Calculation of Receptance of a Structure Modified by Mass and Grounded Spring

Abstract

The dynamic properties of an existing structure are altered, when a mass and/or a spring are added to or removed from the structure. Therefore it is important to know dynamic properties of the structure after modification. One way to determine dynamic properties of the structure is the experimental modal analysis which uses measured Frequency Response Functions (FRFs). In the present study, a general and exact method is presented based on the Sherman-Morrison formula in order to calculate FRF of the structure modified by concentrated mass and grounded spring. The method is very effective and uses only a few FRFs related to modification coordinates of the unmodified structure.

Control of the Vibrations of a Cartesian Automatic Machine

“…When experimental results relative to only a response, an excitation and a modification coordinate are available the modified transfer function (a pqm (ω)) between the response and the excitation coordinate can be calculated according to this equation [4]:…”

“…increasing stiffness or adding lumped masses or tuned vibration absorbers (TVA). In recent years some effective methods for predicting the effects of structural modifications starting from the measured frequency response functions (FRFs) have been developed [14,12,4,10]. These methods are based on the modal analysis approach and typically require a large set of experimentally measured FRFs.…”

Analysis and Control of Vibrations of a Cartesian Cutting Machine Using an Equivalent Robotic Model

“…When the excitation frequency is constant, such as in the present case, a typical structural modification is the introduction of a Tuned Vibration Absorber (TVA). This analysis can be performed using the Sherman-Morrison method [24,25], already shown in References [18,26], which makes it the calculation of the FRF of the modified system possible, starting from few FRFs of the original system and the dynamic stiffness of the lumped element z l (ω) (the TVA). Therefore, starting from the FRFs of the proposed model, it is possible to simulate the effect of the TVA by means of simple calculations.…”

Analysis and Control of Vibrations of a Cartesian Cutting Machine Using an Equivalent Robotic Model

“…Once the model has been validated, it is interesting to evaluate the effect of vibration control strategies, e.g., the installation of a Tuned Vibration Absorber (TVA). This analysis can be performed using the Sherman-Morrison method [11,12], already shown in [13,14], which makes it possible the calculation of the FRF of the modified system, starting from few FRFs of the original system and the dynamic stiffness of the lumped element z l (ω) (the TVA).…”