Frequency analysis of structures by integrated force method (original) (raw)
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Evaluation of Forces on a Steel Truss Structure Using Modified Resonance Frequency
Procedia Engineering, 2014
Structural decay may be defined as any deviation in a structure's original geometry or material properties that may cause undesirable stresses, displacements, and vibrations in structures. To check Structure conditions, a non-destructive testing such as resonance frequency testing, provides an alternative solution. Based on literature studies carried out on resonance frequency testing for the determination of axial forces, a simple truss structure was modelled. The truss structure has 2 members with equal steel section of L.30.30.3, each acting as compression and tension members, and then applied load was accomplished by hanging a steel block on the tip of the truss being tested. Finally, transversal frequency measurements were performed on the truss members under various load levels. The collected resonance frequencies were then evaluated using Bernoulli beam theory to estimate member forces and rotational spring parameter at the ends of the member. This research shows that the error of estimation of member forces in the compression and tension members using modified natural frequency and rotational spring parameter by linear regression method varies from 0.26% to 1.99% and 0.2% to 2.41% respectively. The value of rotational spring parameters indicates that the members have semi rigid behaviour and closer to fixed rather than pinned conditions.
Vibrational Analysis of Framed Structures
— Generally the stress and deformation analysis of any structure is done by constructing and analyzing a mathematical model of a structure. One such technique is Finite element method (FEM). A frame is subjected to both static and dynamic loading with dead load comprising the static load and the all other time varying loads making up the dynamic load. This project titled " Vibration Analysis of Frames " aims at analyzing the frame both statically and dynamically using the matrix approach of FEM by developing generalized codes in MATLAB. The analysis comprises of the static analysis of frame and the variation of various parameters such as displacement, moment etc with increasing number of storey's as well as dynamic analysis wherein a code is developed to find the natural frequency of the structure along with the various other parameters. A structure is always vibrating under dynamic loading such as wind etc and if the vibrating frequency equals the natural frequency of the structure, resonance might take place. It is thus necessary to analyze all these aspects of a structure first which we aim with our study.
EVALUATION OF FORCES ON STEEL TRUSS STRUCTURE USING RESONANCE FREQUENCY ANALYSIS
Structural decay may be defined as any deviation in a structure's original geometry or material properties that may cause undesirable stresses, displacements, or vibrations in the structure. This decay may be due to cracks, loose bolts, broken welds, corrosion, or fatigue. In addition, many bridges are decayed due to age, misuse, lack of repair, and, in some cases, because improper design. Conventional inspection remains the most commonly used method for the structural evaluation of bridges. Conventional visual inspection can be costly and time consuming, especially when disassembly or special rigging is necessary to provide access to the area being inspected. Nondestructive testing such as resonance frequency analysis provides alternative options.
Dynamics Analysis of a Truss System Modelled by the Finite Element Method in the Frequency Domain
2020
The dynamic analysis of a truss system modelled by the finite element method in the frequency domain is studied. The truss system is modelled by 22 elements and has 44 degrees of freedom. The stiffness matrix and mass matrix of the truss system are obtained by using the finite element method. Differential equations of the truss system are obtained by using the obtained stiffness and mass matrix. By applying the Laplace transformation, the displacements of each node are calculated, and the equation is arranged in the frequency domain. The obtained differential equations are solved by using MATLAB. Eigen values are calculated and represented depending on the frequencies. Thus, static displacements, dynamic displacements, static reaction forces and dynamic reaction forces for each frequency are graphically obtained. Additionally, dynamic amplification factors are calculated and simulated depending on the frequencies. Dynamic displacements increased near the eigenvalues, and the dynamic...
Nonlinear analysis of the forced response of structural elements
The Journal of the Acoustical Society of America, 1974
A general procedure is presented for the nonlinear analysis of the forced response of structural elements to harmonic excitations. Internal resonances (i.e., modal interactions) are taken into account. All excitations are considered, with special consideration given to resonant excitations. The general procedure is applied to clamped-hinged beams. The results reveal that exciting a higher mode may lead to a larger response in a lower interacting mode, contrary to the results of linear analyses. Subject Classification: 40.30, 40.22. Recently, Nayfeh t• and Atluri •a applied versions of the method of multiple scales, in place of harmonic balance, to the study of beam vibrations. Three versions 281
Modelling the Vibration Behaviour of Infinite Structures by Fem
Journal of Sound and Vibration, 2000
In vibration power #ow analysis, often the vibration behaviour of in"nite structures is required. The modelling of in"nite structures using the "nite element method has been discussed. By considering the impedance of a "nite beam and "nite plate, theoretical formulae for a spring}damper combination to match these impedances are derived. Examples are given for a rather short (200 mm) beam and a small (400 mm diameter) plate with spring}dampers applied to the edges of the structures using the "nite element method. Results of the driving point mobility indicate that these "nite structures simulate an in"nite beam and an in"nite plate very well. Furthermore, the surface mobility of an in"nite plate over a square contact area subject to a uniform conphase force excitation has been calculated successfully using just under 8 times fewer elements than a previous study.
Journal of Sound and Vibration, 2000
This is the "rst of two companion papers which collectively present a method for the analysis of built-up structures. One such structure is the machinery foundation of a ship which is constructed from a collection of large beams and #exible plates. The heavy vibration sources are supported by the large sti! beams. The power injected into and the power transmitted around the structure is controlled by long-wavelength waves generated in these beams by the vibration sources. As these long waves propagate along the sti! beams they generate short-wavelength #exural waves in the attached #exible plates. The long waves transmit some of their energy to the short-wavelength waves which therefore damp the long waves. The di!erence between the wavelengths of the long waves in the sti! beams and the short waves in the #exible plates is often very large. In this case, the short waves present a locally reacting impedance to the long waves at the structural joints. This paper argues that such a condition allows the vibration to predicted in three steps. First, the long-wave response of the sti! beams is analyzed in isolation of the short-wave response of the #exible plates; second, the short-wave response of the #exible plates is analyzed in isolation of the long-wave response; third, the two separate responses are combined to yield the response of the complete structure due to both the long and the short waves. The method is applied to a simple plate-sti!ened beam consisting of a directly excited sti! beam attached to a large #exible plate which is broadly representative of the machinery foundation. The method predicts the frequency response of the plate-sti!ened beam which compares well with laboratory measurements, thereby supporting the method. In this paper, all three steps are performed analytically which restricts the method to geometrically simple structures. The companion paper presents a hybrid numerical/analytical implementation which accommodates geometrically more diverse structures.
Memoria Investigaciones en Ingeniería N23, 2022
The use of finite element method software allows the modal and spectral analysis of complex structures with an accessible computational cost. In contrast, with the theory of damped systems of a degree of freedom, solutions can be obtained analytically that describe with greater generality the vibrations of structures subjected to variable forces over time. However, with analytical methods, only very simple structures can be studied. This paper presents a method that allows to calculate the rigidity and effective mass of a structure from the values of the angular frequencies of the structure, with their corresponding inertial loads. Next, the structure can be analyzed as a cushioned system of a degree of freedom. In this way, it is possible to calculate the displacements and accelerations that the structure will suffer when it is excited by an external force variable over time. Subsequently, using D'Alembert's principle and a finite element program, the stresses can be calculated by a static analysis.