One-dimensional experimental modal analysis of an unvarnished trapezoidal violin built after the description of F. Savart and an anonymous trapezoidal violin on display in the Music Instrument Museum of Brussels is described. The analysis has revealed ten prominent modes. A mode that may potentially play a role of the “tonal barometer” of the instrument is pointed out. The mode shapes are symmetric and of high amplitude, due to the construction of the instrument. Subjective evaluation of the sound quality demonstrated no pronounced difference between the trapezoidal violin and normal violin.

The examination of a smart beam is presented in the paper. Experimental investigations were carried out for flexible beam with one fixed end and free opposite end. Piezoelectric strips were glued on both sides of the beam. One strip works as a sensor, and the second one as an actuator. It is a single input and single output system. The study focuses on the analysis of natural frequencies and modes of the beam in the relation to the position of the piezo-elements. The natural frequencies, mode shapes, generated control forces, and levels of the measured signals are considered and calculated as a functions of the piezo-element locations. We have found correlations between mode shapes, changes of natural frequencies, control forces and measured signals for the lowest four modes. In this way, we can find the optimal localization of the distributed sensors and actuator on the mechanical structure directly by the using of the finite elements method (FEM).

The aim of this research is to use a simple acoustic method of a very near field recording, which enables measurement and display of oscillation modes, to estimate the velocity of flexural waves, based on the wavelengths of standing waves measured on the sample. The paper analyses cases of 1D geometry, flexural waves that occur on a beam excited by an impulse. Measurements were conducted on two different samples: steel and a wooden beam of the same length. Due to the appearance of evanescent waves at the boundary regions, the distance between the nodes of standing waves that occur deviates from half the wavelength, which can be compensated using a correction factor. Cases of fixed and free boundary conditions were analysed. By quantifying how much the boundary conditions change the mode shape function, it can be predicted how the mode of oscillation changes if the boundary conditions change, which can also find application in musical acoustics and sound radiation analysis.

The basic dynamic characteristics of façade scaffolding are natural frequencies of vibrations and corresponding mode shapes. These properties affect the scaffolding safety, as well as comfort and safety of its users. Many of the dynamic actions present at scaffolding are in the low frequency range, i.e. below 10–15 Hz. The first natural frequency of a structure is usually in the range of 0.7 to 4 Hz which corresponds to resonant frequencies of human body and it means that vibrations induced at scaffolding may strongly affect the human comfort. The easiest way of increasing the rigidity of the structure is by ensuring correct boundary conditions (support, anchorage) and bracing of the structure. The numerical analysis was performed for the real scaffolding structure of medium size. The analysis consisted of natural frequencies calculation for the original structure and for models with modified bracing and anchoring systems. The bracing modifications were introduced by reducing or increasing the number of vertical bracing shafts. The anchor system was modified by reduction of the 6 anchors in the top right corner of the scaffolding in three stages or by evenly removing nearly 1/3 of the total number of anchors. The modifications of bracing and anchor systems resulted in changing the natural frequencies. The increase of natural frequencies due to higher number of anchors and more bracing is not even for all mode shapes. Bracing is more effective in acting against longitudinal vibrations, while anchoring against vibrations perpendicular to the façade.