Identifying the load applied to a sheet by considering damping effects

Master thesis

Mechanical engineering (applied design)

Introduction

Always the question of the generating agent as a dynamic question in all The fields of science have been discussed. Due to the complexity and unforeseen factors and the lack of all-round human mastery over physical issues, it has not been possible to identify the causative factor in many cases, therefore, due to the new look and the recent progress of various sciences, many researchers and scientists have tried to solve the issues in reverse and have another look at the classical issues. Of course, it is a complicated and long way, but it is achievable.

The degree of knowledge of design engineers about the time distribution and the place of dynamic load application is directly related to the way of operation, reliability and serviceability of various structures. Because the distribution and location of dynamic load and impact is not clear in many practical problems. Usually, several different loadings are considered in the stages of analysis and design of such problems. In the old methods, in order to identify the load, access to the place of application of force is required because these methods are based on receiving and measuring the load directly. As it is known, access to the place of application of force is complicated in some cases, dangerous and even inaccessible in some cases. According to the above point, reverse analysis methods seem to be very useful and practical. In general, in reverse analysis, the response of the structure is measured by using several sensors far from the place of force application, and finally the investigated parameters are calculated.

Of course, the measurements are associated with difficulties, because there are many factors to weaken the effect of force and disturbance in it. The more we move away from the place of application of force, the effect of force decreases and in fact the sensors show lower values. In some cases, this distance has a linear relationship with the weakened value, and in some cases, the relationship is nonlinear. It is worth considering that the application of the load is not ideal and the time distribution of the force before solving the inverse problem is unpredictable, and the measurement of the sensor is associated with error. Amplification, transmission and detection of the measurement quantity also introduce some error into the problem. Of course, the calculation error is also added to these errors. These are the factors that make it difficult to solve inverse problems.

Although the first methods presented to solve inverse problems are analytical methods, but due to the limited scope of their application, methods based on numerical solutions are used more. One of the most widely used of these methods is finite difference, finite element and boundary element methods. In the techniques used in recent years, the inverse problem is usually formulated as an optimization problem and then solved by a suitable numerical method.

The most important challenge in solving inverse problems is the inherent complexity [1] of the problem and the lack of a unique solution for it in many problems. The characteristic of body composition includes both permanent and dynamic problems and makes these problems very sensitive to sampling errors, so that the existence of a small error in the sampling data causes a large error in the solution of the problem. In addition, in dynamic problems, due to the fluctuating nature of the measured parameters (such as strain and acceleration), the obtained solutions (loads applied to the structure) will be very sensitive to the input data. This is more obvious when the measured quantity has strong fluctuations.

One ??of the most important inverse problems is estimating the dynamic force and impact on the sheet. Of course, measuring the time distribution of the force can be very useful in practical applications, so it is tried to measure the time distribution of the force and to solve more specialized problems in the field of sheets, it seems that identifying the impact location in a fast and accurate way is one of the requirements. The method of identifying the power location, while being simple, in order to increase the speed of calculations, the fluctuation of the measured data should have a minimal effect on it.

In the second chapter of this thesis, we examine the background of the research that has been done in this field.

In the third chapter, an attempt has been made to review and collect theory and methods about the theory of sheet dynamics and the inverse solution.

In the fourth chapter, with a close look at the inverse sheet problem, an attempt has been made to develop the inverse theory in order to identify the time distribution and identify the location. The effect of force should be used.

Since a part of this thesis is related to practical testing and strain measurement, in the fifth chapter, the mechanisms of strain measurement, its problems and solutions have been considered.

In the sixth chapter, the factors affecting the identification of the time distribution of the force and the location of the force effect have been examined, and a practical problem has been solved in reverse.

At the end, in the seventh chapter, conclusions and suggestions for future research activities are given.

Review of past researches

The first time in 1923 in the research conducted by Hadamard [2] [1], with the concept of entanglement in inverse problems and the absence of a unique answer. Many of these issues have been mentioned. Proving this point led to the relative success of research in this field in the following years. The definition and analysis of inverse problems have been started in various engineering and non-engineering fields since several decades ago, and research in this field is still ongoing. At first, inverse problems were considered in the field of heat transfer, and then they were expanded to other scientific and engineering fields as well. It is worth noting that the amount of research conducted in the field of inverse problems of instruments is very limited compared to many fields.

One ??of the first studies conducted in the field of dynamic load estimation can be mentioned the article by Goodir [3] and colleagues [2]. In this article, the time distribution of the vertical force applied to a half-plane is obtained using an integral equation that uses the response of the structure at points far from the place of force application. Su [4] et al. [3] and Michaels [5] et al. [4] calculated the time distribution of the vertical force on a sheet using a time-combined integral equation [6] that was formulated based on the response of the structure at points close to the place of force application. In the series of articles presented by Doyle[7] [5-7], the transverse impact on beams and sheets has been identified. In these articles, whose effectiveness is determined by practical testing, the problem is solved and the impact time distribution is obtained by using fast Fourier transform [8]. Michel [9] and Pao [10] [8,9] used a double iterative method to detect the oblique impact of an elastic sheet. The force angle and its time distribution have been calculated using the transient response of the structure and with at least two receivers to receive the response waves. The key point in this work has been that the dynamic force can be separated in two domains of time and space, and thus the integral equation, which expresses the relationship between the structural response and the applied impact, has been solved using interpolation functions. The efficiency of this method has been investigated both numerically and experimentally. Hollandsworth [11] and Busby [12] [10] measured the acceleration of a single beam in a time interval of 40 microseconds and then calculated the impact on the beam using the velocity quantity in the inverse algorithm. Wu [13] et al. [11] calculated the impact applied to a composite laminate, assuming the location of the impact is known, using strain values ??as the measured quantity. Ino [14] and colleagues [12], calculated the amount and direction of impact applied to a beam with a simple support in three-dimensional space, the measured quantity in this study was strain. Martin [15] and Doyle [13] used the Fourier transform method together with frequency domain separation [16] to solve the inverse problem. In their research, the amount of acceleration was measured for four examples of a beam with infinite length, a semi-infinite beam, a beam with limited length and also a frame, and then the applied impact was calculated by inverse analysis. Gavel [17] and colleagues [14] detected the waves propagated in the sheet using piezoelectric films and then calculated the impact on the sheet using inverse analysis.