Synchronized switch damping (SSD) technique utilizing piezoelectric elements is one of good methods of vibration control. This work develops numerical tools for dynamic analysis of structures with SSD dampers, and conducts experiments to verify the effectiveness. A cantilevered beam bonded with piezoelectric patches is considered as the host structure. Two types of SSD circuits are considered, one with no subsequent electric element (SSDS) and another with inductance (SSDI). Firstly, a lumped parameter electromechanical coupling model is employed, with parameters determined experimentally. Then, the frequency response curves of the nonlinear vibration systems are analyzed by the multi-harmonic balance method combined with alternating frequency-time techniques (MHBM/AFT). In order to verify the proposed method, an experimental study is performed. In the experiment SSD circuit is realized by an enhanced analog circuit which is more complex but also more stable than the original SSD circuits. The measured results are compared with those obtained by proposed numerical tools with good agreements. It is also shown that the modal frequencies and modal shapes of SSD systems are almost unchanged with the vibration amplitudes, which indicates that the nonlinear force generated by SSD has little influence on the characteristics of linear structure. It is verified both numerically and experimentally that SSDI damper can produce significant damping for multiple modes.