The influence of piezoelectric actuation on transverse vibrations of a slender non uniform elastic sandwich beam with two symmetrically bonded piezoceramic layers and resting on elastic foundation is studied in this work. Three types of supports restraining both beam's ends against axial displacement are investigated. Due to the immovable ends of the beam, an in-plane tensile force appears during the system's vibration. This effect is modified by the piezoelectric force, which dependently on the direction of the electric field vector, either counteract or enlarge the beam's stretching. The governing equations with nonlinear terms are formulated through Hamilton’s principle. Employing a generalized Lindstedt-Poincarè method, according to which the axial force, the lateral displacements and the natural frequency are expanded into exponential series with respect to a small amplitude parameter, an infinite set of consecutive equations of motion and axial force components is derived. The first four equations are solved analytically to derive a transcendental equation for the linear frequency and an equation expressing the amplitude-frequency relationship. The effects of the ratio of the piezosegment’s length to the beam's length and the foundation stiffness on the natural vibration frequency are investigated. Special attention is paid on the influence of applied voltage on the amplitude – nonlinear frequency relationship to demonstrate that the hardening effect dominates the nonlinearity. The tensile piezoelectric force increases the linear natural frequency but decreases the nonlinear effect, while the compressing force decreases the linear frequencies but increases the nonlinear effect. Numerical simulations show the efficiency of the proposed approach.
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