On the determination of the forced vibrations of flexible slab foundation subjected to a point mass on an elastic winkler-fuss foundation
V. G. Shapoval, S. L. Proshyn
State Institution of Higher Education «National Mining University»
Annotation: While solving the practical problems of designing buildings and structures erected on a solid slab foundation, often there is necessity to consider the dynamic effects on the supporting structures of equipment located on the foundation. Therefore, there is a problem of determining the amplitudes and shapes of forced oscillations of slab foundation under machinery. Materials contained in this paper are dedicated to this issue. The analysis of the solutions describing forced oscillations of plates under dynamic loading is performed. As a base of studies dependence of the displacements of smooth plate on time is taken, considering elastic properties of the base described using the coefficient of the bed, as well as the weight applied at the center of the plate. Differential equations and determination of the deflection of the plate is realized using special functions, in particular, the Dirac delta function and the Bessel function of zero index. As a result, the expression for determining the vibration amplitudes and, thus, plate deflections in the framework of the problem of the elastic foundation of Winkler Fuss and applied to the plate weight is obtained. The solution is described as the dependence of the deflections on coordinate and time. Thus, it is seen that the waveform of the plate depends on the parameters of the plate, namely, the thickness and density, as well as frequency of dynamic load and characteristics of a base.
Keywords: forced stationary vibrations, foundations for machinery and equipment, combined massive-slab foundations, an infinite plate stress-strain state.
Pages: 203-208.
Link for citation: Shapoval, V. G.; Proshyn, S. L. On the determination of the forced vibrations of flexible slab foundation subjected to a point mass on an elastic winkler-fuss foundation. – Text : electronic. – In: Modern Industrial and Civil Construction. – 2014. – Vol. 10, N 3. – Р. 203-208. – URL: https://donnasa.ru/publish_house/journals/spgs/2014-3/04_shapoval_proshyn.pdf (date of access: 19.09.2024). (in Russian)
Vol. 10, N 3 (2014)Journal: Modern Industrial and Civil Construction
Publish house: Donbas National Academy of Civil Engineering and Architecture