Flexural motions under moving concentrated masses of elastically supported rectangular plates resting on variable winkler elastic foundation

Abstract

The flexural motions of elastically supported rectangular plates carrying moving masses and resting on variable Winkler elastic foundations is investigated in this work In order to solve the fourth order partial differential equation governing the 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. These equations are then solved using a modification of the Struble's technique and method of integral transformations. Numerical results are then presented in plotted curves. The results show that response amplitudes of the plate decrease as the value of the rotatory inertia correction factor R o increases and for fixed value of R o , the displacements of the elastically supported rectangular plates resting on variable elastic foundations decrease as the foundation modulus F o increases. Also, for fixed R o and F o , 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. Furthermore, the results show that the critical speed for the moving mass problem is reached prior to that of the moving force for the elastically supported rectangular plates on Winkler elastic foundation with stiffness variation.

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

“…It has also become the objective of various investigations in the field of applied Mathematics and Physics. In general, problems of this type are mathematically complex when the inertial effect of the moving load is taken into consideration [Fryba, L., (1972), Milormir et al (1969), Sadiku et al, (1981), Gbadeyan and Oni (1995) Kargarmovin and Younesian (2004), Shahin and Mbakisya (2010), Awodola and Oni (2013), Awodola and Oni (2011), Omolofe (2013)]. …”

Response characteristics of non-uniform beam with time-dependent boundary conditions and under the actions of travelling distributed masses

“…The problem of assessing the dynamic response of a structural elements (beam or plate) which supports moving loads is fundamental in the analysis and design of high way and railway bridges and as such this problem continues to attract the attention of research engineers in the field of civil, mechanical, aerospace, transport engineering and related fields [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Dynamic Characteristics of a Rotating Timoshenko Beam Subjected to a Variable Magnitude Load Travelling at Varying Speed

“…Studies concerning vibrating bodies resting on an elastic foundation carrying moving loads are of considerable practical importance and have been a subject of numerous scientific investigations by different authors in past few years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. In most of the studies available in literature, such as the work of Sadiku and Leipolz [21], Oni and Awodola [22], the scope of the problem of assessing the dynamic response of a structural member under the passage of moving load has been limited to that of thin beam or thick beam.…”