Wave-front sets related to quasi-analytic Gevrey sequences

Quasi-analytic wave-front sets of distributions which correspond to the Gevrey sequence p!s, s\in

Evolution of electromechanical admittance of piezoelectric transducers on a Timoshenko beam from wave propagation perspective

This article analytically formulates and investigates the evolution of electromechanical admittance of piezoelectric transducers collocated on a finite beam from wave propagation perspective. First, the analytic wave solutions are obtained based on the linear piezoelectricity and the Timoshenko beam theory. Then, the evolution of wave propagation to vibration on a finite beam has been formulated in terms of a wave unit which appears periodically due to the multiple reflections at beam supports. The formulation has been extended to describe the underlying mechanism how electromechanical signatures evolve from wave units. The support conditions and material damping of a beam have been considered explicitly for both wave units and electromechanical signatures. The validity of the proposed formulation has been demonstrated through proof-of-concept numerical examples providing valuable physical insights into the relevance between wave units and electromechanical signatures.

Analytic wave functions and energies for two-dimensional $$ \mathcal{P}\mathcal{T} $$-symmetric quartic potentials

Analytic wave functions and the corresponding energies for a class of the $$ \mathcal{P}\mathcal{T} $$-symmetric two-dimensional quartic potentials are found. The general form of the solutions is discussed.