finite integral transform, the use of the expression of the Dirac delta function in series form, a modification of the Struble's asymptotic method and the use of the Fresnel sine and cosine functions is developed to treat this dynamical beam problem and analytical solutions for both the moving force and moving mass model which is valid for all variant of classical boundary conditions are obtained. The proposed analytical procedure is illustrated by examples of some practical engineering interest in which the effects of some important parameters such as boundary conditions, prestressed function, slenderness ratio, mass ratio and elastic foundation are investigated in depth. Resonance phenomenon of the vibrating system is carefully investigated and the condition under which this may occur is clearly scrutinized. The results presented in this paper will form basis for a further research work in this field.