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Simple Vibration Theoretical Concept
Published in Jyoti K. Sinha, Industrial Approaches in Vibration-Based Condition Monitoring, 2020
The natural frequency of this system is estimated as 5 Hz using Equation (2.5). Now the maximum response of the system is then calculated for each forcing frequency using Equation (2.35). The calculated maximum responses are tabulated in Table 2.1. It is clear from Table 2.1 that the vibration amplitudes are completely different ranging from 0.80 to 500 mm for the same applied force, F0 = 1 N but due to different forcing frequencies. When applied frequency is equal to or close to the system natural frequency then the vibration response is very high which has potential to damage the system in few numbers of oscillations. The vibration responses of the system at different frequencies are shown in Figure 2.11.
Noise and Vibration in Switched Reluctance Machines
Published in Berker Bilgin, James Weisheng Jiang, Ali Emadi, Switched Reluctance Motor Drives, 2019
James Weisheng Jiang, Jianbin Liang, Jianning Dong, Brock Howey, Alan Dorneles Callegaro
As discussed in Chapter 12, vibrational resonance, in the form of increasing amplitude of oscillation for a system, happens when the natural frequencies of a system are close to forcing frequencies acting on the structure. The natural frequency is defined as the frequency at which a system’s main mode of vibration oscillates without any external frequential forces. In a motor system, the stator-frame structure acts as the major source of noise. If the forcing frequencies of the radial force harmonics approach the natural frequencies of the stator-frame structure for a certain mode shape, resonance occurs in the stator-frame structure, causing a buildup of noise and vibration.
Optomechanical Design Principles
Published in Anees Ahmad, Handbook of Optomechanical Engineering, 2018
Response of systems to vibration is a complex topic. Considerable insight is derived from the use of a simple, single-degree-of-freedom (SDOF) model. This model is used to determine response of systems to both periodic and random vibration. The most important property of a system exposed to vibration is the natural frequency. The natural frequency of a system is that frequency at which the system will oscillate if perturbed from equilibrium. For a simple SDOF system, the fundamental frequency is given by: fn=12πkm
On the hybrid atomistic-continuum model for vibrational analysis of α-, β-, and γ-graphyne circular nano-plates
Published in Waves in Random and Complex Media, 2022
Babak Azizi, Mohammad Hosseini, Mojtaba Shariati
Discrete Fourier transform (DFT) is computed using the fast Fourier transform (FFT), which is an efficient algorithm. This Fourier transform provides vibration amplitude as a function of frequency so that the analyzer can determine the cause of the vibration. A frequency resolution in an FFT is directly proportional to the signal length and sampling rate. An FFT is simply a DFT with an algorithm that takes advantage of the symmetry in sine waves. To exploit these symmetry effects, the FFT requires a signal length of a power of two for the transformation and splits the process into cascading groups of two. You can use FFT to determine the values of the natural frequency in many applications where the vibration frequency changes over time. It is suggested to consider Figures 6 and 7 simultaneously to better understand the issue.
Nonlinear micromechanically analysis of forced vibration of the rectangular-shaped atomic force microscopes incorporating contact model and thermal influences
Published in Mechanics Based Design of Structures and Machines, 2022
Hossein Saeidi, Asghar Zajkani, Majid Ghadiri
In most structural and mechanical systems, the natural frequencies and mode shapes are important dynamic characteristics of those structures, as they are required in the solution of resonant responses and for forced vibration analysis; so for a dynamic response of the system, especially during the preliminary design studies, the natural frequency is used. Therefore, the recognition of a system requires knowledge of these vibration characteristics of the system (Rao 2007). Most commercial micro-cantilevers are either V-shaped or rectangular beams. One of the most recent geometries used for the AFM probes is a U-shaped geometry. Better balance and a closed circuit that allows the use of piezo materials for the cantilever and the properties of these materials, is one of the advantages of this type of geometry, in comparison to other geometries (Rezaei and Turner 2016; Namvar, Ghadiri, and Rezaei 2018).
Improving the performance of industrial machines with variable stiffness springs
Published in Mechanics Based Design of Structures and Machines, 2022
Tom Verstraten, Pablo López-García, Bert Lenaerts, Branimir Mrak, Dirk Lefeber, Bram Vanderborght
In some cases it is possible to change the imposed motion in such a way that the main natural frequency matches the stiffness setting. This is also a valid option on the studied test setup. As explained in Section 3.1.1.1, the optimal spring stiffness is defined by the imposed frequency of the oscillation, but also by the length of the dwell period (Eq. (9)). Recall from Section 2.2 that only a minimum length of 30% of the total period was set out for the dwell period. By increasing the length W of the dwell period, the range of frequencies which can be attained with a specific spring stiffness can be increased to lower frequencies. This is illustrated in Figure 6. The minimum frequency requirement, 1/3 Hz for slow-motion, is met for stiffness values up to 80 Nm/rad, the optimal stiffness for operation at 7.5 Hz. In other words, trajectory modulation would enable to use of a PEA with fixed stiffness. In conclusion, like variable stiffness, trajectory modulation increases the range of attainable frequencies.