Modes Orthogonality of the Mechanical System Simple Supported Beam-Actuators-Concentrated Masses

Brański, A.

doi:10.12693/aphyspola.121.a-126

Cited by 3 publications

(1 citation statement)

References 17 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the aim of this paper is to formulate a new criterion that would indicate the optimal distribution of a-PZT on an asymmetrical structure. To achieve the aim, asymmetric vibrations of the beam caused by additional concentrated mass were considered (Brański, 2011;2012). It is assumed that the beam is excited by concentrated harmonic force with the first three modes separately.…”

Section: Introductionmentioning

confidence: 99%

Asymmetrical PZT applied to active reduction of asymmetrically vibrating beam – semi-analytical solution

2023

Archives of Acoustics

View full text Add to dashboard Cite

The article extended the idea of active vibration reduction of beams with symmetric modes to beams with asymmetric modes. In the case of symmetric modes, the symmetric PZT (s-PZT) was used, and the optimization of the problem led to the location of the s-PZT centre at the point with the greatest beam curvature. In the latter case, the asymmetric modes that occur due to the addition of the point mass cause an asymmetric distribution of the bending moment and transversal displacement of a beam. In this case, the optimal approach to the active vibration reduction requires both new asymmetric PZT (a-PZT) and its new particular distribution on the beam. It has been mathematically determined that the a-PZT asymmetry point (a-point), ought to be placed at the point of maximum beam bending moment. The a-PZT asymmetry was found mathematically by minimizing the amplitude of the vibrations. As a result, it was possible to formulate the criterion of the maximum bending moment of the beam. The numerical calculations confirmed theoretical considerations. So, it was shown that in the case of asymmetric vibrations, the a-PZTs reduced vibrations more efficiently than the s-PZT.

show abstract

Section: Introductionmentioning

confidence: 99%

Asymmetrical PZT applied to active reduction of asymmetrically vibrating beam – semi-analytical solution

2023

Archives of Acoustics

View full text Add to dashboard Cite

show abstract

Analytical Solutions of Excited Vibrations of a Beam with Application of Distribution

Kozień

2013

Acta Phys. Pol. A

View full text Add to dashboard Cite

In the paper, the analytical solutions of excited vibrations of the Bernoulli-Euler type beam in general case of external loading function is analyzed. The distribution theory is applied to formulate solution when the external functions are the concentrated-force type or the concentrated-moment type. Moreover, two types of excitation in time domain, harmonic and pulsed, are considered. Due to the superposition rule which can be applied in the analyzed linear case, any combination of external loading function can be formulated. The strict analytical solutions are shown for the case of simply supported beam. Describing the external load in the form of concentrated moments makes possible the analytical simulation of the reduction of vibrations of a beam by application of the piezoelectric elements which are in practice the source of external moment-type excitation put in relatively small area of action.

show abstract

Reduction of Vibration of Fluid Loaded Plate with Piezoelectric Elements - a Comparison of Analytical, FEM Harmonic Analysis, and Real Results

Iwański

Wiciak

2013

Acta Phys. Pol. A

View full text Add to dashboard Cite

In the present paper, a comparison of analytical calculations, FEM harmonic analysis, and real data from laboratory stand of uid-loaded structure were taken under consideration. Resonant frequencies of the investigated structure were measured using swept sine technique on laboratory stand. Analytical calculations of the rst twelve modes were made and the numerical model was build using the nite element method. Results from real data, analytical calculations, and numerical calculations are comparable.

show abstract

Modes Orthogonality of the Mechanical System Simple Supported Beam-Actuators-Concentrated Masses

Cited by 3 publications

References 17 publications

Asymmetrical PZT applied to active reduction of asymmetrically vibrating beam – semi-analytical solution

Asymmetrical PZT applied to active reduction of asymmetrically vibrating beam – semi-analytical solution

Analytical Solutions of Excited Vibrations of a Beam with Application of Distribution

Reduction of Vibration of Fluid Loaded Plate with Piezoelectric Elements - a Comparison of Analytical, FEM Harmonic Analysis, and Real Results

Contact Info

Product

Resources

About