F. Length- Frequency chart for **simply** **supported** **beam** at different taper angle in theoretical analysis. By taking different frequencies for different taper angle for **simply** **supported** **beam** and calculating the different frequencies for different length we plot the graph between frequency and length. Figure 8 indicates that frequency will be more for increasing in taper angle along with the length.

Validation studies are carried out on the **simply** **supported** **beam** subjected to step heat source on one surface and insulated on the opposite surface by using the thermal structural data for aluminium **beam** as given by Boley 1972 and Manolis and Beskos 1981. The thermal structural data for the validations of the FEM formulation to analyze thermally induced vibration are reproduced below from Boley 1972 is as follows: b = 1 m, L = 0.254 m, k = 201.87 W/mK, = 22.010 -6 / 0 C, = 2700 kg/m 3 ,

analysis. In this the transverse surface crack is considered to remain open. A local compliance matrix of four degrees of freedom is considered for the modelling of a crack. This compliance matrix contains diagonal and off-diagonal terms. A harmonic force of given amplitude and frequency is used to excite dynamically the **beam**. The present identification algorithms have been illustrated through numerical examples. Hai-Ping Lin [6] has studied an analytical transfer matrix method, is used to solve the direct and inverse problems of **simply** **supported** beams with an open crack. The crack is modelled as a rotational spring with sectional flexibility. The natural frequencies of a cracked system can easily be obtained through many of the structural testing methods. When any two natural frequencies of a cracked **simply** **supported** **beam** are obtained from measurements, the location and the sectional flexibility of the crack can then be determined from the identification equation and the characteristic equation. A.S. Bouboulas, N.K. Anifantis [7] used the FEM method to evaluate different crack scenarios without changing the discretization. a cracked element is developed incorporating a non-propagating edge crack into a structural **beam** member. The additional ﬂexibility that the crack generates is evaluated using strain energy density factors given by linear fracture mechanics. Based on this ﬂexibility the stiffness matrix of the cracked **beam** element is deduced. The governing equations of the element were treated as in the usual way of ﬁnite element procedures. In that formulation, the crack depth and location were considered as independent global design parameters. Thus, that element was appropriate for static and dynamic analysis of skeletal structures with crack-like damages. The convergence, accuracy and computational efﬁciency of the presented element are validated through comparisons with experimental and numerical results available from the literature. Christides and Barr [8] developed a one-dimensional cracked **beam** theory at same level of approximation as Bernoulli- Euler **beam** theory. Dimaragonas [9] presented a review on the topic of vibration of cracked structures. His review contains vibration of cracked rotors, bars, beams, plates, pipes, blades and shells. Shen and Chu [10] and Chati, Rand and Mukherjee [11] extended the cracked **beam** theory to account for opening and closing of the crack, the so called “breathing crack” model. A.S. Sekhar [12] has examined different multiple-cracks, their Effects, identification method in vibration structures such as beams, rotors, pipes, etc. It

A residual modal force based damage detection method is used to locate damage is presented. The residual modal forces are basically caused by changes in structural parameters due to the occurrence of damage. If the relationship between the residual modal force and the change in structural parameters can be found, the information provided by the residual modal force can then be used to determine the physical parameters at the damaged site. The residual force method is used to locate the suspected damaged elements in a **simply** **supported** **beam** model.

analysis. In this the transverse surface crack is considered to remain open. A local compliance matrix of four degrees of freedom is considered for the modelling of a crack. This compliance matrix contains diagonal and off-diagonal terms. A harmonic force of given amplitude and frequency is used to excite dynamically the **beam**. The present identification algorithms have been illustrated through numerical examples. Hai-Ping Lin [6] has studied an analytical transfer matrix method, is used to solve the direct and inverse problems of **simply** **supported** beams with an open crack. The crack is modelled as a rotational spring with sectional flexibility. The natural frequencies of a cracked system can easily be obtained through many of the structural testing methods. When any two natural frequencies of a cracked **simply** **supported** **beam** are obtained from measurements, the location and the sectional flexibility of the crack can then be determined from the identification equation and the characteristic equation. A.S. Bouboulas, N.K. Anifantis [7] used the FEM method to evaluate different crack scenarios without changing the discretization. a cracked element is developed incorporating a non-propagating edge crack into a structural **beam** member. The additional ﬂexibility that the crack generates is evaluated using strain energy density factors given by linear fracture mechanics. Based on this ﬂexibility the stiffness matrix of the cracked **beam** element is deduced. The governing equations of the element were treated as in the usual way of ﬁnite element procedures. In that formulation, the crack depth and location were considered as independent global design parameters. Thus, that element was appropriate for static and dynamic analysis of skeletal structures with crack-like damages. The convergence, accuracy and computational efﬁciency of the presented element are validated through comparisons with experimental and numerical results available from the literature. Christides and Barr [8] developed a one-dimensional cracked **beam** theory at same level of approximation as Bernoulli- Euler **beam** theory. Dimaragonas [9] presented a review on the topic of vibration of cracked structures. His review contains vibration of cracked rotors, bars, beams, plates, pipes, blades and shells. Shen and Chu [10] and Chati, Rand and Mukherjee [11] extended the cracked **beam** theory to account for opening and closing of the crack, the so called “breathing crack” model. A.S. Sekhar [12] has examined different multiple-cracks, their Effects, identification method in vibration structures such as beams, rotors, pipes, etc. It

The research methodology is important for the scope of work to perform this study correctly. All steps of the research work carried out will be described in this chapter. The methodology of this study consists of the specifications of the **beam**, the **beam** **supported** and vibration absorber and the use of ANSYS software and MATLAB for simulation studies. The main part of this study is to identify the vibration of the struc- ture and the location to reduce vibration using a vibration absorber. Such as the design of a vibration absorber that reduces the vibrations of the **beam**. Before starting work simulation, first set the specification, material, weight and size of the **beam**. Type of the **beam** is **simply** **supported** **beam** studied. Next, determine the location of the vibra- tion absorber on any part of the **beam** and increase the number of vibration absorber if necessary to reduce the vibration of the **beam**. Then, using the software of ANSYS and MATLAB to find the characteristics of vibration and the effects and also double shock absorber and absorber on the **beam**.

36 Read more

Fig.5. Effect of crack depth on frequency at CL 320mm Fig.6. Effect of crack depth on frequency at CL 420mm Following table 3 shows, the comparison of experimental and ANSYS results of amplitude for cracked **simply** **supported** **beam** under loading condition. An ANSYS result shows good agreement with experimental results. The average percentage error is 10.50

By using the positive property of Green’s function and the unilateral global bifurcation the- orem, we obtain the global structure of positive solutions for a class of nonlinear discrete **simply** **supported** **beam** equation with the nonlinearity satisfying local linear growth con- ditions. The main results extend the existent results of positive solutions and generalize many related problems in the literature.

14 Read more

This paper demonstrates the feasibility of simultaneously identifying both the location and severity of structural damage in a **beam** by using two independent moving load experiments. First, a simple but sufficiently accurate single degree of freedom model is presented to simulate the structure efficiently over a wide range of relevant inputs. We then introduce a damage sensitive feature (DSF) based on the integral of the velocity time history of the **beam** at its midspan when the load moves over the **beam**. A critical velocity, a function only of the beam’s first natural frequency and length, is obtained for the proposed DSF, upon which the damage can be located more accurately. The only required data for the damage detection is the midspan velocity-time history of the cracked **beam** subjected to a moving load, and the midspan static deflection of the intact **beam** subjected to a load of the same magnitude. In the last section of this paper, the capability of the proposed DSF is examined in the presence of noise. The results demonstrate the capability of the proposed method to find both the damage location and severity successfully, and methods for further reducing the effects of noise are suggested.

16 Read more

In solving partial differential equations, the primary challenge is to create an equation that approximates the equation to be studied , but is numerically stable , meaning that error in the input and intermediate calculation do not accumulate and cause the resulting output to be meaningless. There are many ways of doing this, all with advantages and disadvantage. The finite element method is a good choice for solving partial differential equation over complicated domain (like **beam** or notch analysis etc), when domain changes (as during a solid state reaction with a moving boundary) etc.

Sergio F. Bren and Beth M. Macri, (2004) experimentally carried out tests on eighteen small scale reinforced concrete **beam** strengthened by CFRP composites. Author aimed to understand behaviour of strengthened reinforced concrete beams under different configuration of CFRP. Author used three different type of configuration, in first case laminates were attached only tension face of the **beam**, second case laminate were attached only shear/side face of the **beam** and for third case laminates were attached entire specimen or U shape. They were used strain gauge in a region where crack in concrete were performed to monitor the variation of strains throughout testing. From the experiment they concluded composite pattern/configuration directly affect behaviour of load versus deflection load and deflection of the **beam** were affected by composite configuration. Author observed local strain didn’t provided a realistic representation of the globe **beam** behaviour.

Concrete is most utilized construction materials, it is having many advantages, some are : low cost, long service life (when properly mixed, placed and cured), ease of construction and high compressive strength. In present time the civilization depends upon the available ranges of concrete or reinforced concrete (RC) structures, ranging from domestic structures to heavy structures. However, numerous concrete structures suffer important degradations and damages due to environmental exposure or extraordinary overload or have insufficient strength because of defective construction, increased service load requirements, or updated codes, fiber reinforced polymer (FRP) composites strengthening becoming nowadays a commonly accepted and widespread technique. The research includes static analysis of **beam** under glass fiber composite plate with PCC and RCC to optimize material and cost of **beam** with designed strength.

[4] Dimmerling, A., Miller, R.A., Castrodale, R., Mirmiran, A., Hastak, M. and Base- heart, T.M. (2005) Connections between **Simply** **Supported** Concrete Beams Made Continuous: Results of National Cooperative Highway Research Program Project 12-53. Transportation Research Record : Journal of the Transportation Research Board , 1928, 126-133.

Present theory gives good result as compared to the other shear deformation theories. For **simply** **supported** **beam** with various load the result of present theory are nearly matching with those other higher order shear deformation theory. For **simply** **supported** **beam** with uniformly distributed load the transverse deflection given by present theory is nearly matching with higher order shear deformation theory and in case of various load acting at mid span of **beam**, result obtained by present theory are much closer to the other shear deformation theory. Thus the validity of the present theory is established.

11 Read more

Structural Health Monitoring using raw dynamic measurements is the subject of several studies aimed at identifying structural modifications or, more specifically, focused on damage assessment. Traditional damage detection methods associate structural modal deviations to damage. Nevertheless, the process used to determine modal characteristics can influence the results of such methods, which could lead to additional uncertainties. Thus, techniques combining machine learning and statistical analysis applied directly to raw measurements are being discussed in recent researches. The purpose of this paper is to investigate statistical indicators, little explored in damage identification methods, to characterize acceleration measurements directly in the time domain. Hence, the present work compares two machine learning algorithms to identify structural changes using statistics obtained from raw dynamic data. The algorithms are based on Artificial Neural Networks and Support Vector Machines. They are initially evaluated through numerical simulations using a **simply** **supported** **beam** model. Then, they are assessed through experimental tests performed on a laboratory **beam** structure and an actual railway bridge, in France. For all cases, different damage scenarios were considered. The obtained results encourage the development of computational tools using statistical indicators of acceleration measurements for structural alteration assessment.

17 Read more

The first modeling step is the characterization of the **beam** geometry accounting for the bending behavior of truss. A deformable 3D truss model was generated by means of planar commands. Concerning the meshing of the **beam**, the truss has been discretized by means of shear-flexible elements adopting the global seeds meshing technique. In order to favor convergence and reduce the computational time, the simplest element type has been chosen, the B31, that is a 2-node linear **beam** in space. The boundaries for **simply** **supported** **beam** was used here. The displacements for one side of the truss were constrained in both x direction and y direction. The displacement for the other side of the truss was constrained only in y direction. The concentrated force was exerted on the middle position of truss. A general and static procedure type was chosen to calculate the mechanical response of truss. When the calculations of the mechanical response of truss have been accomplished, the Mises stress and displacement are obtained by means of output databases. Based on the calculated Mises stress and displacement, the stiffness of truss was analyzed.

ABSTRACT: Vibration of a smart **beam** is being controlled. This smart **beam** setup is comprised of actuators and sensors placed at the root of a **simply** **supported** **beam**. Vibrations can be caused by various sources including human activity and nearby motorized equipment. In this case, disturbance is produced by using a Piezoelectric actuators. The piezoelectric sensors are used to detect the vibration. Simultaneously, feedback controller sends correction information to the actuator that minimizes the vibration. To optimize results, controllers were designed using LQR control theory. This theory generally results in high-order controllers. Additionally, optimal control theory is being used to directly optimize low-order controllers.

In the next example, we show the numerical results for identification of a **simply** **supported** **beam** subjected to a uniform load acting over a portion of the **beam**, as indicated in Figure 5. Although a significant overshoot occurred around x = 3.5 and 8.5, on the whole, good identification results were obtained. In this figure, circles at x = 0 and x = 10 denote the vertical reactions at the sup- porting point. Although there was a part disturbed by overshoot, its amount was small and good one was obtained as an estimated value.

The purpose of this paper is to develop an analysis method to solve the free vibration response for a continuous system subjected to an initial velocity profile using an initial velocity approximation based on an equivalent impulse load. It has been shown that for a single degree of freedom system, the initial velocity can be applied as an impulsive loading with a very short duration. The proposed analysis method in this paper is done for a continuous system to show that this approximation works not only for a single degree of freedom system, but for a continuous system as well. The assumed initial velocity profile is from a case of interest to the authors. The available analytical solution for a continuous system such as a **simply** **supported** **beam** subjected to an initial velocity is compared with the finite element solution determined from SAP 2000 using the initial velocity approximation. The SAP2000 solution using the proposed approximation showed an excellent agreement to the analytical solution. Finally, this method can be used to find the dynamic response of complex frames subjected to an initial velocity profile, where the analytical solution for such cases is difficult to find.

There are several types of deck construction divided into **beam**, slab, **beam** and slab and cellular slab. Each type of deck has their different geometric and behavioural characteristics. The method of analysis can be determined based on deck behaviors characteristics. Figure 1.1 shows the component that is usually found on a typical bridge.

22 Read more