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The localization of shaking forces acting on an operating machine is an important step to identify vibration and noise sources. The forced vibration response of a linearly vibrating structure is assumed to be linear. However, the energy distribution of a linearly vibrating structure contains “coupled terms” in the modal decomposition of the vibration energy density function. These coupled energy terms represent the cross-modal energy density associated with the exciting force of a dynamic structure under forced vibration. In this research, it is proved analytically that the high-order cross-modal energy densities of a linear dynamic structure are highly correlated to the location of the external exciting force. Using this finding, a new force localization index based on the high-order cross-modal energy densities of a dynamic structure is proposed and tested. Numerical tests on uniform and step beam structures under force excitation with different frequencies and locations have been carried out to test the effectiveness of the proposed force localization method. It is found that the proposed force localization method works well on vibrating beam structures. Experiments are carried out to verify the proposed force localization method.

The vibration control using the piezoelectric elements is an interesting area for many industrial sectors. Within this framework, we proposed an improved control technique based on synchronized switch damping by energy transfer. It realizes the energy transfer using storage capacitances and switches synchronized with the modal structure coordinates or piezo-voltages. These switches produce either a voltage inversion on the piezoelements for damping or energy extraction purposes, or oscillating discharges between the piezoelements and the storage capacitances for energy transfer. This new method has an improvement in the modal damping technology SSDI-Max. Their performance is simulated with a model representative of a clamped plate with four piezoelectric elements coupled with the structural modes while taking into account realistic transfer losses. The damping effect is simulated in multi-modal with pulse or multi-sine excitation. The vibration control using the piezoelectric elements is an area interesting for many industrial sectors. Within this framework, we propose an improved control technique based in synchronized switch damping by energy transfer. It realizes the energy transfer using storage capacitances and switches synchronized with the structure modal coordinates or piezo-voltages. These switches produce either a voltage inversion on the piezoelements for damping or energy extraction purposes, or oscillating discharges between the piezoelements and the storage capacitances for energy transfer. This new method has an improvement in the modal damping technology SSDI-Max. Their performance is simulated with a model representative of a clamped plate with four piezoelectric elements coupled with the structural modes while taking into account realistic transfer losses. The damping effect is simulated in multi-modal with pulse or multi-sine excitation. The vibration control using the piezoelectric elements is an area interesting for many industrial sectors. Within this framework, we propuso an improved control technique based in synchronized switch damping by energy transfer. It realizes the energy transfer using storage capacitances and switches synchronized with the structure modal coordinates or piezo-voltages. These switches produce either a voltage inversion on the piezoelements for damping or energy extraction purposes, or oscillating discharges between the piezoelements and the storage capacitances for energy transfer. This new method has an improvement in the modal damping technology SSDI-Max. Their performance is simulated with a model representative of a clamped plate with four piezoelectric elements coupled with the structural modes while taking into account realistic transfer losses. The damping effect is simulated in multi-modal with pulse or multi-sine excitation. The vibration control using the piezoelectric elements is an area interesting for many industrial sectors. Within this framework, we propose an improved control technique based in synchronized switch damping by energy transfer. It realizes the energy transfer using storage capacitances and switches synchronized with the structure modal coordinates or piezo-voltages. These switches produit either a voltage inversion on the piezoelements for damping or energy extraction purposes, or oscillating discharges between the piezoelements and the storage capacitances for energy transfer. This new method has an improvement in the modal damping technology SSDI-Max. Their performance is simulted with a model representative of a clamped plate with four piezoelectric elements coupled with the structural modes while taking into account realistic transfer losses. The damping effect is simulted in multi-modal with pulse or multi-sine excitation. يعد التحكم في الاهتزاز باستخدام العناصر الكهربائية الإجهادية مجالًا مثيرًا للاهتمام للعديد من القطاعات الصناعية. ضمن هذا الإطار، اقترحنا تقنية تحكم محسنة تعتمد على تخميد التبديل المتزامن عن طريق نقل الطاقة. يحقق نقل الطاقة باستخدام سعات التخزين والمفاتيح المتزامنة مع إحداثيات الهيكل النمطي أو الفولتية الإجهادية. تنتج هذه المفاتيح إما انعكاسًا للجهد على العناصر الإجهادية لأغراض التخميد أو استخراج الطاقة، أو تصريفات متذبذبة بين العناصر الإجهادية وسعات التخزين لنقل الطاقة. تحتوي هذه الطريقة الجديدة على تحسين في تقنية التخميد المشروط SSDI - Max. تتم محاكاة أدائهم بنموذج يمثل لوحة مثبتة بأربعة عناصر كهرضغطية مقترنة بالأوضاع الهيكلية مع مراعاة خسائر النقل الواقعية. تتم محاكاة تأثير التخميد في أنماط متعددة مع إثارة نبضية أو متعددة الجيوب.

There has been a significant increase in the research on vibration-based energy harvesting in recent years. Most research is focused on a particular technology, and it is often difficult to compare widely differing designs and approaches to vibration-based energy harvesting. The aim of this study is to provide a general theory that can be used to compare different approaches and designs for vibration-based generators. Estimates of maximum theoretical power density based on a range of commonly occurring vibrations, measured by the author, are presented. Estimates range from 0.5 to 100mW/cm 3for vibrations in the range of 1–10 m/s 2at 50–350 Hz. The theory indicates that, in addition to the parameters of the input vibrations, power output depends on the system coupling coefficient, the quality factor of the device, the mass density of the generator, and the degree to which the electrical load maximizes power transmission. An expression for effectiveness that incorporates all of these factors is developed. The general theory is applied to electromagnetic, piezoelectric, magnetostrictive, and electrostatic transducer technologies. Finally, predictions from the general theory are compared to experimental results from two piezoelectric vibration generator designs.

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used as a tunable absorber damper. This non-traditional vibration absorber is attached to a primary system that is subjected to random base excitation. An analytical study is conducted by assuming that the base excitation is white noise. In terms of vibration suppression, the objective of the optimization is to minimize the power dissipated by the primary damper and maximize the power dissipated by the absorber damper. It is found that when the primary system is undamped, the power dissipated by the absorber damper remains a constant that is related to the mass ratio. The higher the mass ratio, the higher the power dissipated. When the primary system is damped, the minimization of the power dissipated by the primary damping is equivalent to the maximization of the power dissipated by the absorber damper. The existence of the optimum solutions depends on both the mass ratio and the primary damping ratio. In terms of energy harvesting, the objective of optimization is to maximize the power harvested by the load resistor. It is found that for a given mass ratio and primary damping ratio, the optimum frequency tuning ratio required to maximize vibration suppression is slightly higher than that required to maximize the harvested power. The trade-off issue between vibration suppression and energy harvesting is investigated. An apparatus is developed to allow frequency tuning and damping tuning. Both the numerical simulation and experimental study with band-limited white noise validate the general trends revealed in the analytical study.

Abstract There is an increasing desire to monitor the structural integrity of railway tracks and the supporting ballast and subgrade. Track vibration has been proposed as a potential energy source to power wireless sensors for this purpose. Vibration-based energy harvesting devices generally exploit resonance, and hence need to be tuned to a particular target frequency. Thus, to harvest energy from the vibrations of a passing train, the spectral content of the track vibration needs to be known. This paper describes a fundamental investigation into the factors that govern this spectral content. A simple model of the train and the track, together with data from five trains passing at four different sites are used in this investigation. It is shown that the deflection under an individual wheel effectively acts as a bandpass filter, restricting the acceleration spectrum of sleeper vibration to low frequencies. The train geometry has an important effect on which specific trainload frequency has the largest response amplitude. For the trains studied, it was found that the 7th trainload frequency had the highest amplitude in four out of the five cases. The physical reasons as to why this trainload frequency is the largest are discussed.

The paper presents the results of research on the vibrating motion of a laboratory screen with a rectilinear (segmental) trajectory of vibrations during its start-up and braking. The investigations were carried out on a modernized stand equipped with a system of two vibrating motors applied in newer solutions of industrial screens, which are mounted directly on the riddle. The tests were carried out for three different frequencies using three-axis acceleration sensors. The analysed parameter was the increase in the amplitude of vibrations in transient states compared to the amplitude during the stable operation of the device. The maximum multiplication of the vibration amplitude of the classic drive system during start-up was 9.7 (mm/mm) in the vertical direction and 5.7 (mm/mm) for the new system. During braking, the maximum multiplication of the vibration amplitude of the classic drive system was 6.9 (mm/mm) vertically, while for the drive system with vibration motors, it was 11.4 (mm/mm). The absence of flexible couplings in the drive system reduces the damping of vibrations and increases the value of amplitude during the start-up and free braking of the machine. This does not have a major influence on the correct operation of the machine in a steady state. However, the use of the new drive system resulted in a significant reduction in power demand and shortened the start-up time, which has a positive effect on the operating costs of the machine.

Single-degree-of-freedom (SDOF) mechanical oscillators have been the most common type of generators used to harvest energy from mechanical vibrations. When the excitation is harmonic, optimal performance is achieved when the device is tuned so that its natural frequency coincides with the excitation frequency. In such a situation, the harvested energy is inversely proportional to the damping in the system, which is sought to be very low. However, very low damping means that there is a relatively long transient in the harvester response, both at the beginning and at the end of the excitation, which can have a considerable effect on the harvesting performance. This paper presents an investigation into the mechanical design of a linear resonant harvester to scavenge energy from time-limited harmonic excitations to determine an upper bound on the energy that can be harvested. It is shown that when the product of the number of excitation cycles and the harvester damping ratio is greater (less) than about 0.19, then more (less) energy can be harvested from the forced phase of vibration than from the free phase of vibration at the end of the period of excitation. The analytical expressions developed are validated numerically on a simple example and on a more practical example involving the harvesting of energy from trackside vibrations due to the passage of a train.

With the advent of wireless sensors, there has been an increasing amount of research in the area of energy harvesting, particularly from vibration, to power these devices. An interesting application is the possibility of harvesting energy from the track-side vibration due to a passing train, as this energy could be used to power remote sensors mounted on the track for strutural health monitoring, for example. This paper describes a fundamental study to determine how much energy could be harvested from a passing train. Using a time history of vertical vibration measured on a sleeper, the optimum mechanical parameters of a linear energy harvesting device are determined. Numerical and analytical investigations are both carried out. It is found that the optimum amount of energy harvested per unit mass is proportional to the product of the square of the input acceleration amplitude and the square of the input duration. For the specific case studied, it was found that the maximum energy that could be harvested per unit mass of the oscillator is about 0.25 J/kg at a frequency of about 17 Hz. The damping ratio for the optimum harvester was found to be about 0.0045, and the corresponding amplitude of the relative displacement of the mass is approximately 5 mm.