Vibration of double beams with an elastic connected layer has been studied in this paper by assuming that the beam is a Bernoulli-Euler beam. The natural frequencies equations of the symmetric double beam have been computed at arbitrary boundary conditions. The behavior of those frequencies has been investigated with a change in the stiffness of connected layer, modulus of elasticity of beam, length of beam, mass density of beam, and thickness of beam. The high effect of the elastic connected layer on the higher natural frequencies of a cantilever double beam is less than that in the clamped and free double beams. The increase in the thickness of upper and lower beams made a high increase in the values of lower natural frequencies in all types of beams. The change in the modulus of elasticity values of double beam becomes high on the lower natural frequencies but without enlarging the influence on the higher frequencies, especially in the cantilever double beam. The similar effect of change in the mass density of the beam resulted in the same influence on the higher and lower natural frequencies in all types of beams. The length of the beam enlarges the influence on the higher natural frequencies of clamped and free.

The importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It proved that there is very little error between the experimental and theoretical results. The vibration signal from the sensors was analyzed using the LABVIEW program. Rayleigh's method was compared to the exact method, and it was considered the most accurate method. It was found that it made very little difference, up to about 0.06%. As for the Dunkerley method, the difference between it and the proper method is about 4%, which is acceptable. Then a comparison was made between Rayleigh's and Dunkerley's methods, and it was found that Dunkerley's method is the most appropriate in the calculations.

Smart materials have a growing technological importance due to their unique thermomechanical characteristics. Shape memory alloys belong to this class of materials being easy to manufacture, relatively lightweight, and able to produce high forces or displacements with low power consumption. These aspects could be exploited in different applications including vibration control. A dynamic vibration absorber (DVA) can be used as an effective vibration control device. It is essentially a secondary mass, attached to an original system via a spring and damper. The natural frequency of the DVA is tuned such that it coincides with the frequency of unwanted vibration in the original system. This work aims to develop a dynamic vibration absorber with the help of shape memory alloy (SMA) springs in order to attenuate the vibration for a range of excitation frequencies. The experimental apparatus consisted of low-friction cars free to move in a rail. A shaker that provides harmonic forcing excites the system. Special attention is dedicated to the analysis of vibration reduction that can be achieved by considering different approaches exploiting temperature variations promoted either by electric current changes or by vibration absorber techniques. The results established that adaptability due to temperature variations is defined by modulus of stiffness

The effect of vibrations on asymmetric double beams is a common engineering problem in various engineering applications. In this paper, the synchronous (lower) and asynchronous (higher) natural frequencies of the asymmetric double beams are calculated using the Bernoulli-Euler method. Where the traditional methods are used to find the frequency equations at different boundary conditions, such as Pinned beam, clamped-Clamped beam, Clamped-Free beam, and Clamped-Pinned beam. The increase in the stiffness of the elastic connected layer leads to an increase in the values of the high frequencies of double beams. The greatest effect of changing the thickness of one of the upper or lower beams is for CF beams and the least effect is for CP beams. The length of the beam affects the higher and lower frequencies in high and close proportions for almost all types of beams, and the least effect is only on the higher frequencies of CF beams. The influence of the modulus elasticity change is relatively small on the lower natural frequencies of all types of beams except for CF beams, and its effect is relatively large on the higher natural frequencies of the most types of beams and comparatively less on the CF beams. The effect of varying the values of mass density is relatively small on the low natural frequencies of all types of beams except for CF beams, and its effect is comparatively large on the higher natural frequencies of all types of beams and relatively less on the CF beams.

In this work, the vibrations in the rotor-bearing system are studied experimentally and theoretically using ANSYS Workbench 2020 R1 software to compute the natural frequencies and mode shapes. In the experimental part, the LABVIEW software was used to examine the signal of the frequency domain values obtained from the accelerometer sensors, based on Fast Fourier Transform (FFT) technology and dynamic response spectrum. in the theoretical part, the natural frequencies are determined based on the finite element method for analyzing the system and knowing its behavior and vibration response level. The results showed that the level of vibration becomes higher at high rotational speeds, and it becomes large when the distances between the bearings are large, according to the bearing position and type used in the system. in this work can be concluded, the system is usually affected by the dynamic response around it and is difficult to separate from it, and the vibrations in the system can be controlled by adding an external damping source, which gives the system more stable. A system operating at high speeds can give a large vibration and an unbalanced response.