A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. (English) Zbl 1147.74330

Summary: A mixed method, which combines the state space method and the differential quadrature method, is proposed for bending and free vibration of arbitrarily thick beams resting on a Pasternak elastic foundation. Based on the two-dimensional state equation of elasticity, the domain along the axial direction is discretized according to the principle of differential quadrature (DQ). As a result, the state equations about the variables at discrete points are established. With consideration of the end conditions and the upper and lower boundary conditions in the derived state equations, governing equations for bending and free vibration problems are formulated. Numerical results prove that the present approach is very efficient and reliable. The effects of Poisson’s ratio and foundation parameters on the natural frequencies are discussed.


74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74J99 Waves in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI


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