An active reduction of transverse vibration of the triangular plate with P-F-F boundary conditions is considered. The cracked plate is idealized research model as partially clamped on one edge with varying clamped length. The active reduction is realised with PZTs. In the paper, assuming the detached base clamped length, the influence of PZTs distribution on the bending moment and the shearing force at the clamped edge is investigated. To realize the purpose two cases are considered. At the former the PZTs are attached at points in which the curvatures of the surface locally take their maximum (MC sub-areas or quasi-optimal ones). At the latter, the PZTs are somewhat shifted. The plate is excited with harmonic plane acoustic wave. The second mode is considered only.The active vibration reduction study with a finite element method (FEM) is carried out. The numerical calculations show that better results are obtained for MC distribution of the PZTs.

The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.

The paper concerns an active vibration protection (p-reduction) of the structure via piezoelectric transducers; p-reduction corresponds to an active vibration reduction (a-reduction). The quantity and effectiveness of the (a-or p-) reduction, among other parameters, depend on the piezoelectric transducers distribution on the structure. The best results are obtained bonding piezoelectric transducers to the structure in the sub-domains with the largest curvatures; it is so-called quasi-optimal distribution of the piezoelectric transducers. Up to now, the quasi-optimal distribution was determined based on heuristic reasons only. The aim of the paper is to confirm quasi-optimal distribution in analytical way. The beam clamped at one end, vibrating with first three modes separately, is chosen as the research object. It is assumed that the piezoelectric transducers are exactly the same. Demanding the vibration amplitude to be equal to zero (i.e. p-reduction condition), the general formula for interacting forces piezoelectric transducers-beam is derived. Next, such an appropriate distribution of piezoelectric transducers is searched analytically, that the minimal forces are achieved; it leads to the best reduction effectiveness. It turned out that the analytical method pointed out quasi-optimal distribution of the piezoelectric transducers. The validation of theoretical considerations is confirmed numerically.

Effectiveness of the active vibration reduction of triangular plate is evaluated by way of the analysis of acoustical field. The active vibration reduction is performed with actuators. The effect is measured by the analysis of the acoustical field both far distance and near one from the plate. As the control parameter, the difference between acoustical pressures is considered. The first pressure and the second one are radiated by the plate without and with the vibration reduction, respectively. The control parameter is calculated for two reduction cases. First case, when actuators are attached at so-called quasi-optimal places and second one, when they are shifted. The numerical calculations show that the acoustical field is sensitive to change of the plate active vibration reduction. It responds to even little changes of the plate vibrations in both active reduction cases mentioned above. So that it is handy indirect control parameter of the active vibration reduction.

This paper deals with an active vibration protection (p-reduction) of the beam-actuators mechanical system, hence it concerns separate modes. The paper's aim is an eectiveness analysis of the p-reduction assuming dierent number of actuators. It is assumed a priori that actuators are bonded to the beam in the sub-domain with the largest curvatures and they are exactly the same. The beam clamped at one end is chosen as the research object. Next, as required by the p-reduction condition, the number and distribution of actuators are changed. It turns out that the best reduction eectiveness, measured via any eectiveness coecient, is obtained for one actuator bonded in the sub-domain with the largest curvature. The validation of theoretical considerations is conrmed numerically.