Antiresonance Assignment in Point and Cross Receptances for Undamped Vibrating Systems

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Roberto Belotti ◽  
Dario Richiedei ◽  
Iacopo Tamellin
Keyword(s):  
Degrees Of Freedom ◽  
Structural Modification ◽  
Original System ◽  
Test Cases ◽  
Optimization Approach ◽  
Modification Method ◽  
Solving Strategy ◽  
Assignment Approach ◽  
Vibrating Systems ◽  
Homotopy Optimization

Abstract This paper proposes an inverse structural modification method for the assignment of antiresonances in undamped vibrating systems by modifying the inertial and elastic properties of the existing degrees of freedom of the original system. Hence, no additional degrees of freedom are added to the system. The problem is formulated as an eigenstructure assignment approach since such a novel formulation is suitable for complex systems, such as those modeled through finite elements. Indeed, these systems are difficult to handle with the methods already proposed in the literature. Additionally, the proposed approach is suitable for both point and cross receptances. Assignment is cast as a constrained non-convex non-linear minimization problem and the proposed solving strategy is based on the homotopy optimization approach. The method effectiveness is shown through three meaningful test cases.

Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Roberto Belotti ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Optimal Solution ◽  
Mode Shapes ◽  
Eigenstructure Assignment ◽  
Optimization Strategy ◽  
Modification Method ◽  
Global Optimal ◽  
The Cost ◽  
Bilinear Terms ◽  
Vibrating Systems ◽  
Homotopy Optimization

This paper proposes an inverse structural modification method for eigenstructure assignment (EA), which allows to assign the desired mode shapes only at the parts of interest of the system. The presence of unimposed eigenvector entries leads to a nonconvex problem. Therefore, to boost the convergence to a global optimal solution, a homotopy optimization strategy is implemented based on the convex approximation of the cost function. Such a relaxation is performed through some auxiliary variables and through the McCormick's relaxation of the occurring bilinear terms. The approach handles general assignment tasks, with an arbitrary number of modification parameters and prescribed eigenpairs.

scholarly journals Robust Assignment of Natural Frequencies and Antiresonances in Vibrating Systems through Dynamic Structural Modification

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Roberto Caracciolo ◽  
Dario Richiedei ◽  
Iacopo Tamellin
Keyword(s):  
Structural Modification ◽  
Natural Frequencies ◽  
Adjoint System ◽  
Global Optimum ◽  
Inverse Eigenvalue Problem ◽  
Partial Assignment ◽  
Inverse Eigenvalue ◽  
Novel Method ◽  
Vibrating Systems ◽  
Homotopy Optimization

This paper proposes a novel method for the robust partial assignment of natural frequencies and antiresonances, together with the partial assignment of the related eigenvectors, in lightly damped linear vibrating systems. Dynamic structural modification is exploited to assign the eigenvalues, either of the system or of the adjoint system, together with their sensitivity with respect to some parameters of interest. To handle with constraints on the feasible modifications, the inverse eigenvalue problem is cast as a minimization problem and a solution method is proposed through homotopy optimization. Variables lifting for bilinear and trilinear terms, together with bilinear and double-McCormick’s constraints, are exploited to provide a convexification of the problem and to boost the attainment of the global optimum. The effectiveness of the proposed method is assessed through four numerical examples.

Structural Modification Simulation: Sensitivity Analysis and the Reanalysis of Modified Structure

1991 ◽  
Author(s):  
Debao Li ◽  
Fangze Li ◽  
Peiming Xu
Keyword(s):  
Sensitivity Analysis ◽  
Transfer Function ◽  
Coordinate Transformation ◽  
Degrees Of Freedom ◽  
Structural Modification ◽  
Function Analysis ◽  
Dump Truck ◽  
Analysis Method ◽  
Transfer Function Analysis ◽  
Dynamic Modification

Abstract This paper deals with the dynamic modification simulation of the structure. The expressions of sensitivity analysis of the system with non-proportional damping and proportional damping are derived at first. As for the reanalysis of modified structure, here we deal with the system to which the modification do not cause any change of the degrees of freedom. Transfer function analysis method and the method of twice coordinate transformation are expounded. As a successful example, the modification simulation of the frame of a dump truck is explained.

Posture Prediction Versus Inverse Kinematics

2001 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Wei Yu ◽  
Zan Mi ◽  
E. Tanbour ◽  
M. Jaber
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Human Performance ◽  
Inverse Kinematic ◽  
Cost Functions ◽  
Optimization Approach ◽  
Final Position ◽  
Serial Robot ◽  
Posture Prediction

Abstract Inverse kinematics is concerned with the determination of joint variables of a manipulator given its final position or final position and orientation. Posture prediction also refers to the same problem but is typically associated with models of the human limbs, in particular for postures assumed by the torso and upper extremities. There has been numerous works pertaining to the determination and enumeration of inverse kinematic solutions for serial robot manipulators. Part of these works have also been directly extended to the determination of postures for humans, but have rarely addressed the choice of solutions undertaken by humans, but have focused on purely kinematic solutions. In this paper, we present a theoretical framework that is based on cost functions as human performance measures, subsequently predicting postures based on optimizing one or more of such cost functions. This paper seeks to answer two questions: (1) Is a given point reachable (2) If the point is reachable, we shall predict a realistic posture. We believe that the human brain assumes different postures driven by the task to be executed and not only on geometry. Furthermore, because of our optimization approach to the inverse kinematics problem, models with large number of degrees of freedom are addressed. The method is illustrated using several examples.

scholarly journals Structural Reanalysis Based on FRFs Using Sherman–Morrison–Woodbury Formula

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jun Ren ◽  
Qianghao Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Salient Feature ◽  
Original System ◽  
Modal Testing ◽  
Structural Dynamic ◽  
Structural Dynamic Modification ◽  
Modal Model ◽  
Dynamic Modification ◽  
One Step ◽  
Stiffness And Damping

Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.

A Modal Approach for Chaotic Vibrations of a Drillstring

2009 ◽  
Author(s):  
Kathira Mongkolcheep ◽  
Alan Palazzolo ◽  
Annie Ruimi ◽  
Randall Tucker
Keyword(s):  
Lyapunov Exponents ◽  
Oil Recovery ◽  
Degrees Of Freedom ◽  
Nonlinear Effects ◽  
Contact Friction ◽  
Element Approach ◽  
Rigid Body Modes ◽  
Quadratic Damping ◽  
Vibrating Systems ◽  
Drill Collar

The purpose of this paper is to present a methodology to predict vibrations of drilllstrings for oil recovery service. The paper extends a previous model in the literature to include drill collar flexibility utilizing a modal coordinate condensed, finite element approach. The nonlinear effects of drillstring / borehole contact, friction and quadratic damping are included. Bifurcation diagrams are presented to illustrate the effects of speed, friction, stabilizer gap and drill collar length on chaotic vibration response. A study is conducted on factors for improving the accuracy of Lyapunov Exponents to predict the presence of chaos. This study considers the length of time to steady state, the number and duration of linearization sub-intervals, the presence of rigid body modes and the number of finite elements and modal coordinates. The results may be helpful for computing Lyapunov exponents of other types of nonlinear vibrating systems with many degrees of freedom.

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