Application of block Lanczos method for analysis of cyclic symmetric structures

In this study, an output-only modal identification approach is proposed for decentralized wireless sensor nodes used for linear structural systems. The following approaches are implemented to achieve the objective. Firstly, an output-only modal identification method is selected for decentralized wireless sensor networks. Secondly, the effect of time-unsynchronization is assessed with respect to the accuracy of modal identification analysis. Time-unsynchronized signals are analytically examined to quantify uncertainties and their corresponding errors in modal identification results. Thirdly, a modified approach using complex mode shapes is proposed to reduce the unsynchronization-induced errors in modal identification. In the new way, complex mode shapes are extracted from unsynchronized signals to deal both with modal amplitudes and with phase angles. Finally, the feasibility of the proposed approach is evaluated from numerical and experimental tests by comparing with the performance of existing approach using real mode shapes.

This article presents a damage identification method based on structural natural frequencies and mode shape points. According to the well-posedness analysis of this method, an algorithm is proposed to find the optimal combination of natural frequencies and mode shape points. Then, an integrated scheme that consists of the optimal point selection, the damage identification and the measurement noise updating is presented. In such a way, the damage identification errors due to measurement noises can be greatly suppressed. Numerical examples demonstrate that although structural damage parameters are very sensitive to the measurement noises, especially the noises in natural frequencies, they can be reliably identified if the natural frequencies and mode shape points are properly selected using the proposed method.

Interval natural frequency and mode shape analysis for truss structures with interval parameters

The rotor is a key element of rotating machinery that can be used in different of mechanical devices such as gas turbines, industrial compressors, motors, and aero engines. The dynamic analysis of a rotor system with active magnetic bearings is presented in this paper. This system consists of a flexible shaft with a rigid disk and flexible bearings. An sys Workbench is used to study a 3D simulation of a finite element model. Correct estimation of the rotor's natural frequencies and mode shapes is required for rotating machinery safety procedures. In order to compute the natural frequencies and mode shapes of this system, in the first case it is assumed a free-free system in which no bearings are used, and the natural frequencies and mode shapes are calculated without rigid body modes. In the second case, the natural frequencies and mode shapes are determined with bearing stiffness. The natural frequencies are also evaluated using finite elements based on matlab code. A comparison between the two methods was carried out.

This paper presents and discusses an Arnoldi‐based eigensolution technique for evaluating the complex natural frequencies and mode shapes from frequency dependent quadratic eigenproblems associated with vibration analysis of damped structures. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices. This modelling provides the ability to represent a frequency dependent damping matrix in vibration analysis of skeletal systems.The eigensolution methodology presented here is based upon the ability to evaluate a specific set of parametrized curves for the non‐linear eigenvalue problem at given values of the parameter. Numerical examples illustrate that this method, used in conjunction with a secant interpolation, accurately evaluates the complex natural frequencies and modes of the quadratic non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models.

In this study, 4 different pieces of automotive rear lamp lenses which are made of Polymethylmethacrylate (PMMA) and have different geometries have been inspected. Free-free natural frequencies and mode shapes of lenses have been estimated by the help of ANSYS WB® Finite Element Analysis (FEA) software. Meanwhile, by the help of Experimental Modal Analysis (EMA) methods; natural frequencies, damping ratios and mode shapes of the lenses have been determined. Finally, mode shapes calculated by FE and measured by EMA were compared and Modal Assurance Criteria matrix (MAC) was determined. After experimental modal tests, FRF’s were calculated by DEWESoft® X3 software then natural frequencies, damping ratios and mode shapes were calculated by the use of ME’scope® VESVT-570 Visual Modal software. In addition, MAC was calculated by the help of MEScope® software. The main reason for the use of such experimental methods was to understand if the assumptions made before theoretical analysis were satisfied in reality or not.

A new exact approach for determining natural frequencies and mode shapes of non-uniform shear beams with arbitrary distribution of mass or stiffness

The vibration behavior of a cracked cantilever beam with a stationary roving mass and rotary inertia is investigated. The beam is modeled as an Euler-Bernoulli beam with rectangular cross section. The transverse deformation and axial deformation of the cracked beam are coupled through a stiffness matrix which is determined based on fracture mechanics principles. The analytical solutions are obtained for the natural frequencies and mode shapes of a cracked cantilever beam with a roving mass and rotary inertia. The effects of the location and depth of the crack, the location and the weight of the roving mass and rotary inertia on the natural frequencies and mode shapes of the beam are investigated. The numerical results show that the coupling between the transverse and axial vibrations for moderate values of crack depth and/or roving mass and rotary inertia is weak. Increasing the crack depth and the mass and rotary inertia will increase the coupling effect. Detection of the crack location using natural frequencies and mode shapes as parameters is also discussed.

Two methods (equivalent force method and segmental mode assuming method) of calculating the natural frequencies and mode shapes of a free-free-multi-supported beam subjected to an axial load is found, considering the structure characteristic of the guide bar, which has long length but small section, and supported by many bearings. The calculation shows that these two methods are convenient for computer programing and have the same results in obtaining the natural frequencies and mode shapes of a free-free-multi-supported beam subjected to an axial load, solving the problem that the vibration function of this kind of beam is hard to deal with because it cannot be simplified with the boundary condition of two ends. Then the segmental mode assuming method is used to analyze the impact of the support location on the natural frequencies and mode shapes of the guide bar. The relation graphs of the natural frequencies with support location, as well as the support locations where the natural frequencies reached the maximum and the minimum are found, providing a reference for the support location selection for the guide bar. The changing curves of the mode shapes with support location are plotted, which show that the bending deformation is homogeneous when the length of each segment is approximately equal, avoiding the phenomenon that bending stresses concentrates at the large-amplitude segments and cause breakage while less stress exists in small-amplitude segments and hinder the exploiting of their performance, providing a reference for the structure design of the guide bar.

Determination of the natural frequencies and mode shapes for large structures by accelerated Newton-Raphson method

Retrofitting is a technique in damaged structure is strengthened to original design requirements. The recent earthquake occurred in India during 2001 in Gujarat, damaged many buildings that were seismically deficient. So there is an urgent need for retrofitting of damaged buildings. This calls for techniques that are technically sound and economically feasible to upgrade deficient and damaged structures. Also, Portland cement (PC) production is under critical review due to high amount of carbon dioxide gas released to the atmosphere and Portland cement is also one among the most energy-intensive construction materials. The current contribution of greenhouse gas emission from Portland cement production is about 1.5 billion tons annually or about 7 % of the total greenhouse gas emissions to the earth’s atmosphere. So retrofitting of existing deficient building using eco-friendly material which could promise higher structural performance than the original building is essential. Many retrofitting methods such as epoxy injection, CFRP, GFRP wrappings etc. are used currently, but there is a mismatch in tensile strength and stiffness of these materials with that of concrete structure. The Geopolymer concrete (GPC) is fire and acid resistant, highly durable, less shrinkage, low permeable and attains strength within 3 days of ambient air curing. So the feasibility study of geopolymer concrete in retrofitting of damaged reinforced concrete (RC) beams and RC building is presented in this paper. An open ground three storey seismically damaged RCC building is retrofitted with GPC at cracked portions. And free vibration test is carried out using reaction mass shaker to obtain the natural frequencies and mode shapes. Also using finite element method in ANSYS software modal analysis is done on the building for natural frequencies and mode shapes. This paper presents the experimental and analytical results of natural frequencies and mode shapes.

The natural modes of flexural vibration of a circular plate with a solid shaft and a solid cylinder, which is a simple model of aircraft gears, were theoretically analyzed with a new method proposed by the authors. The calculated natural frequencies and mode shapes coincided well with the values measured by experimental modal analysis. Using the calculated natural frequencies and mode shapes, the three parameters required for the estimation of radiating sound power—total loss factor, radiation loss factor, and driving point mobility—were calculated, and then the radiating sound power from the circular plate was estimated by the estimation theory proposed by the authors in other papers. The frequency response of the estimated sound power coincided well with the values measured by the sound intensity method.

The study of vibration is critical in most engineering structures, with natural frequency and mode shape being two key parameters of a vibrating body. Identifying these parameters can be achieved through modal analysis, which is essential in designing mechanical systems. This paper investigates the vibration characteristics of a cantilever beam, aiming to determine its natural frequency and mode shape using finite element analysis (FEA) software. Determining the natural frequency of a beam involves calculating it based on physical properties and boundary conditions. Identifying the mode shapes of a beam involves recognizing the distinct deformation patterns that occur at specific frequencies. The natural frequencies and mode shapes are obtained using ANSYS software. The study focuses on a mild steel rectangular cantilever beam in a free-fixed condition, computing its modes and natural frequencies through FEA in ANSYS. The results are then utilized for further design processes. Key Words: Modal Analysis, Natural Frequency, Mode Shapes, FEA.

A combined experimental and finite element approach was used to compare the vibrational response of the composite beams with different configurations of internal taper and uniform cross sections. Composite beams were made using the hand lay-up process. Glass fibre was used as reinforcement in the form of a bidirectional fabric and a general-purpose epoxy resin as the matrix for the composite material. Experimental dynamic tests were carried out on FFT analyzer using specimens with different taper configurations. From the results, the effect of different taper configurations on the flexural natural frequencies and mode shapes was investigated. Finite element analysis of the same problem was carried out on software package ANSYS and the results were validated using the experimental results. From the results, a thorough comparison was made between the natural frequencies, loss factors, displacements and mode shapes of the specimens with different taper configurations and uniform cross sections considered. The aerospace implications are provided.

A quasi-statically growing stable crack, if perturbed from its equilibrium position, will accelerate back towards it. Within quasi-static, ideal, Griffith fracture theory, vibrations of the crack and the structure have characteristic natural frequencies. We explore this feature of Griffith fracture theory in two simple geometries: a crack between a bar and a substrate, and a crack in a double-cantilever beam (DCB) specimen. For small perturbations about the stable quasi-static configuration, the dynamic equations of motion reduce to simple eigenvalue problems, leading to exact expressions for natural frequencies and mode shapes. An interesting feature of the mode shapes is that they correspond to force-free or moment-free conditions at the crack tip. Using an extended form of Hamilton's principle, we have developed a variable-length finite element technique to calculate natural frequencies and mode shapes of deformations perturbed from the stable equilibrium state. Its accuracy is demonstrated by application to the two problems analyzed previously. The possibility of crack tip oscillations in real brittle materials with irreversibility in crack tip decohesion is discussed in light of Rice's generalization of the Griffith theory.