In a single-degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibrat...

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time ...

We establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations).

The nonlinear vibro-acoustic response of solid samples containing quite a small amount of defects can be anomalously high in magnitude compared to the case of undamaged intact solids. Functional dependencies of the nonlinear effects often exhibit rather interesting behavior which cannot be explained by manifestations of conventional nonlinear elasticity or hysteretic nonlinearity of the materia...

in this paper, the effects of transverse cracks on rotating shaft were studied. according to earlier works, crack shaft failure decrease the critical speed of the shaft and also exhibit a nonlinear vibration behaviour leading to increases the amplitude of 1x and 2x harmonics (first and second order of rotational speed in torsional vibration). this suggests that the application of order analysis...

Vibration phenomena that might be modelled well using linear vibration theory include small amplitude vibrations of long, slender objects like long bridges, aeroplane wings, and helicopter blades; small rocking motions of ships in calm waters; the simplest whirling motions of flexible shafts, and so on. However, interactions between bridges and foundations, between wings/blades and air, between...

This paper describes an active control method to prevent unwanted nonlinear vibration response modes of a rotordynamic system. Nonlinear stiffness of components that support or surround a machine rotor can cause a response branch that extends critical vibration (resonance) over a wide interval of rotational speeds. Within this interval, jump transitions between alternative low amplitude and hig...

Static deflection as well as free and forced nonlinear vibration of thin square plates made of hyperelastic materials are investigated. Two types of materials, namely rubber and soft biological tissues, are considered. The involved physical nonlinearities are described through the Neo-Hookean, Mooney-Rivlin, and Ogden hyperelastic laws; geometrical nonlinearities are modeled by the Novozhilov n...