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Thanks for your question.
vibration in the absence of any pain in right lower abdomen is likely related to the muscle twitchings.
The abdominal muscles can twitch giving vibration sensations.
This can happen due to:
1. Dehydration---common cause. Plenty of fluids ( sports drinks like Gatorade) should resolve the issue
2. Nerve impingement---nerve impingement at the lower spine can cause vibration sensation.
3. Systemic conditions: diabetes, vitamin deficiencies can affect the local nerves causing this sensation.
Improve your diet & take a multivitamin supplement daily.
Get checked for diabetes ( blood sugar).
Thanks for additional information.
The pain may be related to your intestine like colitis, diverticulitis, polyps or tumors.
Obesity or weight gain increases the risk of arthritis affecting your hip joints & lower back.
Sudden weight gain can be caused by diabetes, thyroid disorder or adrenal gland dysfunction.
You should see your doctor for relevant testing.