This paper develops an averaging analysis for qualitative and quantitative study of switched piezostructural systems. The study of piezostructural systems including passive and active shunt circuits has been carried out for some time. Far less is known regarding analytical methods for the study of switched piezostructural systems. The technique developed in this paper is motivated by the success of averaging methods for the analysis of switched power supplies. In this paper it is shown that averaging analysis provides a means of determining time domain as well as frequency domain response characteristics of switched piezostructural systems that include switched capacitive shunt circuits. The time domain and frequency domain performance of a tunable piezoceramic vibration absorber is derived via averaging in this paper. The proposed switching architecture provides an essentially continuous range of tunable notch frequencies, in contrast to a finite and fixed collection of discrete notch frequencies available in some implementations of capacitively shunted piezostructures. The technique for analysis appears promising for the study of vibration damping and energy harvesting piezostructures whose underlying operating principle is similar.