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Effect of Vibration
Published in Verna Wright, Eric L. Radin, Mechanics of Human Joints, 2020
J. E. Smeathers, P. S. Helliwell
The frequency, or the number of oscillations per second (measured in Hertz, Hz), is the most important quantity that an engineer needs to know about any practical vibration problem. The fundamental frequency fn of vibration is governed by the mass and stiffness of the structure. fn=12π×[(stiffness, Nm−1)(mass, kg)]12 Hz
Introduction to geotechnical engineering
Published in Hsai-Yang Fang, John L. Daniels, Introductory Geotechnical Engineering, 2017
Hsai-Yang Fang, John L. Daniels
The basic parameters of particle dynamics are velocity, acceleration, mass, force, work, energy, wave, vibration, etc. In a liquid or gas, compression waves are called sound waves. The characteristics of sound waves include the pulse, frequency, and type, that is transverse or longitudinal. When Newtonian mechanics is applied to the motion of a system, it is found that motion can be regarded as a wave motion called normal modes of vibration. The frequency of oscillation in a normal mode is termed as the natural frequency of the system. The lowest natural frequency is called the fundamental frequency. When the driving frequency is near a natural frequency of the vibrating body, the amplitude of these forces oscillating becomes exceptionally large. It is for this reason that knowledge of the natural frequency of a structure is of particular importance when assessing seismic stability. The large response at a certain driving frequency is called resonance. A great variety of particle resonance is possible in natural systems.
Sources of sound
Published in John Watkinson, The Art of Sound Reproduction, 2012
Some drums have an open structure so that both sides of the diaphragm can radiate. In others, the rear of the diaphragm is enclosed. The air trapped beneath the diaphragm acts as a spring which provides a further restoring force when the diaphragm is deflected. The result is that the same fundamental frequency is obtained with less tension. However, the trapped air does not affect the higher modes so much because in these some of the diaphragm is moving out whilst another part is moving in. Consequently the timbre and the directivity of an enclosed drum differ from that of an open drum.
Topology optimization of the vibrating structure for fused deposition modelling of parts considering a hybrid deposition path pattern
Published in International Journal of Computer Integrated Manufacturing, 2022
Yifan Guo, Rafiq Ahmad, Yongsheng Ma
where represents the natural frequency. In general, the fundamental frequency refers to the lowest nature frequency . is the eigenvector corresponding to and represents the displacement of vibration. and denote the global stiffness and mass matrix of the structure, respectively. They can be calculated as follows:
Topological optimization of continuum structures for additive manufacturing considering thin feature and support structure constraints
Published in Engineering Optimization, 2021
Bin Xu, Yongsheng Han, Lei Zhao, Yi Min Xie
The fundamental frequency is the smallest natural frequency of the structure itself. In principle, a continuum structure has an infinite number of natural frequencies, but when the natural frequencies are calculated, the problem is usually solved by dividing the structure into finite order, and the lowest natural frequency is the fundamental frequency of the structure. The fundamental frequency of the structure is a very important piece of data. The fundamental frequency of the structure is related to whether it is vulnerable to the resonance failure of some kind of out-of-frequency load, so this article maximizes the fundamental frequency of the structure.
Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the first-order shear deformation theory
Published in Mechanics of Advanced Materials and Structures, 2020
Zheng Zhang, Yang Li, Helong Wu, Huanqing Zhang, Huaping Wu, Shaofei Jiang, Guozhong Chai
For the vibration Figure 9, Figure 10analysis, the fundamental frequencies for GOPRC beams are listed in Table 7. From the comparison, the C-C beam has a higher fundamental frequency than the beam with H-H boundary condition. It is also observed that the fundamental frequency decreases as slenderness ratio increases. As expected, the X-GOPRC beam has the highest fundamental frequency, followed by the U-GPORC and O-GPORC beams.