The Influence of Concentrated Masses and Pasternak Soil on the Free Vibrations of Euler Beams—exact Solution

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

“…The dimensionless natural frequencies β i obtained by the current method in this paper are listed with those in reference [14] in Table 6, which show that the results of two approaches have excellent agreement.…”

“…Other studies of the influences of variable attachments on slender beam vibrations are given in Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

“…Exact solutions for free vibration of uniform beam can be obtained from [41,42] along with the results computed from other numerical methods. De Rosa and Maurizi [43] have given exact solution for free vibration frequencies of a beam with flexible ends resting on Pasternak soil in the presence of a concentrated mass at an arbitrary intermediate abscissa. A mixed method combining state space method and differential quadrature method has been implemented by Chen et al [44] in bending and free vibration of arbitrarily thick beams resting on a Pasternak elastic foundation.…”

Wave Propagation Characteristics in Functionally Graded Double-Beams

“…In the study, shape function is chosen as 0 so as to correspond to Euler-Bernoulli beam theory. When the stress-strain relations are substituted into the force and moment definitions: (6) the following constitutive equations are obtained as follows: (7) where: A ij , B ij and D ij denote the extensional, coupling and bending stiffnesses respectively. The extensional, coupling and bending stiffnesses are defined in the following way: (8) The governing equations of the beam can be obtained variationally by use of Hamilton's principle as follows: (9) where: the subscript ",tt" denotes the derivation with respect to time.…”