An analytical solution for nonlinear vibration of an initially stressed beam with elastic end restraints resting ona nonlinear elastic foundation is obtained. As a first step in solving nonlinear vibration equation, the linear vibration modefunctions for a beam with elastic end restraints resting on a linear elastic foundation are obtained. Then, the nonlinearvibration equation is solved by employing the linear mode functions to obtain frequency equation and nonlinear responseusing Jacobi elliptic integral. The nonlinearity due to lateral vibrations, the nonlinearity of foundations and lateraldisplacement due to lateral elastic restraints at beam ends not included in previous analytical work are considered in thepresent work. The effects of spring stiffness at the beam ends, foundation stiffness, axial load and vibration amplitude onthe frequency parameter are studied. The present solution can be used to measure the accuracy of approximate methods.
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