Sentence analysis: Smoking is harmful to health.

Harm is a noun in a sentence, so it needs a predicate verb. The phrase we often use is do harm to, and to is a preposition.

Only bad people hurt animals. Only bad people hurt animals.

Smoking is harmful to health. Usually we can use its adjective form.

Smoking is harmful to your health.

Of course, when a sentence has a predicate, auxiliary verbs are sometimes used to express emphasis.

For example: I understand. I see.

If you want to emphasize that I really understand this sentence, you can say that I do understand it.