Optimisation of Periodic Structure Subject to Parametric Alteration

2007 ◽  
Author(s):  
Yu-Ming Chen ◽  
Teng-Yuan Wu ◽  
Lai-Sheng Chen
Keyword(s):  
Computational Model ◽  
Objective Function ◽  
Periodic Structure ◽  
Ritz Method ◽  
Dynamic Responses ◽  
Cantilever Beams ◽  
Antenna Structure ◽  
Stiffness Properties ◽  
Structure Vibration ◽  
Lumped Masses

The dynamic responses of repetitive system are relatively sensitive to modification where slight changes in the geometric parameters can destroy the structure symmetry. This paper treats antenna structure as a study example and investigates its vibration behaviors subject to parametric changes. An analytically derived computational model based on the Rayleigh-Ritz method for modeling the periodic structure is produced. This is particularly useful in treating continuous structure with non-uniform mass and/or stiffness properties. The antenna structure is represented by a number of cantilever beams elevated at an angle and built-in into a hub and coupled by springs. This work performs two optimizations separately: (a) by optimizing the location of equally weighted lumped masses along each cantilever beams and, (b) optimizing the location of springs. Effects of altering these parameters with the objective function of minimizing the structure vibration is addressed in this work.

Study on the Measure of Reducing Noise and Vibration of Over-Track Buildings Induced by Crane Load

2013 ◽  
Vol 788 ◽  
pp. 493-497
Author(s):  
Hua Jie Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Responses ◽  
Concrete Column ◽  
Noise And Vibration ◽  
The People ◽  
Steel Column ◽  
Practical Engineering ◽  
Structure Vibration

Big vibration will be cause by train load and crane load in the over-track buildings, and then generate structure-borne moise in the buildings, which will affect the live quality of the people lived in the buildings greatly. Focusing on this proble, three finite element method is established based on a practical engineering. The measures of reducing noise and vibration is proposed according the characteristics of the building, which is to replace the steel column as concrete column. The dynamic responses of the building under the two cases are calculated and analyzed. The computation results show that the measurement can reduced structure vibration significantly, and accordingly, the structure-borne noise is also reduced greatly. The research results in the paper have strong engineering practicability and can provide some references for some other projections in China in future.

scholarly journals Optimized lattice-based metamaterials for elastostatic cloaking

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210418
Author(s):  
E. D. Sanders ◽  
M. A. Aguiló ◽  
G. H. Paulino
Keyword(s):  
Objective Function ◽  
Uniaxial Tension ◽  
Weighted Least Squares ◽  
Elliptical Hole ◽  
Adjoint System ◽  
System Optimization ◽  
Small Region ◽  
Shear Loading ◽  
Stiffness Properties ◽  
Stiffness Characteristics

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Free and Forced Vibration of Beams Reinforced by 3D Graphene Foam

2020 ◽  
Vol 12 (05) ◽  
pp. 2050056 ◽  
Author(s):  
Feng Liu Yang ◽  
Yan Qing Wang
Keyword(s):  
Forced Vibration ◽  
Lagrange Equation ◽  
Mass Density ◽  
Slenderness Ratio ◽  
Ritz Method ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Graphene Foam ◽  
3D Graphene ◽  
Reinforced Beams

In this paper, free and forced vibrations of nanocomposite beams reinforced by 3D graphene foam (3D-GrF) are studied. Different distributions of 3D-GrF in the beam thickness direction are considered. In accordance with the rule of mixture, the effective Young’s modulus, Poisson’s ratio and mass density of the 3D-GrF reinforced beams are predicted. Based on the Timoshenko beam theory, the governing equation of the 3D-GrF reinforced beam is derived by using the Lagrange equation. The natural frequencies and dynamic responses of the 3D-GrF reinforced beam are solved by the Ritz method and the Newmark-[Formula: see text] method, respectively. Results show that the foam coefficient, the 3D-GrF distribution, the slenderness ratio and the 3D-GrF mass fraction play important roles on free and forced vibration characteristics of the 3D-GrF reinforced beams.

Resonance Analysis of Cantilever Plates Subjected to Moving Forces by a Semi-Analytical Method

2020 ◽  
Vol 20 (04) ◽  
pp. 2050049
Author(s):  
Qi Li ◽  
Xing Li ◽  
Qi Wu
Keyword(s):  
Analytical Method ◽  
Ritz Method ◽  
High Order Mode ◽  
Dominant Frequency ◽  
High Order ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Superposition Method ◽  
Cantilever Plate ◽  
Exciting Frequency

Cantilever plate structures are widely used in civil and aerospace engineering. Here, a semi-analytical method is proposed to calculate the dynamic responses of cantilever plates subjected to moving forces. The Rayleigh–Ritz method is used to obtain the semi-analytical modal frequencies and shapes of a thin, isotropic, and rectangular cantilever plate using the assumed mode shapes that fulfill the boundary conditions of the plate. The modal superposition method is used to decouple the motion equations of the cantilever plate to obtain a series of modal equations. Then, the generalized forces are transformed into a Fourier series in terms of discrete harmonic forces. The dynamic responses of the cantilever plate are obtained by superimposing the analytical responses of a number of single-degree-of-freedom modal systems under discrete harmonic forces. The proposed semi-analytical method is verified through comparison with the numerical method. Then, the vibration of the cantilever plate under the action of moving forces is investigated based on the semi-analytical results. It is found that the contribution of the high-order modes to the dynamic responses of the plate cannot be ignored. In addition, the wavelengths of the mode shapes not only affect the magnitude of the modal forces but also the dominant frequency of the modal forces. Resonant responses of the plate are produced by the moving forces when the load interval equals the wavelength of the mode shape of a high-order mode and the exciting frequency of the moving forces equals the natural frequency of this mode.

The Use of the Fixed Points Method for Optimal Damping of Harmonically Forced Cantilever Beams

2011 ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Point Force ◽  
Cantilever Beams ◽  
Two Dimensional ◽  
Optimal Damping ◽  
Active Peak

The use of viscous dampers for vibration attenuation in harmonically forced cantilever beams is studied. The system considered is a cantilever beam with a point harmonic force applied at a given location and a viscous damper attached to it from one end, and grounded from the other. An assumed mode model of the system is derived using the first two transverse modes of the beam. For any given positions of the point force and damper, the optimal damping constant which minimizes the maximum of the frequency response function at the tip of the beam is determined analytically. It is shown that the objective function passes through a number of points independent of the damping constant. These inevitable points are used in the determination of the maximum allowable value of the objective function. As the locations of the point force and damper are varied separately from the fixed end of the beam to its tip, a two dimensional region plot is generated illustrating the different regions where each of these points is the highest. The optimal damping constant is determined analytically by forcing the frequency response function to pass horizontally through the highest fixed point which is referred to as the active peak. Four different damping ratios are determined and depending on the positions of the force and damper, the two dimensional map is consulted in the selection of the correct optimal damping ratio. The solution obtained is unique except when the active peak is the static fixed point. In this case, the solution is made unique by modifying the objective function to further enhance the solution at high frequencies.

Dynamics of the Elastica With End Mass and Follower Loading

1990 ◽  
Vol 57 (1) ◽  
pp. 203-208 ◽  
Author(s):  
J. M. Snyder ◽  
J. F. Wilson
Keyword(s):  
Internal Pressure ◽  
Large Deformations ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Cantilever Beams ◽  
Static Responses ◽  
Tube Type ◽  
Payload Mass ◽  
Nonlinear Equations Of Motion ◽  
Special Case

Orthotropic, polymeric tubes subjected to internal pressure may undergo large deformations while maintaining linear moment-curvature behavior. Such tubes are modeled herein as inertialess, elastic cantilever beams (the elastica) with a payload mass at the tip and with internal pressure as the eccentric tip follower loading that drives the configurations through large deformations. From the nonlinear equations of motion, dynamic beam trajectories are calculated over a range of system parameters for the special case of a point mass at the tip and a terminated ramp pressure loading. The dynamic responses, which are unique because the loading history and the range of motion are fully defined, are presented in nondimensional form and are compared to static responses presented in a companion study. These results are applicable to the dynamic design of high flexure, tube-type, robotic manipulator arms.

The Normal Modes of Vibrations of Beams Having Noncollinear Elastic and Mass Axes

1940 ◽  
Vol 7 (3) ◽  
pp. A97-A105
Author(s):  
Clyne F. Garland
Keyword(s):  
Physical Properties ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Normal Modes ◽  
Longitudinal Axis ◽  
Cantilever Beams ◽  
Amplitude Ratios ◽  
Numerical Example ◽  
Modes Of Vibration ◽  
Axis Passing

Abstract This analysis deals with vibration characteristics of cantilever beams in which the longitudinal axis, passing through the mass centers of the elementary sections, is not collinear with the longitudinal axis about which the beam tends to twist under the influence of an applied torsional couple. Expressions are derived from which the natural frequencies and normal modes of vibration of such a beam can be determined. The Rayleigh-Ritz method is employed to determine the frequencies and amplitude ratios. Following the development of the general expressions, more specific equations are derived which express the natural frequencies and relative amplitudes of motion in each of two normal modes of vibration. The theoretical relationships of the several physical properties of the beam to the natural frequencies of vibration are shown graphically. Finally a numerical example is presented for a particular beam, and the computed natural frequencies and normal modes are compared with those determined experimentally.

Suppression Vibration Adaptive Inverse Dynamics Control of Flexible Plate with Piezoelectric Layers

2011 ◽  
Vol 403-408 ◽  
pp. 618-624
Author(s):  
Mohammad Azadi ◽  
Mehdi Roopaei ◽  
Mohammad Eghtesad ◽  
S. Ahmad Fazelzadeh
Keyword(s):  
Adaptive Control ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Flexible Plate ◽  
Sensors And Actuators ◽  
Piezoelectric Layers ◽  
Flexible Panel ◽  
Lumped Masses ◽  
Adaptive Control Algorithm

Micro-Vibrations, generally defined as low amplitude vibrations at frequencies up to 1 kHz, are now of critical importance in a number of areas. One such area is onboard spacecraft carrying sensitive payloads where the micro-vibrations are caused by the operation of other equipment. In this paper a rectangular simply supported flexible panel is considered. The equipments are located on this panel as lumped masses and the micro-vibrations are induced by some concentrated forces. The piezoelectric layers are attached on both sides of the panel as sensors and actuators. The governing equations of motion are derived based on Lagrange-Rayleigh-Ritz method. An adaptive control scheme is applied to reduce the panel vibrations. Finally the simulation results show the advantages of the adaptive control algorithm.

Adjustment of a Rotor Model to Achieve Agreement between Calculated and Experimental Natural Frequencies

1979 ◽  
Vol 21 (6) ◽  
pp. 389-396 ◽  
Author(s):  
G. T. S. Done
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Turbine Rotor ◽  
Beam Elements ◽  
Stiffness Properties ◽  
Standard Values ◽  
Lumped Masses ◽  
The Mathematical Model ◽  
Best Fit ◽  
Rotor Model

This paper is concerned with the problem of adjusting the mathematical model of a system such that the computed natural frequencies coincide with those measured experimentally. The particular system considered is a laboratory turbine-rotor model, modelled mathematically by 42 Timoshenko beam elements and lumped masses. Model adjustments are made by assuming, firstly, Young's modulus and the modulus of rigidity to be variable, a change from standard values representing overall stiffness deficiencies in the mathematical model. In this case, a best fit to the lowest six natural frequencies, as measured experimentally, is made. Secondly, stiffness diameters are assumed variable, thereby allowing for deficiencies in the model near discontinuous changes of section, and in this case, the lowest six natural frequencies are matched exactly, but an overall measure of the differences between the actual and the stiffness diameters is minimized. An analysis for the rates of change of natural frequency with the various stiffness properties (i.e. the sensitivities) is presented, and the results of the manipulation discussed.

scholarly journals A two-step method for damage identification in beam structures based on influence line difference and acceleration data

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878740 ◽  
Author(s):  
D Tan ◽  
ZR Lu ◽  
JK Liu
Keyword(s):  
Objective Function ◽  
Structural Damage ◽  
Damage Identification ◽  
Dynamic Responses ◽  
Beam Structure ◽  
Modal Assurance Criterion ◽  
Beam Structures ◽  
Influence Line ◽  
Acceleration Data ◽  
Bird Mating Optimizer

This article presents a two-step approach for structural damage identification in beam structure. Damages are located using the influence line difference before and after damage, the calculation of damage severity is accomplished by acceleration data and bird mating optimizer algorithm. Local damages are simulated as the reduction of both the elemental Young’s modulus and mass of the beam. The technique for damage localization based on displacement influence line difference and its derivatives for beam structure has been outlined. An objective function that comprises dynamic acceleration is utilized in bird mating optimizer. All data are originated from only a few measurement points. Two numerical examples, namely, a simply supported beam and a four-span continuous beam, are investigated in this article. Identification results from different objective functions are compared with results from objective function conventional modal assurance criterion, which shows the superiority of the proposed function. In addition, results of dynamic responses under different types of excitation are presented. The effect of measurement noise level on damage identification results is studied. Studies in the article indicate that the proposed method is efficient and robust for identifying damages in beam structures.

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