The modes, resonances and forced response of elastic structures under heavy fluid loading

1984 ◽  
Vol 312 (1521) ◽  
pp. 295-341 ◽  
Keyword(s):  
Order Approximation ◽  
Low Frequency ◽  
Forced Response ◽  
Mode Shapes ◽  
Thin Elastic Plate ◽  
Fluid Loading ◽  
Heavy Fluid ◽  
Elastic Structures ◽  
Strip Plate ◽  
First Time

This paper reports analytical studies of problems that involve the motion of plane elastic structures under conditions of heavy fluid loading. The main aspect concerns the description of the vibration response of a thin elastic plate (or membrane), of finite extent in at least one dimension, when the structure is excited by concentrated mechanical drive along a line or at a point; and as part of this the possibility of resonant response is discussed, and the resonance conditions and free modes of oscillation are obtained. There is also some discussion of the acoustic fields radiated by the structures under localized mechanical excitation. The analysis makes extensive use of results for the reflection of a structural wave (subject to heavy fluid loading) at an edge, and the paper gives results for that reflection process covering waves incident normally on eight different edge configurations and waves incident obliquely on two edge configurations. These results include the reflection coefficient (whose magnitude is unity in the leading-order approximation of low-frequency heavy fluid loading), and the amplitude and directivity of the edge-scattered sound. By using the argument that edge reflection is a local process, the response is then calculated for a strip plate, under both line and point forcing, and the response is, for the first time, obtained for structures finite in both dimensions and subject to heavy fluid loading. Specifically, solutions are given here for a circular plate with eccentric drive, and for a membrane model of a rectangular panel, with central point drive. For some conditions and geometries expressions in simple form are found for the natural frequencies and mode shapes, and for the off-resonance forced response. Expressions for the drive admittances are found which display a variety of interesting features.

Design Methods of Friction Damping at Blade-Disk Joints

2009 ◽  
Author(s):  
Jie Hong ◽  
Lulu Chen ◽  
Yanhong Ma ◽  
Xin Yang
Keyword(s):  
Low Frequency ◽  
Harmonic Balance Method ◽  
Large Error ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Tracking Motion ◽  
Nonlinear Force ◽  
Free Mode

Friction at blade-disk joints is an important source of damping that reduces low frequency resonant amplitudes to acceptable levels in blade-disk assemblies. An effective method is proposed to predict nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints in frequency domain, which syncretizes the excellencies of harmonic balance method, dynamic softness method and tracking motion method. Constrained Mode Shapes are introduced to express the relative motion which occurs at the contact interfaces of blade roots. Compared to using free mode shapes, fewer number of constrained mode shapes is required in order to obtain the accurate resonant response of a system with friction dampers when the contact state is fully stick. It is more efficient to predict the nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints. Based on this method, the effect of Boundary Conditions on the resonant frequencies and forced response levels under different engine rotational speeds is investigated. Large error in the prediction of forced response levels under low engine rotational speed by using traditional methods is found. The effects of preload distribution at blade roots and excitation level are also investigated.

A nonlinear model of the dynamics of a large elastic plate with heavy fluid loading

2006 ◽  
Vol 462 (2072) ◽  
pp. 2205-2224 ◽  
Author(s):  
N Peake ◽  
S.V Sorokin
Keyword(s):  
Elastic Plate ◽  
Plane Waves ◽  
Travelling Wave ◽  
Plane Motion ◽  
Transverse Motion ◽  
Thin Elastic Plate ◽  
Transverse Displacement ◽  
Fluid Loading ◽  
Heavy Fluid ◽  
Wave Solutions

In this paper, we derive weakly nonlinear equations for the dynamics of a thin elastic plate of large extent under conditions of heavy fluid loading. Two situations are then considered. First, we consider the case in which transverse motion of the plate generates a weaker in-plane motion, which is in turn coupled back to the evolution of the transverse motion. This results in the familiar nonlinear Schrödinger equation for the amplitude of a transverse plane wave, and we show that solitary-wave solutions are possible over the range of (non-dimensional) frequencies ω > ω c , which depends on the material properties. Dimensional values of ω c are physically realizable for a typical composite material underwater. Second, we consider the case in which the amplitudes of the transverse and in-plane motion are of the same order of magnitude, possible at a single resonant frequency, which leads to an evolution equation of rather novel type. We find a range of travelling-wave solutions, including cases in which incident in-plane waves can generate localized regions of transverse displacement.

scholarly journals Dynamic Analysis of a Rigid Body Mounting System with Flexible Foundation Subject to Fluid Loading

2001 ◽  
Vol 8 (1) ◽  
pp. 33-47 ◽  
Author(s):  
J.S. Tao ◽  
G.R. Liu ◽  
K.Y. Lam
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Infinite Plate ◽  
Low Frequency ◽  
Fluid Loading ◽  
Force Transmission ◽  
Heavy Fluid ◽  
Low Frequencies ◽  
Force Reduction ◽  
Flexible Foundation

This paper presents an investigation of the force transmission from a rigid body mounting system to a flexible foundation with light and heavy fluid loading under the force and moment excitation. The analytical expression has been derived in which the flexible foundation effects are incorporated into a revised system stiffness matrix that is derived from the receptance matrix at mounting points. A typical case with a thin infinite plate as the foundation has been studied with the point and transfer receptances theoretically and numerically analysed in the case of light and heavy fluid loading. The results show that, compared with the rigid foundation, the force transmission is reduced and system natural frequencies are shifted. The detailed analysis demonstrates that the force reduction and frequency shifting are more obvious at low frequencies where the receptance value is significant. The study is also carried out to compare the transfer receptances from different waves in plate as it couples with water with the objective to simplify the calculation of receptance. It is found that, in the low frequency and after a short distance from driving point, the transfer receptance calculation for the heavy fluid loading can be simplified by only accounting the contribution from free wave which may easily be evaluated from the point receptance in air. It implies the plate response under heavy fluid loading could be directly derived from that with light fluid loading.

scholarly journals (Bi)-orthogonality relation for eigenfunctions of self-adjoint operators

2019 ◽  
Vol 377 (2156) ◽  
pp. 20190112 ◽  
Author(s):  
L. S. Ledet ◽  
S. V. Sorokin
Keyword(s):  
Energy Flow ◽  
Orthogonality Relation ◽  
Thin Elastic Plate ◽  
Fluid Loading ◽  
Heavy Fluid ◽  
Theme Issue ◽  
Structured Media ◽  
Flow Components ◽  
Adjoint Operators ◽  
Dynamic Phenomena

The bi-orthogonality relation for eigenfunctions of self-adjoint operators is derived. Its composition is explained in view of the structure of a characteristic equation and of the energy flow components. Application of the bi-orthogonality relation for solving forcing problems is generalized and the connection between the bi-orthogonality relation and the virtual wave method is highlighted. Technicalities are illustrated in a non-trivial example of propagation of free/forced cylindrical waves in a thin elastic plate under heavy fluid loading. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

scholarly journals Reduction of Unsteady Blade Loading by Beneficial Use of Vortical and Potential Disturbances in an Axial Compressor With Rotor Clocking

1998 ◽  
Vol 120 (4) ◽  
pp. 705-713 ◽  
Author(s):  
S. T. Hsu ◽  
A. M. Wo
Keyword(s):  
Large Scale ◽  
Axial Compressor ◽  
Leading Edge ◽  
Forced Response ◽  
Suction Surface ◽  
Blade Loading ◽  
Beneficial Use ◽  
Unsteady Loading ◽  
Vortical Disturbance ◽  
First Time

This paper demonstrates reduction of stator unsteady loading due to forced response in a large-scale, low-speed, rotor/stator/rotor axial compressor rig by clocking the downstream rotor. Data from the rotor/stator configuration showed that the stator response due to the upstream vortical disturbance reaches a maximum when the wake impinges against the suction surface immediately downstream of the leading edge. Results from the stator/rotor configuration revealed that the stator response due to the downstream potential disturbance reaches a minimum with a slight time delay after the rotor sweeps pass the stator trailing edge. For the rotor/stator/rotor configuration, with Gap1 = 10 percent chord and Gap2 = 30 percent chord, results showed a 60 percent reduction in the stator force amplitude by clocking the downstream rotor so that the time occurrence of the maximum force due to the upstream vortical disturbance coincides with that of the minimum force due to the downstream potential disturbance. This is the first time, the authors believe, that beneficial use of flow unsteadiness is definitively demonstrated to reduce the blade unsteady loading.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Review of piezoelectric impedance based structural health monitoring: Physics-based and data-driven methods

2021 ◽  
pp. 136943322110384
Author(s):  
Xingyu Fan ◽  
Jun Li ◽  
Hong Hao
Keyword(s):  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Structural Damage ◽  
Low Frequency ◽  
Data Driven ◽  
Mode Shapes ◽  
Monitoring Methods ◽  
Destructive Testing ◽  
Electromechanical Impedance ◽  
Structural Health

Vibration based structural health monitoring methods are usually dependent on the first several orders of modal information, such as natural frequencies, mode shapes and the related derived features. These information are usually in a low frequency range. These global vibration characteristics may not be sufficiently sensitive to minor structural damage. The alternative non-destructive testing method using piezoelectric transducers, called as electromechanical impedance (EMI) technique, has been developed for more than two decades. Numerous studies on the EMI based structural health monitoring have been carried out based on representing impedance signatures in frequency domain by statistical indicators, which can be used for damage detection. On the other hand, damage quantification and localization remain a great challenge for EMI based methods. Physics-based EMI methods have been developed for quantifying the structural damage, by using the impedance responses and an accurate numerical model. This article provides a comprehensive review of the exciting researches and sorts out these approaches into two categories: data-driven based and physics-based EMI techniques. The merits and limitations of these methods are discussed. In addition, practical issues and research gaps for EMI based structural health monitoring methods are summarized.

Sign in / Sign up

Export Citation Format

Share Document