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Introduction to Electric Motors
Published in Wei Tong, Mechanical Design and Manufacturing of Electric Motors, 2022
In general, damping can be divided into three types: viscous damping, coulomb or dry-friction damping, and hysteretic or structural damping. From the standpoint of physics, viscous damping is the dissipation of energy as occurred in liquid or air between moving parts. An example of viscous damping is ball-bearing lubrication. It results in lower torque delivered at the output shaft to the torque developed at the rotor. Viscous damping in a single-degree-of-freedom torsional system is referred to as torsional viscous damping Kvd,t, which is directly proportional to the damping torque Td and inversely proportional to the angular velocity ω and is always opposite to the direction of motion, that is, Kvd,t=Tdω
Vibration and damping, sandwich structures
Published in József Farkas, Károly Jármai, Analysis and Optimum Design of Metal Structures, 2020
In general, damping can be classified into two basic categories: Material damping and nonmaterial damping. — Material damping. Every material has an internal damping, but it can be very different. Comparing different materials under exactly same boundary conditions, same geometrical dimensions, the same magnitude of periodic forcing with the same frequency of excitation we find, that one material may oscillate shorter with smaller amplitude than the other. This is due to the difference in material properties. The damping force due to internal molecular friction in material is more than at the other material. This kind of damping is called material damping. — Nonmaterial damping. Another types of damping are friction damping, viscous and acoustic radiation damping. For example, a vibratory structural system will oscillate much longer in the air than in water. This kind of damping is called viscous damping. The viscous damping force depends on the property of the surrounding medium and the velocity of motion. The friction damping is caused by friction in the joints.
Damping in high strength concrete beams – prediction and comparison
Published in Peter J. Moss, Rajesh P. Dhakal, Progress in Mechanics of Structures and Materials, 2020
Viscous damping is a common form of damping where the damping force is proportional to the first power of the velocity across the damper. The damping force always opposes the motion so that it is a continuous linear function of the velocity. The measurement method that relates to viscous damping with its exponential decay characteristics, is the logarithmic decrement, δ, by which the amplitudes of two cycles n cycles apart can be related in the form δ=1n amplitude at cycle 1 amplitude at cycle (n+1) The damping coefficient C, or alternatively the damping ratio §, where § = C/Cc, given that Cc is the critical damping constant, are related to δ as: δ=2πξ1−ξ2=πCmωd where m and ωd represent the mass and the damped natural frequency of free vibration. Viscous damping serves to limit resonant motion and is easily incorporated into most mathematical models.
Experimental study on wide-shallow composite bucket foundation for offshore wind turbine under cyclic loading
Published in Marine Georesources & Geotechnology, 2019
Xuyue Wang, Puyang Zhang, Hongyan Ding, Yonggang Liu
One of the main effects of damping in a dynamic system is the consumption of energy. Real damping of a dynamic system is complex, therefore, the concept of equivalent viscous damping is used to evaluate the energy dissipation capacity of the system and maintains the simplicity of linear viscous damping. The concept of equivalent viscous damping is based on the premise that energy dissipated in a viscous damping mechanism is equivalent to that dissipated in a known nonviscous damping mechanism. According to the theory of structural dynamics (Craig Jr 1981), the work performed by the damp force is the energy dissipated by viscous damping in every cyclic hysteresis loop. The equation for the work performed by damp force iswhere WD is the work performed by damp force, c is viscous damping coefficient, is the first derivative of displacement, ω is oscillating frequency, and U is displacement. Based on Eq. (8), the equation for an equivalent viscous damping coefficient is given as follows,
Multi-hazard loss analysis of tall buildings under wind and seismic loads
Published in Structure and Infrastructure Engineering, 2018
Ilaria Venanzi, Oren Lavan, Laura Ierimonti, Stefano Fabrizi
Typically, a viscous damping model is used in engineering practice as it leads to a linear equation of motion. In absence of full-scale measurement on the considered building, the modal damping ratios are chosen from Codes on the basis of the material of construction (steel-framed, reinforced concrete, steel-framed reinforced concrete) or taken from full-scale data available in literature (Fukuwa, Nishizaka, Yagi, Tanaka, & Tamura, 1996; Satake, Suda, Arakawa, Sasaki, & Tamura, 2003). Several authors agree that structural damping is dependent on natural frequency and response amplitude (Çelebi, 1996). Damping predictors based on full-scale data have been proposed, among others, by Jeary (1986), Lagomarsino (1993), and Satake et al. (2003). All models include frequency-dependent and amplitude-dependent terms but their application is limited to a specific range of buildings. In this Section, the uncertainty in structural damping is included in life-cycle cost estimation. Damping ratio is considered as the uncertain structural parameter (SP) which appears in Equation (6).
Effect of Damping Modeling and Characteristics on Seismic Vulnerability Assessment of Multi-Frame Bridges
Published in Journal of Earthquake Engineering, 2021
Mohammad Abbasi, Mohamed A. Moustafa
To determine the dynamic response of structures through NTHA, damping modeling is required. Generally, in the absence of more accurate structural damping models, linear viscous damping is usually utilized for convenience. Rayleigh damping is the most common model of classical viscous damping. The Rayleigh damping matrix c is given in several textbooks such as Chopra [2007] as shown in Equation 4.