Subordinate Oscillator Array Layout for Flat-Band Vibration Attenuation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for vibration attenuation in structures using subordinate oscillator arrays are inadequate due to sensitivity to errors in mass and stiffness distributions, leading to compromised performance and undesirable artifacts from manufacturing tolerances and environmental factors.
Innovation Solution
A novel design strategy for subordinate oscillator arrays that incorporates 3D-printing or piezoelectric components, allowing for precise control of mass and stiffness distributions to achieve a flat frequency response across a desired band, with the option to bond piezoelectric bimorphs for environmental compensation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional subordinate oscillator arrays are used for vibration attenuation, then vibration absorption is achieved at specific frequencies, but the system becomes highly sensitive to manufacturing tolerances and environmental variations
Solution Approach 1:
The patent transforms the discrete mass-spring parameters of traditional oscillators into continuous density and stiffness distribution fields. By using density function ρ(x) and stiffness function k(x) instead of discrete masses and springs, the system becomes insensitive to individual component variations while maintaining vibration attenuation performance across the desired frequency band.
Solution Approach 2:
The patent replaces the mechanical assembly of discrete oscillators with a continuous elastic foundation model governed by partial differential equations. This substitution eliminates the need for precise mechanical fabrication of individual oscillator components, as the vibration attenuation is achieved through the continuous elastic properties of the foundation material.
2Reliability
If discrete oscillator components are assembled to form an array, then vibration absorption is achieved, but manufacturing complexity and assembly tolerance accumulation increase
Solution Approach 1:
The patent merges multiple discrete oscillator components into a single continuous elastic foundation structure. Instead of assembling N separate mass-spring units, the invention uses one integrated elastic medium with spatially varying density and stiffness, thereby eliminating assembly complexity and tolerance accumulation while achieving the same vibration absorption function.
Solution Approach 2:
The patent segments the continuous elastic foundation into discrete computational elements for analysis and design purposes, while the physical implementation remains continuous. This allows the use of numerical methods to optimize density and stiffness distributions without requiring physical segmentation of the actual structure.
3Reliability
If traditional vibration absorbers are designed for single frequency targets, then peak attenuation is achieved, but side frequency amplification occurs
Solution Approach 1:
The patent applies local quality by varying the density and stiffness properties at different spatial locations within the elastic foundation. The density function ρ(x) and stiffness function k(x) are specifically tailored at each position to shape the frequency response, enabling flat attenuation across a broad frequency band while suppressing side frequency amplification through localized property optimization.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The approach effectively mitigates sensitivity to errors and environmental changes, providing robust vibration attenuation with increased damping and flexibility in frequency response shaping, ensuring reliable performance even with manufacturing tolerances and environmental variations.
Implementation Method 1
a subordinate oscillator array includes a series of beams whose isolated natural frequencies form a certain frequency band throughout which the vibration of a master structure is attenuated
Implementation Method 2
bond piezoelectric bimorphs for environmental compensation
Data Source
AI summary
An exemplary inventive subordinate oscillator array (SOA) includes two or more vibration attenuation devices (oscillators) that are sequentially arranged (e.g., via beams in the SOA) so that their respective anti-vibratory influences overlap. To design the SOA, an optimal number N of oscillators is calculated according to the equation N=ηQΔ, where η is the modal overlap, Q is the quality factor, and Δ is the desired fractional bandwidth. Each oscillator is akin to a conventional dynamic vibration absorber (DVA) and is characterized by its own mass, stiffness, damping, and geometry (e.g., length, width, and height). The respective characteristics of the oscillators are selected and the oscillators are distributed so that the SOA, when suitably attached to a vibrative structure, attenuates the vibrations of the structure so as to approximately flatten the structure's vibrations over a frequency band of interest.