scholarly journals Dynamic behaviour of a gymnasium floor

1986 ◽  
Vol 13 (3) ◽  
pp. 270-277 ◽  
Author(s):  
J. H. Rainer ◽  
J. C. Swallow
Keyword(s):  
Concrete Slab ◽  
Damping Ratio ◽  
Mode Shapes ◽  
Resonant Frequencies ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Load Factors ◽  
Resonance Frequencies ◽  
Floor Vibrations ◽  
Vibration Tests

Ten mode shapes, natural frequencies, and modal damping values have been measured for a steel-joist concrete-slab floor spanning 32.1 m. From ambient vibrations and steady-state shaker tests the frequency of the fundamental mode was determined to be 3.5 Hz, and the modal damping ratio to be approximately 1% of critical. A comparison of vibration criteria in Appendix G of CAN3-S16.1-M84 confirms satisfactory performance for walking, but for other rhythmic exercises disturbing vibrations developed. These occurred primarily at the forcing frequency of the exercises and not at floor resonance frequencies. Values of dynamic load factors, α, for rhythmic loadings of this floor were evaluated in accordance with the guidelines on floor vibrations in the Commentary to the National Building Code of Canada 1985. Key words: floors, gymnasiums, vibration tests, resonant frequencies, mode shapes, dynamic loads, dynamic response.

scholarly journals Coupling of Flexural and Longitudinal Damped Vibration in a Two-Layered Beam

1998 ◽  
Vol 5 (5-6) ◽  
pp. 337-341
Author(s):  
F. Pourroy ◽  
S. Shakhesi ◽  
P. Trompette
Keyword(s):  
Damping Ratio ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Layered Beam ◽  
Flexural Vibrations

In dynamics, the effect of varying the constitutive materials’ thickness of a two-layered beam is investigated. Resonance frequencies and damping variations are determined. It is shown that for specific thicknesses the coupling of longitudinal and flexural vibrations influences the global modal damping ratio significantly.

ANALYTICAL RANDOM VIBRATION ANALYSIS OF BOUNDARY-EXCITED THIN RECTANGULAR PLATES

2013 ◽  
Vol 13 (03) ◽  
pp. 1250062 ◽  
Author(s):  
ASHKAN HAJI HOSSEINLOO ◽  
FOOK FAH YAP ◽  
NADER VAHDATI
Keyword(s):  
Random Vibration ◽  
Printed Circuit Boards ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Jet Impingement ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Frequency Range ◽  
Modal Damping Ratio ◽  
Modal Damping

Fatigue life, stability and performance of majority of the structures and systems depend significantly on dynamic loadings applied on them. In many engineering cases, the dynamic loading is random vibration and the structure is a plate-like system. Examples could be printed circuit boards or jet impingement cooling systems subjected to random vibrations in harsh military environments. In this study, the response of thin rectangular plates to random boundary excitation is analytically formulated and analyzed. In the presented method, closed-form mode shapes are used and some of the assumptions in previous studies are eliminated; hence it is simpler and reduces the computational load. In addition, the effects of different boundary conditions, modal damping and excitation frequency range on dynamic random response of the system are studied. The results show that increasing both the modal damping ratio and the excitation frequency range will decrease the root mean square acceleration and the maximum deflection of the plate.

Nonlinear Span Assessment by Amplitude-Dependent Linearization

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Ralf Peek
Keyword(s):  
Eigenvalue Problem ◽  
Current Practice ◽  
Nonlinear Eigenvalue Problem ◽  
Damping Ratio ◽  
Mode Shapes ◽  
Inelastic Behavior ◽  
Modal Damping Ratio ◽  
Linear Behavior ◽  
Modal Damping ◽  
Vortex Induced Vibrations

Abstract Although it has long been recognized that vortex-induced vibrations of subsea pipeline spans involve nonlinear and inelastic behavior, the current practice to assess such spans for fatigue and ultimate loading conditions is based on the modal analysis assuming linear behavior. Nevertheless, nonlinearity can be captured approximately by making the linearization amplitude dependent. The eigenvalue problem to be solved for the natural frequencies and mode shapes then involves a stiffness matrix that depends on the mode shape and amplitude of vibration. An important part of the nonlinearity comes from the soil, which is generally represented by springs. This paper presents a simple and particularly effective algorithm to solve this nonlinear eigenvalue problem by using the same algorithm that serves to track the bifurcated solution branches in quasi-static structural stability (buckling) analyses. This method is applied to an example in which the nonlinearity comes from the soil springs. The results demonstrate the importance of the nonlinearity, even at relatively low vortex-induced vibrations (VIV) amplitudes typical of the pure inline response. The inelasticity of the soil springs is also used to calculate the associated contribution to the modal damping ratio.

Experimental Study the Vibro-Acoustic Performance of a Double Glazed Window

2012 ◽  
Vol 503-504 ◽  
pp. 1129-1132
Author(s):  
Qi Bo Mao
Keyword(s):  
Damping Ratio ◽  
Normal Wave ◽  
Sound Transmission ◽  
Least Square ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Reverberation Chamber ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Complex Exponential

This paper presents an experimental investigation of the sound transmission and structural vibration characteristics of the double glazed window. The laboratory experiments were performed placing the window between reverberation chamber and anechoic chamber. The window was subject to diffuse field, approximate normal wave and oblique wave acoustic excitations. The sound transmission performances at far-field were measured. Furthermore, experimental modal analysis has been performed. The Least square complex exponential algorithm is used to extract the modal parameters, i.e. mode shapes, natural frequencies and modal damping ratio of the structure. The results also show that the highest sound transmission of this experimental double glazed window appears around the mass-air-mass resonance frequency.

scholarly journals Dynamics of a Pipeline Span on an Elastic Seabed

2021 ◽  
Author(s):  
Ralf Peek ◽  
Matt Witz ◽  
Knut Vedeld
Keyword(s):  
Axial Force ◽  
Exact Analytical Solution ◽  
Damping Ratio ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Vortex Induced Vibrations ◽  
Arch Action

Natural frequencies, mode shapes and modal damping ratios must be estimated to assess subsea pipeline spans for vortex-induced vibrations (VIV) and response to direct wave loading. Several approximate solutions exist for a linearly elastic pipe under constant axial force supported by linearly elastic springs beyond the span’s shoulders. An exact analytical solution has only recently been published. That solution is used here in a Rayleigh-Ritz approximation to account for arch action arising from combined effects of sag under gravity loads and axial restraint at the shoulders. The method allows survey data to be used directly to quantify arch action. Its accuracy is confirmed by finite element analysis. Further, the modal damping ratio is estimated based on the fractions of the potential energy in bending, the axial force, and the soil springs, all of which are determined analytically. Thus, it is found that the effective modal damping ratio increases without a bound as the axial load approaches the buckling load in compression.

scholarly journals Model Updating for Systems with General Proportional Damping Using Complex FRFs

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xinhai Wu ◽  
Huan He ◽  
Yang Liu ◽  
Guoping Chen
Keyword(s):  
Model Updating ◽  
Damping Ratio ◽  
Viscous Damping ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Updating Procedure ◽  
Damping Model

In this paper, we propose a model updating method for systems with nonviscous proportional damping. In comparison to the traditional viscous damping model, the introduction of nonviscous damping will not only reduce the vibration of the system but also change the resonance frequencies. Therefore, most of the existing updating methods cannot be directly applied to systems with nonviscous damping. In many works, for simplicity, the Rayleigh damping model has been applied in the model updating procedure. However, the assumption of Rayleigh damping may result in large errors of damping for higher modes. To capture the variation of modal damping ratio with frequency in a more general way, the diagonal elements of the modal damping matrix and relaxation parameter are updated to characterize the damping energy dissipation of the structure by the proposed method. Spatial and modal incompleteness are both discussed for the updating procedure. Numerical simulations and experimental examples are adopted to validate the effectiveness of the proposed method. The results show that the systems with general proportional damping can be predicted more accurately by the proposed updating method.

scholarly journals Effect of architectural components on the dynamic properties of a long-span floor system

1987 ◽  
Vol 14 (4) ◽  
pp. 461-467 ◽  
Author(s):  
G. Pernica
Keyword(s):  
Fundamental Mode ◽  
Composite Structures ◽  
Dynamic Properties ◽  
Damping Ratio ◽  
Long Span ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Vibration Tests ◽  
Comparison Of The Results ◽  
Floor System

Vibration measurements were taken to determine the effects of architectural components on the dynamic properties (modal frequency, modal damping ratio, and mode shape) of a long-span floor system. The floor was located above a two-storey gymnasium in a recently constructed three-storey elementary school. The dynamic properties of the bare floor system were measured during the construction phase, immediately after the main structural components and the exterior masonry walls were in place. Six months later, with construction completed and the school ready for occupancy, the properties of the finished floor system, complete with internal partitions, mechanical ducts, furnishings, and carpeting, were again obtained.A comparison of the results of the two test series indicated that the dynamic properties of the floor system were altered by the addition of the architectural components. The fundamental frequency rose by 3% and the frequencies of the higher modes by 23%, even though the static load on the floor increased by about 26%. The substantial stiffening of the floor system necessary to precipitate these increases in frequency was linked to the presence of the internal partitions. A full-span partition was also found to behave as a floor support, creating an additional set of modes which were not previously present. Except for the fundamental mode, damping ratios increased by about 2% of critical, from 1.5% to 3.5% of critical. For the fundamental mode, the negligible increase in damping from 4.1 to 4.2% of critical could not be explained. Key words: floors, composite structures, vibration tests, spectrum analysis, resonant frequency, vibration damping.

Modal damping ratio analysis of dynamical system with non-stationary responses

2016 ◽  
Vol 59 ◽  
pp. 138-146 ◽  
Author(s):  
Da Tang ◽  
Ran Ju ◽  
Qianjin Yue ◽  
Shisheng Wang
Keyword(s):  
Dynamical System ◽  
Damping Ratio ◽  
Ratio Analysis ◽  
Modal Damping Ratio ◽  
Modal Damping
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