I am trying to shear thin a liquid using external vibratory influence and am having a hard time determining if I should be looking to achieve mechanical resonance or an anti-resonate freq.
Anti resonance to me means a node... no movement. I think what you are looking for is a resonance... maximum movement.
Maybe you can describe the setup you have in mind better.
Solid plate moving tangentially to the fluid?
One thing that comes to mind is that shear represents damping so I think you have high damping and don't think there will be one frequency with dramatic increased movement.
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My set up is a bulk package that weighs 2400 lbs. Fixed on a large vibrating platform. The materials viscosity is 50,000 cps but can be easily sheared down to 4,000 cps using direct agitation. I am using 2 5hp electric motors controlled by VFD turning eccentric arms. The platform is fixed to vibrate up and down for maximum amplitude.