The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defining the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.

JO - Archives of Civil Engineering L1 - http://www.journals.pan.pl/Content/83976/mainfile.pdf L2 - http://www.journals.pan.pl/Content/83976 PY - 2014 IS - No 4 EP - 440 KW - Bernoulli-Euler beam KW - Timoshenko beam KW - elastic foundations KW - stability KW - vibration A1 - Obara, P. PB - WARSAW UNIVERSITY OF TECHNOLOGY FACULTY OF CIVIL ENGINEERING COMMITTEE FOR CIVIL ENGINEERING POLISH ACADEMY OF SCIENCES JF - Archives of Civil Engineering DA - 31.12.2014 T1 - Vibrations and stability of bernoulli-euler and timoshenkobeams on two-parameter elastic foundation SP - 421 UR - http://www.journals.pan.pl/dlibra/docmetadata?id=83976 ER -