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Resonance frequencies of a mechanical system are the most important parameters that determine the dynamic characteristics of the system. When the frequencies of the harmonic forces under the influence of the system coincide with the resonance (natural) frequencies of the system, a resonance situation occurs and the mechanical system vibrates with high amplitudes. This can cause serious damage to the system by causing effects such as break, fatigue, impact, noise on the bearings, connections and elements in the system. It is possible to eliminate some resonance frequencies of mechanical systems in an examined frequency range using pole-zero cancellation methods by shifting a resonance frequency of the system to an anti-resonance frequency or an anti-resonance frequency to a resonance frequency. Thus, a solution can be obtained for some vibration problems. In this study, a new method using the Sherman-Morrison formula is presented to eliminate some of the resonance frequencies for some FRFs (Frequency Response Functions) of mechanical systems with pole-zero cancellation. In order to eliminate a selected resonance frequency of the system in any FRF determined using the presented method, a mass (kg) and a grounded spring (N/m) modification are made and the required modification values for this are calculated by solving the obtained non-linear equation set numerically. With the proposed method, it is aimed to contribute to the literature by presenting an alternative approach for the solution of vibration problems by cancelling some selected resonance frequencies. The main highlight of the method is there is no need of a matrix inversion for calculating the required modification values. This provides a very fast solution. In addition, the proposed method uses directly the FRFs of the active coordinates (response, excitation and modification) only, which makes the method very useful for practical engineering applications. [ABSTRACT FROM AUTHOR]

Multi-segment shell typical of underwater vehicles is currently important underwater equipment. Stealth performance is a key indicator to improve the working capacity of underwater vehicles. Low-noise design is an important means to improve stealthy performance. Accurate and effective identification of its structure Frequency Response Function (FRF) is the premise of low-noise design. However, the multi-section shell joint interface has many connection points, complex transmission path and typical nonlinear characteristics, which challenges the acquisition of its structural FRF. The Receptance Coupling Substructure Analysis (RCSA) is used to segment the multi-stage shell, which can realize the integration of finite element method and experimental method, and provide an effective way to obtain the FRF of multi-segment shell. At the same time, the multi-segment shell is a typical thin-wall structure, and its actual buckling process under impact is a nonlinear (large deformation) process. Therefore, the nonlinear joint interface is constructed based on linear connection, and the RCSA for nonlinear joint interface is studied. On the basis of accurately obtaining the FRF, it is of theoretical and application significance to study the low noise design of shell. [ABSTRACT FROM AUTHOR]

In many mechanical systems, it is very common to bring together different structural elements or subsystems produced by different producers and create a whole coupled system. It is often not possible to manufacture an entire mechanical system in one place. Although the dynamic properties of each of the subsystems produced by different manufacturers are known, it is a matter that should be known and studied how the dynamic behavior of the new system will be after the creation of a new system by combining these subsystems. In this study, a method for structural coupling of mechanical systems is presented in order to contribute to the solution of structural dynamic problems. It is based on Sherman–Morrison formula known for solving mathematical inverse problems of modified matrices. The method is very useful and practical for real mechanical engineering applications due to only the frequency response functions belong to the coupling coordinates of the subsystems are used. The main highlight of the presented method is there is no need a matrix inversion for calculations. [ABSTRACT FROM AUTHOR]

Dynamic load of compressors is of great concern to designers of refrigeration products since pipes and sheet metals are easy to be excited, leading to noise or fatigue failure. The excitation is impossible to measure directly and difficult to calculate according to generation mechanism; thus, dynamic load identification which skips the mechanism is a more practicable way. However, the reported approaches have the problems of inaccuracy and clumsy. Therefore, an easy-to-implement approach is proposed, in which the accelerations and the frequency response functions from test are transformed to an arbitrarily given point based on rigid body dynamics, and then the equivalent six-degrees of freedom dynamic load of this point is calculated. This approach is validated using a motor with eccentric mass, whose centrifugal force is identified with the proposed approach and also calculated in analytical way. Comparison indicates that the error is within 5% except for the rotational speeds close to natural frequencies. Curve fitting or interpolation is recommended to correct the data in order to reduce the influence of natural frequencies. Cases studies with a rotary compressor and a scroll compressor respectively are presented. For the rotary compressor, the force magnitudes in X and Y directions are almost the same and pretty close to their quadratic polynomial fitting curves with zero intercept respectively, conforming to the characteristics of centrifugal force; the RZ component is larger than the RX and RY components as expected, but the latter two are not negligible; and there is a step change at 45 rps due to the removal of torque compensation. For the scroll compressor, the force magnitudes in X and Y directions are different, but very close to their quadratic polynomial fitting curves, respectively; the Z component has a jump in high-speed range; and there is no significant difference of dynamic force in the cooling and the heating modes. [ABSTRACT FROM AUTHOR]

Plates with periodic cavities show excellent vibration attenuation characteristics. This behavior can be attributed to the presence of frequency bandgaps on account of interference between the incident wave and the reflected wave from the cavities. The present work investigates the vibration attenuation/bandgap characteristics of plates with varying shapes of periodic cavities, such as square, circular, vertical rectangle, and horizontal rectangle, through experiments and simulation. Vibration responses of different periodic plates have been studied by carrying out frequency sweep on a vibration shaker. The investigation has been restricted to flexural vibrations of the plates, which are the predominant mode of vibration in many practical vibration scenarios. The frequency bandgaps, observed through the experiment, have been compared with the numerical simulation by harmonic analysis and by carrying out dispersion analysis on a unit cell of the periodic structure using Floquet–Bloch theory. Dispersion curves of the periodic plates yielded bandgaps, which were observed to be in agreement with the bandgaps from the experiment. The effect of variation in the aspect ratio of the cavities, that is length-to-width ratio, on the bandgaps has also been examined. It has been demonstrated that by suitable selection of the shape/size of the periodic cavity, desired vibration attenuation bandgaps can be realized for a 2-dimensional structure. [ABSTRACT FROM AUTHOR]

Recently, the demand for higher performing underwater structures under diverse conditions has increased. Examples include improved precision and speed of the position control of robot manipulators. To prevent the control spillover problems when active controls are used, a control system is typically constituted with a low-pass filter to eliminate all modes except for the target modes. However, experimentally measuring the dynamic properties of an underwater structure in an environment where the structure and a fluid continuously influence each other is difficult. We have recently proposed a noncontact vibration testing method for dynamic characterizations of underwater structures in which the response to a laser ablation excitation force is measured by laser Doppler vibrometer. Integrating passive control using a vibration-damping material affixed onto the underwater structure and active control constituted with the low-pass filter may realize a more cost-effective system. To develop this combined control into a practical method, the reliability of the measured frequency response function must be validated. Additionally, the applicable frequency range must be expanded to encompass the high-frequency region (several tens of kHz) so that the vibration suppression quality of underwater structures can be evaluated. Herein we quantify the effect of random measurement errors on the measured frequency response function with a reliability factor based on the concept of coherence functions. Using the measured frequency response function with a reliability factor, we demonstrated that our method can evaluate passive vibration suppression effect of an underwater structure with a damping material in high-frequency ranges up to 20 kHz. [ABSTRACT FROM AUTHOR]

In this paper, a finite element model updating method using frequency response functions is experimentally validated. The method is a sensitivity-based model updating approach which utilizes a pseudo-linear sensitivity equation. The method is robust against the adverse effects of incomplete measurement, measurement errors and modeling errors. The experimental setup consists of a free-free aluminum beam, where changes are introduced by reducing the stiffness and attaching lumped mass at certain parts of the beam. The method is applied to identify the location and amount of the changes in structural parameters. The results indicate that the location and the size of different level of changes in the structure can be properly identified by the method. In addition, a study is done on the influence of the number of impacts and sensors on the quality of the identified parameters. [ABSTRACT FROM AUTHOR]

A pulsed-laser ablation method for non-contact experimental vibration analysis of completely submerged underwater structures is proposed. Although impact testing with an impulse hammer is commonly used for vibration analysis due to its simplicity, impact testing has limited use in underwater conditions. An input-detection-free frequency response function measurement in water will greatly contribute to the development of high-precision and high-speed positioning autonomous underwater vehicles, underwater vehicle-manipulators, underwater robots, submarines, etc., which are used in dangerous conditions (e.g., deep oceans, under ice, and nuclear reactor plants). To achieve these high-performance underwater systems, vibrations due to hydrodynamic parameters (such as added mass, buoyant force, drag force, and damping coefficient) should be suppressed, and vibration tests should be conducted on the actual equipment submerged in water. The proposed method yields the frequency response function by applying a pulsed-laser-ablation excitation force to an underwater structure and measuring the output using a laser Doppler vibrometer. Because the direction, strength, and effective duration of the pulsed-laser-ablation force are essentially constant, this force can be estimated by measuring these properties in advance. Hence, the proposed method realizes input-detection-free frequency response function measurements in underwater conditions. [ABSTRACT FROM AUTHOR]

Based on a step-by-step decoupling method, an inverse substructuring method is developed for the analysis of the dynamic characteristics of a single-coordinate coupled three-substructure system. The closed-form analytical solution to inverse substructuring analysis of the system is derived. The proposed method is validated by a lumped mass-spring-damper model, the predicted frequency response functions (FRFs) of substructures and the coupling stiffness; in addition, the most relevant system-level FRFs are compared with the direct computations, showing exact agreement. Finally, the sensitivity of the proposed method to measurement error is studied. The method developed offers an approach to extract the unknown substructure-level FRFs and coupling stiffness from system-level FRFs purely for single-coordinate coupled substructures. [ABSTRACT FROM PUBLISHER]

Nonlinearities in mechanical systems demand extensive efforts both in modeling their dynamics and identification of their parameters. In this paper an identification approach is proposed for nonlinear multi-degree-of-freedom systems when there is a single nonlinear element in the system and its location is known. The proposed method is an extension of the frequency response function (FRF) sensitivity method used in the linear systems. The method uses measured nonlinear FRFs and employs a reduced order model for sensitivity calculations. Numerical and experimental case studies are used to verify the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

An inverse substructure method is developed for the analysis of the dynamical characteristics of a three-substructures coupled system based on the inverse substructure method of a two-substructures coupled system. The unknown substructure-level frequency response functions (FRFs) and coupling stiffness can be predicted, and the system-level response of key components can be obtained by using the method when the system-level FRFs needed are all measured. To verify the validity of the inverse substructure method of a three-substructures coupled system, a lumped mass-spring-damper model with three substructures coupled is taken as an example for numerical validation. The prediction is exactly the same as the ‘‘Given’’. To further check out the accuracy of the method, the experiment of a physical prototype is carried out, and the predicted substructure-level FRFs are in good agreement with those that are measured. The method is applied to the analysis of a product-transport-system, which is treated as a coupled system composed of a key component, a product and a vehicle. The effect of the coupling stiffness on the dynamic response of key components is investigated. The result indicates that reducing the coupling stiffness of the product-vehicle interface can largely lower the response of key components. [ABSTRACT FROM PUBLISHER]

The dynamic properties of an existing structure are altered when the mass and stiffness properties of the structure are modified. In some cases it can be desired that a specific natural frequency of the structure should not change after modifications. In case of adding a number of masses on the structure, one of the pre-specified natural frequencies can be preserved by attaching a grounded spring on it. In the present study, a new method is developed based on the Sherman-Morrison formula in order to determine the necessary spring coefficient. The performance of the developed method for damped structures is also investigated. Furthermore, an approach based on minimization of the described objective function is introduced for prediction of the best spring location. [ABSTRACT FROM PUBLISHER]

It has been observed that finite element or finite difference models of order n can approximate with fair accuracy less than one-third of the eigenvalues of the underlying continuous system corresponding to the low spectrum. We present a new spectral conforming discrete model that estimates n the lowest eigenvalues of the continuous system with uniform accuracy. The building block of the model is the fundamental inverse eigenvalue problem of reconstructing the chain of a mass-spring system with a prescribed spectrum. We present applications of the model in vibration control of continuous systems by using small-order spectral conforming models, and spectrum estimation of non-uniform systems. [ABSTRACT FROM AUTHOR]